Opsta teorija relativnostich18mws
Transcript of Opsta teorija relativnostich18mws
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 3/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 4/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 5/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 6/2950
> restart: # 18.1
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 7/2950
> with(tensor):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 8/2950
> coords := [t, x, y, z]:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 9/2950
g := array(symmetric, sparse, 1..4, 1..4):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 10/2950
g[1,1] := -c^2 - 2*Phi(x,y,z): g[2,2] := 1 - 2*Phi(x,y,z)/c^2: g[3,3]:= g[2,2]: g[4,4] := g[2,2]:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 11/2950
metric := create([-1,-1], eval(g));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 12/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 13/2950
> tensorsGR(coords, metric, contra_metric, det_met, C1, C2, Rm, Rc,R, GEin, C):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 14/2950
> rGEin := raise(contra_metric, GEin, 1):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 15/2950
> comp_rGEin := get_compts(rGEin);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 16/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 17/2950
> comp_rGEin[1,1];
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 18/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 19/2950
> limit(comp_rGEin[1,1]*c^2, c=infinity);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 20/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 21/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 22/2950
> restart: # 18.2
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 23/2950
> Eq1 := G*M*m/r^2 = m*w^2*r;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 24/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 25/2950
> Soln1 := solve(Eq1, r);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 26/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 27/2950
> rsat := Soln1[1];
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 28/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 29/2950
> G:=6.673e-11; c:=299792458; M:=5.974e24; rearth:=6.38e6;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 30/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 31/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 32/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 33/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 34/2950
> Tsat := 12*60*60; Tearth := 24*60*60;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 35/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 36/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 37/2950
> wsat := 2*Pi/Tsat:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 38/2950
> rsat := eval(rsat,w=wsat):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 39/2950
> rsat := evalf(rsat);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 40/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 41/2950
> vsat := wsat*rsat:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 42/2950
> vsat := evalf(vsat);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 43/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 44/2950
> vearth := 2*Pi*rearth/Tearth:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 45/2950
> vearth := evalf(vearth);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 46/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 47/2950
> Digits := 20:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 48/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 49/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 50/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 51/2950
> restart: # 18.3
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 52/2950
> with(tensor):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 53/2950
> coords:=[t, r, theta,phi]:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 54/2950
g := array(symmetric, sparse, 1..4, 1..4):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 55/2950
g[1,1] := -(c^2 - 2*G*m/r): g[2,2] := -c^2/g[1,1]: g[3,3] := r^2:g[4,4] := r^2*sin(theta)^2:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 56/2950
metric := create([-1,-1], eval(g));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 57/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 58/2950
> tensorsGR(coords, metric, contra_metric, det_met, C1, C2, Rm, Rc,R, GE, C):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 59/2950
> displayGR(Christoffel2, C2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 60/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 61/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 62/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 63/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 64/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 65/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 66/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 67/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 68/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 69/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 70/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 71/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 72/2950
> Eqns := geodesic_eqns(coords, s, C2 );
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 73/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 74/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 75/2950
> restart: # 18.4
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 76/2950
> f := 1/2*(-(c^2 - 2*G*M/r(s))*diff(t(s),s)^2 + 1/(1 -2*G*M/(c^2*r(s)))*diff(r(s),s)^2 + r(s)^2*diff(phi(s),s)^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 77/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 78/2950
> f1 := subs({t(s)=var1, diff(t(s),s)=var2, r(s)=var3,diff(r(s),s)=var4, phi(s)=var5, diff(phi(s),s)=var6}, f):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 79/2950
> Epr11 := diff(f1, var2):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 80/2950
> Epr12 := diff(f1, var1):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 81/2950
> Epr13 := subs({var1=t(s), var2=diff(t(s),s), var3=r(s), var5=phi(s), var4=diff(r(s),s), var6=diff(phi(s),s)}, Epr11):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 82/2950
> Eq14 := Epr13 = -a/c;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 83/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 84/2950
> Epr21 := diff(f1, var4):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 85/2950
> Epr22 := diff(f1, var3):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 86/2950
> Epr23 := subs({var1=t(s), var2=diff(t(s),s), var3=r(s), var5=phi(s), var4=diff(r(s),s), var6=diff(phi(s),s)}, Epr21):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 87/2950
> Epr24 := subs({var1=t(s), var2=diff(t(s),s), var3=r(s), var5=phi(s), var4=diff(r(s),s), var6=diff(phi(s),s)}, Epr22):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 88/2950
> Epr25 := diff(Epr23, s):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 89/2950
> Eq26 := Epr25 - Epr24 = 0;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 90/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 91/2950
> Epr31 := diff(f1, var6):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 92/2950
> Epr32 := diff(f1, var5):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 93/2950
> Epr33 := subs({var1=t(s), var2=diff(t(s),s), var3=r(s), var5=phi(s), var4=diff(r(s),s), var6=diff(phi(s),s)}, Epr31):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 94/2950
> Eq34 := Epr33 = h/c;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 95/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 96/2950
> Eq53 := isolate(Eq14, diff(t(s),s));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 97/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 98/2950
> Eq54 := isolate(Eq34, diff(phi(s),s));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 99/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 100/2950
> Eq55 := eval(Eq26, {Eq53, Eq54});
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 101/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 102/2950
> M := 1; G := 1; c := 1;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 103/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 104/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 105/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 106/2950
> Eq77 := r(0) = 11;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 107/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 108/2950
> Eq78 := D(r)(0) = 0;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 109/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 110/2950
> Eq79 := phi(0) = 0;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 111/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 112/2950
> Eq80 := D(phi)(0) = 0.0295;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 113/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 114/2950
> h := eval(lhs(Eq34), {r(s)=rhs(Eq77), diff(phi(s),s)=rhs(Eq80)});
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 115/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 116/2950
> a := sqrt((1 - 2*M/rhs(Eq77))*(1 + h^2/rhs(Eq77)^2));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 117/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 118/2950
> Vsq := sqrt((1 - 2*M/x)*(1 + h^2/x^2)):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 119/2950
> plot([Vsq, a], x=2..25, a-0.01*a..a+0.01*a, legend=["effective potential", "energy"]);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 120/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 121/2950
> ini := Eq77, Eq78, Eq79;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 122/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 123/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 124/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 125/2950
> with(plots):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 126/2950
> polarplot([rhs(Eq91(s)[3]), rhs(Eq91(s)[2]), s=0..500],scaling=constrained);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 127/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 128/2950
> p1 := plot3d([x*cos(t), x*sin(t), sqrt(8*(x-2))], x=2..14,t=0..2*Pi, style=hidden):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 129/2950
> p2 := spacecurve([rhs(Eq91(s)[3]), rhs(Eq91(s)[2]),sqrt(8*(rhs(Eq91(s)[3])-2)), s=0..500], coords=cylindrical,color=black, numpoints=400):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 130/2950
> display([p1, p2]);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 131/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 132/2950
> animate(polarplot, [[rhs(Eq91(s)[3]), rhs(Eq91(s)[2]), s=0..t]],t=0..500, scaling=constrained);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 133/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 134/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 135/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 136/2950
> m:=me;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 137/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 138/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 139/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 140/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 141/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 142/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 143/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 144/2950
Examples
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 145/2950
Define the coordinates and covariant metric for the Schwarzschild metric:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 146/2950
> with(tensor):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 147/2950
> coords:=[t, r, theta,phi]:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 148/2950
g:=array (symmetric, sparse, 1..4, 1..4):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 149/2950
g[1,1]:=(1-2*m/r): g[2,2]:=-1/g[1,1]: g[3,3]:=-r^2: g[4,4]:=-r^2*sin(theta)^2:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 150/2950
metric:=create([-1,-1], eval(g));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 151/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 152/2950
> metric := TABLE([index_char = [-1, -1], compts =linalg['eigenvalues'](matrix([[1-2*m/r, 0, 0, 0], [0, -1/(1-2*m/r),0, 0], [0, 0, -r^2, 0], [0, 0, 0, -r^2*sin(theta)^2]]))]);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 153/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 154/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 155/2950
Compute the curvature (without the print option)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 156/2950
> tensorsGR(coords,metric,contra_metric,det_met, C1, C2, Rm, Rc, R,G, C):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 157/2950
Error, invalid input: tensorsGR expects its 1st argument, coord, to be of type list(name), but received [t,
0.5100000000e-10, theta, phi]
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 158/2950
Use displayGR to show that it is a vacuum solution of the Einstein field equations:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 159/2950
> displayGR(Einstein,G);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 160/2950
`type/tensor_type` : "1" is not a table.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 161/2950
Error, (in displayGR) Einstein tensor, 1, has invalid input: %1 expects its %-2 argument, %3, to be of
type %4, but received %5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 162/2950
Use displayGR to show the nonzero Christoffel symbols of the first kind:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 163/2950
> displayGR(Christoffel1,C1);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 164/2950
`type/tensor_type` : "C1" is not a table.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 165/2950
Error, (in displayGR) Christoffel symbols of the 1st kind, C1, has invalid input: %1 expects its %-2
argument, %3, to be of type %4, but received %5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 166/2950
Display everything using display_allGR :
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 167/2950
> display_allGR (coords,metric,contra_metric, det_met, C1, C2, Rm,Rc, R, G, C);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 168/2950
Error, invalid input: display_allGR expects its 1st argument, coord, to be of type list(name), but
received [t, 0.5100000000e-10, theta, phi]
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 169/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 170/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 171/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 172/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 173/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 174/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 175/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 176/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 177/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 178/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 179/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 180/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 181/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 182/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 183/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 184/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 185/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 186/2950
Iz mase elektrona naci klasicni radijus elektrona pomocu koeficijenta srazmernosti. Maple je to gore
uradio.Iz bekerela je nadjena masa elektrona.Treci primer :iz slozene formule naci masu sunca pomocu
koeficijenta srazmernosti.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 187/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 188/2950
> #------UNITS, PHYSICAL CONSTANTS, AND DATA----
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 189/2950
#-------Warren D. Smith 1998-------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 190/2950
#This useful file causes MAPLE to know about
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 191/2950
#fundamental physical constants, useful data, and units.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 192/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 193/2950
#I feel cgs, emu, esu units are an abomination.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 194/2950
#If you want to have no units, go totally dimensionless
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 195/2950
#(for example, the Planck units). If you want to have units,
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 196/2950
#use SI. The cgs, emu, esu systems are a silly halfassed attempt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 197/2950
#to have it both ways and get rid of some units and keep others.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 198/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 199/2950
# The present file features conversion factors to random non-SI
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 200/2950
#units like foot, horsepower, pound, ounce. The entire group
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 201/2950
#of units is known to it, so all quantities are dimensioned
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 202/2950
#automatically. Meter, second, coulomb, kelvin, and kg are
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 203/2950
#my fundamental units. (Arguably kelvin is not needed.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 204/2950
#Also for radiation dose units, I use the "disintegration", e.g.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 205/2950
#disintegration/second.)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 206/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 207/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 208/2950
#The old definition was...
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 209/2950
#candle = 1/60 the luminous intensity of 1 cm^2 of a Blackbody atthe
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 210/2950
#melting Temperature of platinum (2042.15 kelvin) = 1.6437 *watt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 211/2950
#= meter^2 / 600000 * sigmasb * platinummelttemp^4;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 212/2950
#a candela is the light intensity from a candle (now redefined
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 213/2950
#as "1/683 watt per steradian" of 555nm wavelength light (which theeye
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 214/2950
#is maximally sensitive to).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 215/2950
#Note, this seems to be a lot smaller than the old defn.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 216/2950
#Huh? Then lumen = candela*steradian = 1/683 *watt;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 217/2950
#lux = lumen/meter^2 = 1/683 *watt/meter^2; candlepower = candela.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 218/2950
#Yuk!
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 219/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 220/2950
#I also hate the "radian" and "steradian"; they should be
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 221/2950
#dimensionless, in my view.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 222/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 223/2950
# Finally, decibels and bels are another abomination.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 224/2950
# decibels = 10*bels = 10*log10(Intensity/ReferenceIntensity);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 225/2950
#and for use in auditory work, one uses
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 226/2950
#ReferenceIntensity = 1 phon = 10^(-16) *watt/cm^2/sec at 1000*hertz.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 227/2950
#Idiotic - haven't these guys heard of scientific notation to dealwith
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 228/2950
#logarithms?
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 229/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 230/2950
# This MAPLE code does not know about precision (usually the
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 231/2950
#last 2 digits of our numbers are imprecise). My values
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 232/2950
#are CODATA values plus miscellaneous sources like
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 233/2950
#CRC handbook. If you really care about errors you have to know
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 234/2950
#about the correlations among the errors in the
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 235/2950
#fundamental constants (many errors are highly correlated)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 236/2950
#and that would require a lot of extra software, which I
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 237/2950
#didn't feel like trying to write.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 238/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 239/2950
#Update 1999:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 240/2950
#PJ Mohr BN Taylor
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 241/2950
#CODATA recommended values of the fundamental physical constants 1998
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 242/2950
#J Phys Chem Ref Data 28 (1999)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 243/2950
#finally came out
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 244/2950
#http://physics.nist.gov/cgi-bin/cuu/
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 245/2950
# http://physics.nist.gov/PhysRefData/contents.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 246/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 247/2950
#The 1998 CODATA
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 248/2950
#Recommended Values of the Fundamental Physical
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 249/2950
#Constants, Web Version 3.0," available at
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 250/2950
#http://physics.nist.gov/constants (National Institute of
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 251/2950
#Standards and Technology, Gaithersburg, MD 20899,
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 252/2950
#release date 23 July 1999).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 253/2950
#http://physics.nist.gov/cuu/Constants/index.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 254/2950
#http://physics.nist.gov/constants
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 255/2950
#http://www.codata.org/
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 256/2950
#http://pdg.lbl.gov/1998/astrorpp.ps
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 257/2950
#these sites very recommended - can now download any correlationcoeff too
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 258/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 259/2950
#A detailed description of the data and its analysis that led tothese
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 260/2950
#values will be published by early 2000 in the Journal of Physical
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 261/2950
#and Chemical Reference Data.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 262/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 263/2950
#"Review of particle properties", Phys Rev D50 (1994) 1-.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 264/2950
#PRD 54 (July 1996) 1-720.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 265/2950
#C.Caso et al.: Review of particle physics, Europ. Phys. J. C3 (1998)1-.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 266/2950
#http://pdg.lbl.gov
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 267/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 268/2950
#---------units (and data):---------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 269/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 270/2950
#prefixes:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 271/2950
zepto := 10^(-21);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 272/2950
atto := 10^(-18);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 273/2950
femto := 10^(-15);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 274/2950
pico := 10^(-12);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 275/2950
nano := 10^(-9);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 276/2950
micro := 10^(-6);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 277/2950
milli := 10^(-3);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 278/2950
centi := 10^(-2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 279/2950
kilo := 10^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 280/2950
mega := 10^6;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 281/2950
giga := 10^9;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 282/2950
tera := 10^12;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 283/2950
peta := 10^15;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 284/2950
exa := 10^18;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 285/2950
zetta := 10^21;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 286/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 287/2950
joule := meter^2 * kg / second^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 288/2950
watt := joule/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 289/2950
mole := 6.02214199 * 10^(23); #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 290/2950
ampere := coulomb/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 291/2950
hertz := 1/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 292/2950
newton := meter*kg/second^2; #force
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 293/2950
pascal := newton/meter^2; #pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 294/2950
poise := pascal*second; #absolute viscosity
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 295/2950
stokes := meter^2 /second; #kinematic viscosity
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 296/2950
volt := watt/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 297/2950
farad := coulomb/volt;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 298/2950
ohm := volt/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 299/2950
mho := 1/ohm;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 300/2950
siemens := 1/ohm;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 301/2950
weber := volt*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 302/2950
tesla := weber/meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 303/2950
henry := weber/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 304/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 305/2950
sipole := meter*coulomb/second; #my own unit of magentic monopolecharge
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 306/2950
#One SIpole is the amount of magnetic charge that would
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 307/2950
#experience a force of 1 Newton if placed in a 1 Tesla magnetic
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 308/2950
#field.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 309/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 310/2950
becquerel := disintegration/second; #radioactivity unit
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 311/2950
gray := joule/kg; #for measuring absorbed radiation dose
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 312/2950
#a sievert is the amount of radiation equivalent in health effect to1 gray
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 313/2950
#of some kind of standard type of radiation.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 314/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 315/2950
minute := 60*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 316/2950
hour := 60*minute;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 317/2950
solarday := 24*hour; #increases 1 millisecond/century
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 318/2950
starday := 86164.09 * second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 319/2950
year := 365.24219879 *solarday;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 320/2950
month := year/12;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 321/2950
century := 100*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 322/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 323/2950
denier := kg/meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 324/2950
dyne := 10^(-5) *newton;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 325/2950
erg := 10^(-7) *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 326/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 327/2950
gauss := 10^(-4) * tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 328/2950
maxwell := 10^(-8) *weber;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 329/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 330/2950
horsepower := 746 * watt; #several definitions exist 735 to 746watt.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 331/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 332/2950
jansky := 10^(-26) * watt * second / meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 333/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 334/2950
oersted := 7.957747 * ampere/meter; #says CRC handbook
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 335/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 336/2950
parsec := cot(1 * angularsecond) * astronomicalunit;#3.085678*10^(16) *meter; 3.26*lightyear
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 337/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 338/2950
lb := .45359237 *kg; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 339/2950
poundmass := lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 340/2950
ounce := lb/16;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 341/2950
shortton := 2000 *lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 342/2950
longton := 2240 *lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 343/2950
grain := lb/7000;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 344/2950
slug := 14.59390 *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 345/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 346/2950
lbf := 4.4482216152605 * newton; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 347/2950
poundforce := lbf;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 348/2950
psi := lbf/inch^2; #6895*pascal
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 349/2950
torr := 133.322 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 350/2950
mmhg := torr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 351/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 352/2950
liter := 10^(-3) *meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 353/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 354/2950
sverdrup := 10^6 *meter^3/second; #volume flux. Used in oceanography.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 355/2950
kayser := 1/(centi*meter); #used in spectroscopy
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 356/2950
cc := (centi*meter)^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 357/2950
micron := 10^(-6) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 358/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 359/2950
metricton := 10^3 *kg; #also "tonne"
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 360/2950
#electron-volt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 361/2950
ev := 1.602176462 * 10^(-19) *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 362/2950
km := 10^3 *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 363/2950
mm := 10^(-3) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 364/2950
cm := 10^(-2) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 365/2950
astronomicalunit := 149597900 *km: #earth-sun distance
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 366/2950
nauticalmile := 1852*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 367/2950
#nauticalmile := 6076.115486*foot:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 368/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 369/2950
angstrom := 10^(-10) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 370/2950
barn := 10^(-28) *meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 371/2950
fermi := 10^(-15) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 372/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 373/2950
bar := 10^(5) *pascal:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 374/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 375/2950
abampere := ampere/10;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 376/2950
abcoulomb := coulomb/10;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 377/2950
statampere := 3.335641 * 10^(-10) *ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 378/2950
statcoulomb := 3.335641 * 10^(-10) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 379/2950
curie := 3.7*10^(10) *becquerel;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 380/2950
roentgen := 2.58 * 10^(-4) *coulomb/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 381/2950
rad := 10^(-2) *gray;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 382/2950
remunit := 10^(-2) *sievert;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 383/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 384/2950
pi := evalf(Pi);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 385/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 386/2950
radian := 1;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 387/2950
revolution := evalf(2*Pi*radian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 388/2950
angulardegree := evalf(Pi/180 *radian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 389/2950
angularminute := angulardegree/60;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 390/2950
angularsecond := angularminute/60;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 391/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 392/2950
fullsphere := evalf(4*Pi*steradian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 393/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 394/2950
knot := nauticalmile/hour;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 395/2950
hectare := 10^4 *meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 396/2950
angstrom := 10^(-10)*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 397/2950
inch := 2.54 * 10^(-2)*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 398/2950
foot := 12*inch;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 399/2950
yard := 3*foot;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 400/2950
printerpoint := 0.13837 *inch; #or is it inch/72? close
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 401/2950
mile := 5280*foot:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 402/2950
acre := mile^(2) /640; #acre := 43560 *foot^2
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 403/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 404/2950
usgallon := 231 * inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 405/2950
brgallon := 277.420 *inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 406/2950
quart := usgallon/4;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 407/2950
pint := quart/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 408/2950
cup := pint/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 409/2950
gill := cup/2; #british cups, pints, gills are each a bit bigger
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 410/2950
fluidounce := cup/8;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 411/2950
tablespoon := fluidounce/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 412/2950
teaspoon := tablespoon/3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 413/2950
boardfoot := 144 *inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 414/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 415/2950
gram := 10^(-3) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 416/2950
carat := .2 *gram;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 417/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 418/2950
btu := 1.055056 * 10^(3) * joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 419/2950
ustherm := 1.054804 * 10^(8) *joule; #used by US natural gasindustry
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 420/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 421/2950
watertripletemp := 273.16 *kelvin; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 422/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 423/2950
watertriplepressure := 611.73 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 424/2950
platinummelttemp := (1769.0+273.15) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 425/2950
waterfreezetemp := 273.15 *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 426/2950
waterboiltemp := 373.15 *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 427/2950
#celsius := waterfreeze + kelvin. fahrenheit := celsius * (5/9) + 32;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 428/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 429/2950
caloriethermo := 4.184 *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 430/2950
calorieintl := 4.1868 *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 431/2950
calorie := calorieintl;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 432/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 433/2950
#weapons kiloton is by convention 10^(12) calories.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 434/2950
kiloton := 10^(12) * calorie;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 435/2950
mageaton := 10^(3) * kiloton;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 436/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 437/2950
rankine := (5/9) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 438/2950
standardatmosphere := 101325 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 439/2950
standardgravity := 9.80665 *meter/second^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 440/2950
vsoundair := 331.4 *meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 441/2950
specheatair := 1010 *joule/kg/kelvin: #at const pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 442/2950
densityair := 1.21 * kg/meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 443/2950
vsoundwater := 1496.7 *meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 444/2950
densitywater := 1000*kg/meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 445/2950
specheatwater := 4190 *joule/kg/kelvin; #at const pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 446/2950
heatfusionwater := 333 * kilo*joule/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 447/2950
heatvapwater := 2260* kilo*joule/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 448/2950
indexrefwater := 1.33; #at 589 nm
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 449/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 450/2950
resistivitysilver := 1.587 * 10^(-8) * ohm * meter; #at 293 Kelvin
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 451/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 452/2950
radgeosync := 42200 * kilo * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 453/2950
vescapeearth := 11200 * meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 454/2950
muearth := 8.0*10^(22) *joule/tesla; #magnetic dipole moment
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 455/2950
efieldearth := 150 * volt/meter; #down. At earth's surface. mean.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 456/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 457/2950
suntemp := 5780*kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 458/2950
sunluminosity := 3.846 * 10^(26) * joule/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 459/2950
solarconst := evalf(sunluminosity / (4*Pi*astronomicalunit^2));#varies 2%
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 460/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 461/2950
mmilkyway := 2.2*10^(41) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 462/2950
moceans := 1.4 *10^(21) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 463/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 464/2950
velocorbitalgalaxy := 220 * km/second; #of solar system round milkyway galaxy
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 465/2950
velocwrtcosmicbackground := 369.3 * km/second; #+-2.5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 466/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 467/2950
disttocenterofmilkyway := 8.0 * mega * parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 468/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 469/2950
distproximacentauri := 4.22 * c*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 470/2950
#**Alpha Centauri system:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 471/2950
#Separation between Alpha Centauri A and B varies from 11 to 35 AU;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 472/2950
#they take 80 years to orbit around each other.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 473/2950
#Proxima Centauri is currently 13,000 AUs from A and B; no orbital
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 474/2950
#parameters of it are known.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 475/2950
# A B proxima sun
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 476/2950
# 5800K 5300K 2700K 5800K
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 477/2950
# 4.35 4.35 4.22 0 lightyears away
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 478/2950
# Yellow Orange Red Yellow
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 479/2950
distandromedagalaxy := 2*10^(22) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 480/2950
distlargemagellaniccloud := 55*kilo*parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 481/2950
distvirgocluster := 20*mega*parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 482/2950
disttouniverseedge := 10^(26) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 483/2950
distearthmoon := 384404 *km; #+3 cm per year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 484/2950
periodmoon := 27 *solarday: #??? +2 milliseconds/century
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 485/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 486/2950
distsunmercury := .38 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 487/2950
distsunvenus := .72 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 488/2950
distsunearth := 1.0 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 489/2950
distsunmars := 1.52 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 490/2950
distsunjupiter := 5.20 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 491/2950
distsunsaturn := 9.5 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 492/2950
distsunuranus := 19.2 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 493/2950
distsunneptune := 30.0 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 494/2950
distsunpluto := 39.5 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 495/2950
#pluto has 1 satellite "charon" with about .1 its mass;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 496/2950
#it has day 6.38 earth days.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 497/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 498/2950
#radiusearth := 6371.006 *km:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 499/2950
radiusearth := 6378.140 *km:#equatorial
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 500/2950
radiusmoon := 1738 *km;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 501/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 502/2950
radiusmercury := .38 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 503/2950
radiusvenus := .96 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 504/2950
radiusmars := .53 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 505/2950
radiusjupiter := 10.8 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 506/2950
radiussaturn := 9.0 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 507/2950
radiusuranus := 4.1 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 508/2950
radiusneptune := 3.85 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 509/2950
radiuspluto := 1137 *km: #+-8
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 510/2950
radiussun := 695990 *km: #equatorial
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 511/2950
radiussunschwarzschild := 2.95325008 * km;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 512/2950
radiusmilkyway := 15 * kilo *parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 513/2950
thicknessmilkyway := 1 * kilo *parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 514/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 515/2950
mmercury := .33022 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 516/2950
mvenus := 4.8690 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 517/2950
mearth := 5.97370 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 518/2950
mmoon := .073483 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 519/2950
mmars := .64191 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 520/2950
mjupiter := 1898.8 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 521/2950
msaturn := 568.50 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 522/2950
muranus := 86.625 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 523/2950
mneptune := 102.78 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 524/2950
mpluto := 1.27 * 10^(22) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 525/2950
msun := 1.98892 * 10^(30) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 526/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 527/2950
hubnum := .5: #could be anywhere .2 to 1.0
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 528/2950
hubbleconst := 70*hubnum*km/second/(mega*parsec);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 529/2950
#http://ucsu.colorado.edu/~lisle/main.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 530/2950
#``The cosmological implications of Hipparcus''
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 531/2950
#direct trig parallax distance measurement to nearby Cepheids with
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 532/2950
#Hipparcus satellite. Leads to 10% revision of Hubble constant, now
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 533/2950
#about 60 km/s/Mpc.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 534/2950
#another place claims 60-80 is the range; I'm going with it.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 535/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 536/2950
criticaldensity := 3*hubbleconst^2/(8*pi*G); #needed to close theuniverse
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 537/2950
#matter density is supposed to be .2 to 1.0 times this
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 538/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 539/2950
entropydensityofuniverse := 2899.3 * (2.853/2.728)^3 * kb / cc;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 540/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 541/2950
tempuniversebackground := 2.853 * kelvin; #plus or minus .002
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 542/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 543/2950
lightyear := c*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 544/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 545/2950
#various rough estimates of universe-quantities on Misner-Thorne- Wheeler p738:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 546/2950
#max radius 19*10^9 lightyear
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 547/2950
#time start to max 3*10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 548/2950
#time bang to crunch 6*10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 549/2950
#age now 10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 550/2950
#radius now 13*10^9 lightyear note: larger than age
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 551/2950
#volume now 3.83*10^79 meter^3
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 552/2950
#density at maximum 5*10^(-30) * gram/cc
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 553/2950
#rate of increase of radius now .66 lightyear/year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 554/2950
#amount of matter 5.68*10^(53) kg
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 555/2950
#baryon number 3.39*10^(80)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 556/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 557/2950
#MTW 29.6p796
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 558/2950
#density of universe now is <10^(-28) g/cc and >2*10^(-31) g/cc
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 559/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 560/2950
#MTW when universe about 10^5 years old, density was 10^(-20) g/ccand temp 3000K
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 561/2950
#and then:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 562/2950
#1. radiation ceased to domaine, now matter
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 563/2950
#2. universe became transparent
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 564/2950
#3. hydrogen atoms began to form (no longer ionized perpetually)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 565/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 566/2950
#------------------fundamental constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 567/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 568/2950
#these constants suffice to define the planck units:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 569/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 570/2950
#speed of light in vacuum exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 571/2950
c := 299792458 * meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 572/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 573/2950
#boltzmann constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 574/2950
kb := 1.3806503 * 10^(-23) *joule/kelvin; #1700 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 575/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 576/2950
#permittivity & permeability of vacuum
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 577/2950
mu0 := evalf(4*Pi*1.0 * 10^(-7)) *henry/meter; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 578/2950
eps0 := 1/(c^2 * mu0); #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 579/2950
#eps0 := 8.854187817 * 10^(-12) *farad/meter
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 580/2950
#mu0*eps0*c^2=1
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 581/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 582/2950
#newton gravitational constant (force = G*m1*m2/r^2)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 583/2950
G := 6.673 * 10^(-11) *newton*meter^2/kg^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 584/2950
#+- .010; huge relative uncert .0015
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 585/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 586/2950
#coulomb law constant (force = coulombconst * q1*q2/r^2)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 587/2950
coulombconst := 1/ (4 * pi *eps0);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 588/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 589/2950
#planck's constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 590/2950
h := 6.62606876 * 10^(-34) *joule*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 591/2950
hbar := 1.054571596 * 10^(-34) *joule*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 592/2950
#hbar = evalf(h/(2*Pi)):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 593/2950
#78 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 594/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 595/2950
#------------planck length, mass, time, charge:--------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 596/2950
#These are the fundamental units of
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 597/2950
#length, mass, time, charge, temperature
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 598/2950
#in a unit system where c=G=hbar=kb=1 and
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 599/2950
#where coulombconst*qplanck^2 = G*mplanck^2.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 600/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 601/2950
lplanck := sqrt(hbar*G/c^3);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 602/2950
mplanck := sqrt(hbar*c/G);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 603/2950
tplanck := sqrt(hbar*G/c^5);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 604/2950
qplanck := evalf(sqrt(4*Pi*hbar*c*eps0));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 605/2950
#qplanck / qe = 1/sqrt(alpha), reciprocal sqrt of fine structureconstant!
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 606/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 607/2950
tempplanck := (mplanck*c^2)/kb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 608/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 609/2950
# lplanck := 1.616048609*10^(-35) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 610/2950
# tplanck := 5.390557920*10^(-44) *second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 611/2950
# mplanck := 2.176714074*10^(-8) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 612/2950
# qplanck := 1.875546788*10^(-18) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 613/2950
# tempplanck := 1.416957021*10^(32) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 614/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 615/2950
# qplanck = 11.7062 charge quanta = sqrt(137).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 616/2950
# mplanck = 2.389527889 * 10^(22) electron masses.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 617/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 618/2950
#------other fundamental constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 619/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 620/2950
#charge of proton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 621/2950
qe := 1.602176462 * 10^(-19) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 622/2950
#39 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 623/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 624/2950
#atomic mass unit
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 625/2950
amu := 10^(-3) * kg/mole;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 626/2950
#amu := 1.66053873*10^(-27) *kg: #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 627/2950
#mole is number of carbon-12 atoms in 12 grams, amu is
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 628/2950
#1/12 mass of a carbon-12 atom.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 629/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 630/2950
#rest mass of electron, proton, neutron, muon, deuteron, alpha particle
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 631/2950
#me := 9.10938188 * 10^(-31) *kg: #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 632/2950
me := 5.48579903 * 10^(-4) * amu; # +- .00000013
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 633/2950
me := .510998902 * mega * ev/c^2; #40 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 634/2950
#failed excited lepton searches: e >86 GeV, muon >=86 GeV, tau>72 GeV
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 635/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 636/2950
mp := 1.67262158* 10^(-27) *kg; #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 637/2950
mp := 938.271998 * mega * ev / c^2; #40 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 638/2950
mp := 1.00727646688 * amu; # .13ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 639/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 640/2950
mpbyme := 1836.1526675; #2.1ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 641/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 642/2950
#mn := 1.6749286 * 10^(-27) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 643/2950
mn := 1.008664904 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 644/2950
# +-.000000014
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 645/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 646/2950
#mmu := 1.8835327*10^(-28) *kg:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 647/2950
mmu := .113428913 * amu: # +- .000000017
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 648/2950
mmu := 105.658389 * mega * ev/c^2; #+-.000034 (1998 value)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 649/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 650/2950
mdeuteron := 3.3435860 * 10^(-27) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 651/2950
mdeuteron := 1875.612762 * mega * ev/c^2; #40 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 652/2950
mtriton := 3.015500 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 653/2950
m3he := 3.014932 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 654/2950
malpha := me / (1.37093354 * 10^(-4));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 655/2950
#malpha := 4.001505 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 656/2950
mpi := 135.0 * mega*ev/c^2; #mass of pi
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 657/2950
mpi0 := 139.6 * mega*ev/c^2; #mass of pi_0^{+-}
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 658/2950
mtau := 1777.05 * mega * ev / c^2; #+.29, -.26 (1998 value)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 659/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 660/2950
#heavy lepton searches supposedly go up to 81.5GeV now with 95% conf
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 661/2950
#nothing charged there. Ackerstaff Euro Phys J C1 (1998) 45
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 662/2950
#also 95% conf nothing uncharged below 69GeV
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 663/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 664/2950
mquarku := 3.25 * mega * ev/c^2; #charge +2/3 (1.5 to 5)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 665/2950
mquarkd := 6 * mega * ev/c^2; #charge -1/3 #??? wrong way ??? (3to 9)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 666/2950
mquarks := 115 * mega * ev/c^2; #charge -1/3 (60 to 170)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 667/2950
mquarkc := 1.25 * giga * ev/c^2; #charge +2/3 (1.25 +-.15)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 668/2950
mquarkb := 4.25 * giga * ev/c^2; #charge -1/3 (4.25 +- .15)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 669/2950
mquarkt := 174.3 * giga * ev/c^2; #charge +2/3. 174.3+-5.1
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 670/2950
#all quarks spin 1/2, baryon # 1/3, RGB or anti-RGB color.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 671/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 672/2950
mw := 80.41 * giga * ev/c^2; #+-.4 Gev. Charge +-1. Spin 1. W boson.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 673/2950
mz := 91.187 * giga * ev/c^2; #+-.031 Gev. Charge 0. Spin 1. Z boson.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 674/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 675/2950
#particle mean lifetimes
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 676/2950
meanlifemu := 2.19703 * micro * second;#uncert .00004
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 677/2950
meanlifetau := .2900 * pico * second; #+-.0012
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 678/2950
meanlifen := 888.6 * second; #+- 3.5 second
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 679/2950
#meanlifep > 10^31 years for some investigated modes
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 680/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 681/2950
#Bohr magneton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 682/2950
bohrmag := qe*hbar/(2*me);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 683/2950
#bohrmag = mue/1.001159652:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 684/2950
#bohrmag := 9.2740154 * 10^(-24) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 685/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 686/2950
#Nuclear magneton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 687/2950
nucmag := qe*hbar/(2*mp);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 688/2950
#nucmag := 5.0507866*10^(-27) * joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 689/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 690/2950
#magnetic moment of electron, proton, neutron, muon, deuteron
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 691/2950
#mue := 9.2847701 * 10^(-24) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 692/2950
#mue := 1.001159652193 * bohrmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 693/2950
# +- .000000000010
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 694/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 695/2950
#mup := 1.41060761 * 10^(-26) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 696/2950
mup := 2.792847386 * nucmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 697/2950
# +- .000000063
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 698/2950
;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 699/2950
#mun := 9.6623707 * 10^(-27) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 700/2950
mun := 1.91304275 * nucmag; #has negative sign, incidentally
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 701/2950
# +-.00000045
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 702/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 703/2950
mumu := 4.4904514 * 10^(-26) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 704/2950
mudeuteron := 4.3307375 * 10^(-27) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 705/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 706/2950
#------------"atomic units":--------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 707/2950
#mass me
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 708/2950
#charge qe
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 709/2950
#action hbar
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 710/2950
#length rbohr
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 711/2950
#energy hartree
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 712/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 713/2950
#Bohr radius (estimate, for hydrogen atom)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 714/2950
rbohr := evalf(4*Pi*eps0*hbar^2/(me*qe^2));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 715/2950
#rbohr := 5.29177208 * 10^(-11) *meter: #3.7ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 716/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 717/2950
#hartree energy unit, about 27 ev
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 718/2950
#hartree := 2*rydberg*h*c := 4.3598 * 10^(-18) *joule:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 719/2950
hartree := hbar^2 / (me*rbohr^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 720/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 721/2950
atomictimeunit := hbar / hartree;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 722/2950
atomicvelocityunit := rbohr / atomictimeunit; #about c/137
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 723/2950
atomicforceunit := hartree / rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 724/2950
atomicmomentumunit := hbar / rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 725/2950
atomiccurrentunit := qe / atomictimeunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 726/2950
atomicefieldunit := hartree/(qe*rbohr);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 727/2950
atomicpotentialunit := hartree/qe;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 728/2950
atomicedipoleunit := qe*rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 729/2950
atomicmagfieldunit := hbar / (qe*rbohr^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 730/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 731/2950
atomicmagdipoleunit := 2*bohrmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 732/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 733/2950
#------derived constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 734/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 735/2950
#magnetic flux quantum
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 736/2950
phi0 := h/(2*qe);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 737/2950
#phi0 := 2.06783461 * 10^(-15) *weber
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 738/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 739/2950
#alpha = fine structure constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 740/2950
#alpha := 1/137.0359895;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 741/2950
alpha := evalf(qe^2 / (4*Pi*eps0*hbar*c));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 742/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 743/2950
#stefan-boltzmann constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 744/2950
sigmasb := evalf(Pi^2*kb^4/(60*hbar^3*c^2));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 745/2950
#sigmasb := 5.670400*10^(-8) *watt/meter^2/kelvin^4; #7000 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 746/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 747/2950
#first radiation constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 748/2950
c1radiation := evalf(2*Pi*h*c^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 749/2950
#c1radiation := 3.7417749 * 10^(-16) watt/meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 750/2950
c2radiation := h*c/kb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 751/2950
#c2radiation := 0.01438769 *meter*kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 752/2950
#The max intensity lambda in blackbody radiation is
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 753/2950
#wienconst*T*cm/kelvin, where
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 754/2950
wienconst := c2radiation / 4.965114231;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 755/2950
#wienconst := 0.2897756 *cm/kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 756/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 757/2950
#rydberg (approx hydrogen waves per meter, infinite mass nuc)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 758/2950
rydberg := me*c*alpha^2/(2*h);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 759/2950
#rydberg := 10973731.56834(24) /meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 760/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 761/2950
#classical electron radius
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 762/2950
#re := 2.817940285 * 10^(-15) *meter; #11 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 763/2950
re := alpha^2 * rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 764/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 765/2950
#compton wavelengths of electron, proton, neutron, muon
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 766/2950
e_compton := h/(me*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 767/2950
p_compton := h/(mp*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 768/2950
n_compton := h/(mn*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 769/2950
mu_compton := h/(mmu*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 770/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 771/2950
fermicouplingconst := 1.16639 * 10^(-5) / (giga * ev)^2; #9000 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 772/2950
sinsquaredweakmixingangle := 0.23124; #.001 relative uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 773/2950
#codata says .2235 +- .0023
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 774/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 775/2950
strongcouplingconst := .119;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 776/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 777/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 778/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 779/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 780/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 781/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 782/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 783/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 784/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 785/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 786/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 787/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 788/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 789/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 790/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 791/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 792/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 793/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 794/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 795/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 796/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 797/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 798/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 799/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 800/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 801/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 802/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 803/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 804/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 805/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 806/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 807/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 808/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 809/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 810/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 811/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 812/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 813/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 814/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 815/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 816/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 817/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 818/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 819/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 820/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 821/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 822/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 823/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 824/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 825/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 826/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 827/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 828/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 829/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 830/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 831/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 832/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 833/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 834/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 835/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 836/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 837/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 838/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 839/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 840/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 841/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 842/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 843/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 844/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 845/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 846/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 847/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 848/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 849/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 850/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 851/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 852/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 853/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 854/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 855/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 856/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 857/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 858/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 859/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 860/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 861/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 862/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 863/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 864/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 865/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 866/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 867/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 868/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 869/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 870/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 871/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 872/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 873/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 874/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 875/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 876/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 877/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 878/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 879/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 880/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 881/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 882/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 883/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 884/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 885/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 886/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 887/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 888/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 889/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 890/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 891/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 892/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 893/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 894/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 895/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 896/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 897/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 898/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 899/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 900/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 901/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 902/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 903/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 904/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 905/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 906/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 907/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 908/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 909/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 910/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 911/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 912/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 913/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 914/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 915/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 916/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 917/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 918/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 919/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 920/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 921/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 922/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 923/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 924/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 925/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 926/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 927/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 928/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 929/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 930/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 931/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 932/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 933/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 934/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 935/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 936/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 937/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 938/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 939/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 940/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 941/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 942/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 943/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 944/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 945/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 946/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 947/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 948/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 949/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 950/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 951/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 952/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 953/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 954/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 955/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 956/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 957/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 958/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 959/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 960/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 961/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 962/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 963/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 964/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 965/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 966/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 967/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 968/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 969/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 970/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 971/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 972/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 973/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 974/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 975/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 976/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 977/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 978/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 979/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 980/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 981/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 982/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 983/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 984/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 985/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 986/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 987/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 988/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 989/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 990/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 991/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 992/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 993/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 994/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 995/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 996/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 997/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 998/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 999/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1000/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1001/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1002/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1003/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1004/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1005/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1006/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1007/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1008/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1009/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1010/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1011/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1012/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1013/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1014/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1015/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1016/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1017/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1018/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1019/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1020/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1021/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1022/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1023/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1024/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1025/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1026/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1027/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1028/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1029/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1030/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1031/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1032/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1033/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1034/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1035/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1036/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1037/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1038/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1039/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1040/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1041/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1042/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1043/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1044/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1045/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1046/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1047/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1048/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1049/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1050/2950
Error, invalid function arguments
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1051/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1052/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1053/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1054/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1055/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1056/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1057/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1058/2950
Ovde se vidi da i Maple moze da radi sa koeficijentima srazmernosti. Prema tpme Maple biva mocniji
od Mathcada
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1059/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1060/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1061/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1062/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1063/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1064/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1065/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1066/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1067/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1068/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1069/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1070/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1071/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1072/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1073/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1074/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1075/2950
> m:=me;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1076/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1077/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1078/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1079/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1080/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1081/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1082/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1083/2950
Examples
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1084/2950
Define the coordinates and covariant metric for the Schwarzschild metric:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1085/2950
> with(tensor):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1086/2950
> coords:=[t, r, theta,phi]:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1087/2950
g:=array (symmetric, sparse, 1..4, 1..4):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1088/2950
g[1,1]:=(1-2*m/r): g[2,2]:=-1/g[1,1]: g[3,3]:=-r^2: g[4,4]:=-r^2*sin(theta)^2:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1089/2950
metric:=create([-1,-1], eval(g));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1090/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1091/2950
> metric := TABLE([index_char = [-1, -1], compts =linalg['eigenvalues'](matrix([[1-2*m/r, 0, 0, 0], [0, -1/(1-2*m/r),0, 0], [0, 0, -r^2, 0], [0, 0, 0, -r^2*sin(theta)^2]]))]);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1092/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1093/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1094/2950
Compute the curvature (without the print option)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1095/2950
> tensorsGR(coords,metric,contra_metric,det_met, C1, C2, Rm, Rc, R,G, C):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1096/2950
Error, invalid input: tensorsGR expects its 1st argument, coord, to be of type list(name), but received [t,
0.5100000000e-10, theta, phi]
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1097/2950
Use displayGR to show that it is a vacuum solution of the Einstein field equations:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1098/2950
> displayGR(Einstein,G);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1099/2950
`type/tensor_type` : ".6673000000e-10*meter^3/kg/second^2" is not a table.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1100/2950
Error, (in displayGR) Einstein tensor, 0.6673000000e-10*meter^3/(kg*second^2), has invalid input:
%1 expects its %-2 argument, %3, to be of type %4, but received %5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1101/2950
Use displayGR to show the nonzero Christoffel symbols of the first kind:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1102/2950
> displayGR(Christoffel1,C1);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1103/2950
`type/tensor_type` : "C1" is not a table.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1104/2950
Error, (in displayGR) Christoffel symbols of the 1st kind, C1, has invalid input: %1 expects its %-2
argument, %3, to be of type %4, but received %5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1105/2950
Display everything using display_allGR :
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1106/2950
> display_allGR (coords,metric,contra_metric, det_met, C1, C2, Rm,Rc, R, G, C);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1107/2950
Error, invalid input: display_allGR expects its 1st argument, coord, to be of type list(name), but
received [t, 0.5100000000e-10, theta, phi]
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1108/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1109/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1110/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1111/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1112/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1113/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1114/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1115/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1116/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1117/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1118/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1119/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1120/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1121/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1122/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1123/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1124/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1125/2950
Iz mase elektrona naci klasicni radijus elektrona pomocu koeficijenta srazmernosti. Maple je to gore
uradio.Iz bekerela je nadjena masa elektrona.Treci primer :iz slozene formule naci masu sunca pomocu
koeficijenta srazmernosti.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1126/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1127/2950
> #------UNITS, PHYSICAL CONSTANTS, AND DATA----
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1128/2950
#-------Warren D. Smith 1998-------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1129/2950
#This useful file causes MAPLE to know about
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1130/2950
#fundamental physical constants, useful data, and units.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1131/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1132/2950
#I feel cgs, emu, esu units are an abomination.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1133/2950
#If you want to have no units, go totally dimensionless
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1134/2950
#(for example, the Planck units). If you want to have units,
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1135/2950
#use SI. The cgs, emu, esu systems are a silly halfassed attempt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1136/2950
#to have it both ways and get rid of some units and keep others.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1137/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1138/2950
# The present file features conversion factors to random non-SI
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1139/2950
#units like foot, horsepower, pound, ounce. The entire group
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1140/2950
#of units is known to it, so all quantities are dimensioned
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1141/2950
#automatically. Meter, second, coulomb, kelvin, and kg are
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1142/2950
#my fundamental units. (Arguably kelvin is not needed.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1143/2950
#Also for radiation dose units, I use the "disintegration", e.g.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1144/2950
#disintegration/second.)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1145/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1146/2950
# I have so far been unable to stomach the "candela".
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1147/2950
#The old definition was...
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1148/2950
#candle = 1/60 the luminous intensity of 1 cm^2 of a Blackbody atthe
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1149/2950
#melting Temperature of platinum (2042.15 kelvin) = 1.6437 *watt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1150/2950
#= meter^2 / 600000 * sigmasb * platinummelttemp^4;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1151/2950
#a candela is the light intensity from a candle (now redefined
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1152/2950
#as "1/683 watt per steradian" of 555nm wavelength light (which theeye
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1153/2950
#is maximally sensitive to).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1154/2950
#Note, this seems to be a lot smaller than the old defn.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1155/2950
#Huh? Then lumen = candela*steradian = 1/683 *watt;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1156/2950
#lux = lumen/meter^2 = 1/683 *watt/meter^2; candlepower = candela.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1157/2950
#Yuk!
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1158/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1159/2950
#I also hate the "radian" and "steradian"; they should be
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1160/2950
#dimensionless, in my view.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1161/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1162/2950
# Finally, decibels and bels are another abomination.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1163/2950
# decibels = 10*bels = 10*log10(Intensity/ReferenceIntensity);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1164/2950
#and for use in auditory work, one uses
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1165/2950
#ReferenceIntensity = 1 phon = 10^(-16) *watt/cm^2/sec at 1000*hertz.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1166/2950
#Idiotic - haven't these guys heard of scientific notation to dealwith
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1167/2950
#logarithms?
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1168/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1169/2950
# This MAPLE code does not know about precision (usually the
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1170/2950
#last 2 digits of our numbers are imprecise). My values
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1171/2950
#are CODATA values plus miscellaneous sources like
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1172/2950
#CRC handbook. If you really care about errors you have to know
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1173/2950
#about the correlations among the errors in the
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1174/2950
#fundamental constants (many errors are highly correlated)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1175/2950
#and that would require a lot of extra software, which I
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1176/2950
#didn't feel like trying to write.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1177/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1178/2950
#Update 1999:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1179/2950
#PJ Mohr BN Taylor
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1180/2950
#CODATA recommended values of the fundamental physical constants 1998
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1181/2950
#J Phys Chem Ref Data 28 (1999)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1182/2950
#finally came out
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1183/2950
#http://physics.nist.gov/cgi-bin/cuu/
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1184/2950
# http://physics.nist.gov/PhysRefData/contents.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1185/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1186/2950
#The 1998 CODATA
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1187/2950
#Recommended Values of the Fundamental Physical
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1188/2950
#Constants, Web Version 3.0," available at
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1189/2950
#http://physics.nist.gov/constants (National Institute of
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1190/2950
#Standards and Technology, Gaithersburg, MD 20899,
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1191/2950
#release date 23 July 1999).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1192/2950
#http://physics.nist.gov/cuu/Constants/index.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1193/2950
#http://physics.nist.gov/constants
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1194/2950
#http://www.codata.org/
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1195/2950
#http://pdg.lbl.gov/1998/astrorpp.ps
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1196/2950
#these sites very recommended - can now download any correlationcoeff too
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1197/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1198/2950
#A detailed description of the data and its analysis that led tothese
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1199/2950
#values will be published by early 2000 in the Journal of Physical
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1200/2950
#and Chemical Reference Data.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1201/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1202/2950
#"Review of particle properties", Phys Rev D50 (1994) 1-.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1203/2950
#PRD 54 (July 1996) 1-720.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1204/2950
#C.Caso et al.: Review of particle physics, Europ. Phys. J. C3 (1998)1-.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1205/2950
#http://pdg.lbl.gov
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1206/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1207/2950
#---------units (and data):---------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1208/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1209/2950
#prefixes:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1210/2950
zepto := 10^(-21);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1211/2950
atto := 10^(-18);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1212/2950
femto := 10^(-15);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1213/2950
pico := 10^(-12);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1214/2950
nano := 10^(-9);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1215/2950
micro := 10^(-6);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1216/2950
milli := 10^(-3);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1217/2950
centi := 10^(-2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1218/2950
kilo := 10^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1219/2950
mega := 10^6;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1220/2950
giga := 10^9;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1221/2950
tera := 10^12;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1222/2950
peta := 10^15;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1223/2950
exa := 10^18;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1224/2950
zetta := 10^21;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1225/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1226/2950
joule := meter^2 * kg / second^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1227/2950
watt := joule/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1228/2950
mole := 6.02214199 * 10^(23); #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1229/2950
ampere := coulomb/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1230/2950
hertz := 1/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1231/2950
newton := meter*kg/second^2; #force
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1232/2950
pascal := newton/meter^2; #pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1233/2950
poise := pascal*second; #absolute viscosity
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1234/2950
stokes := meter^2 /second; #kinematic viscosity
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1235/2950
volt := watt/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1236/2950
farad := coulomb/volt;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1237/2950
ohm := volt/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1238/2950
mho := 1/ohm;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1239/2950
siemens := 1/ohm;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1240/2950
weber := volt*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1241/2950
tesla := weber/meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1242/2950
henry := weber/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1243/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1244/2950
sipole := meter*coulomb/second; #my own unit of magentic monopolecharge
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1245/2950
#One SIpole is the amount of magnetic charge that would
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1246/2950
#experience a force of 1 Newton if placed in a 1 Tesla magnetic
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1247/2950
#field.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1248/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1249/2950
becquerel := disintegration/second; #radioactivity unit
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1250/2950
gray := joule/kg; #for measuring absorbed radiation dose
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1251/2950
#a sievert is the amount of radiation equivalent in health effect to1 gray
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1252/2950
#of some kind of standard type of radiation.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1253/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1254/2950
minute := 60*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1255/2950
hour := 60*minute;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1256/2950
solarday := 24*hour; #increases 1 millisecond/century
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1257/2950
starday := 86164.09 * second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1258/2950
year := 365.24219879 *solarday;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1259/2950
month := year/12;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1260/2950
century := 100*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1261/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1262/2950
denier := kg/meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1263/2950
dyne := 10^(-5) *newton;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1264/2950
erg := 10^(-7) *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1265/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1266/2950
gauss := 10^(-4) * tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1267/2950
maxwell := 10^(-8) *weber;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1268/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1269/2950
horsepower := 746 * watt; #several definitions exist 735 to 746watt.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1270/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1271/2950
jansky := 10^(-26) * watt * second / meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1272/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1273/2950
oersted := 7.957747 * ampere/meter; #says CRC handbook
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1274/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1275/2950
parsec := cot(1 * angularsecond) * astronomicalunit;#3.085678*10^(16) *meter; 3.26*lightyear
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1276/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1277/2950
lb := .45359237 *kg; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1278/2950
poundmass := lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1279/2950
ounce := lb/16;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1280/2950
shortton := 2000 *lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1281/2950
longton := 2240 *lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1282/2950
grain := lb/7000;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1283/2950
slug := 14.59390 *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1284/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1285/2950
lbf := 4.4482216152605 * newton; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1286/2950
poundforce := lbf;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1287/2950
psi := lbf/inch^2; #6895*pascal
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1288/2950
torr := 133.322 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1289/2950
mmhg := torr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1290/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1291/2950
liter := 10^(-3) *meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1292/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1293/2950
sverdrup := 10^6 *meter^3/second; #volume flux. Used in oceanography.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1294/2950
kayser := 1/(centi*meter); #used in spectroscopy
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1295/2950
cc := (centi*meter)^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1296/2950
micron := 10^(-6) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1297/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1298/2950
metricton := 10^3 *kg; #also "tonne"
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1299/2950
#electron-volt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1300/2950
ev := 1.602176462 * 10^(-19) *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1301/2950
km := 10^3 *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1302/2950
mm := 10^(-3) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1303/2950
cm := 10^(-2) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1304/2950
astronomicalunit := 149597900 *km: #earth-sun distance
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1305/2950
nauticalmile := 1852*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1306/2950
#nauticalmile := 6076.115486*foot:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1307/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1308/2950
angstrom := 10^(-10) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1309/2950
barn := 10^(-28) *meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1310/2950
fermi := 10^(-15) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1311/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1312/2950
bar := 10^(5) *pascal:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1313/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1314/2950
abampere := ampere/10;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1315/2950
abcoulomb := coulomb/10;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1316/2950
statampere := 3.335641 * 10^(-10) *ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1317/2950
statcoulomb := 3.335641 * 10^(-10) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1318/2950
curie := 3.7*10^(10) *becquerel;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1319/2950
roentgen := 2.58 * 10^(-4) *coulomb/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1320/2950
rad := 10^(-2) *gray;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1321/2950
remunit := 10^(-2) *sievert;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1322/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1323/2950
pi := evalf(Pi);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1324/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1325/2950
radian := 1;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1326/2950
revolution := evalf(2*Pi*radian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1327/2950
angulardegree := evalf(Pi/180 *radian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1328/2950
angularminute := angulardegree/60;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1329/2950
angularsecond := angularminute/60;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1330/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1331/2950
fullsphere := evalf(4*Pi*steradian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1332/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1333/2950
knot := nauticalmile/hour;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1334/2950
hectare := 10^4 *meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1335/2950
angstrom := 10^(-10)*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1336/2950
inch := 2.54 * 10^(-2)*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1337/2950
foot := 12*inch;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1338/2950
yard := 3*foot;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1339/2950
printerpoint := 0.13837 *inch; #or is it inch/72? close
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1340/2950
mile := 5280*foot:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1341/2950
acre := mile^(2) /640; #acre := 43560 *foot^2
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1342/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1343/2950
usgallon := 231 * inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1344/2950
brgallon := 277.420 *inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1345/2950
quart := usgallon/4;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1346/2950
pint := quart/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1347/2950
cup := pint/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1348/2950
gill := cup/2; #british cups, pints, gills are each a bit bigger
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1349/2950
fluidounce := cup/8;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1350/2950
tablespoon := fluidounce/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1351/2950
teaspoon := tablespoon/3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1352/2950
boardfoot := 144 *inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1353/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1354/2950
gram := 10^(-3) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1355/2950
carat := .2 *gram;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1356/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1357/2950
btu := 1.055056 * 10^(3) * joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1358/2950
ustherm := 1.054804 * 10^(8) *joule; #used by US natural gasindustry
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1359/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1360/2950
watertripletemp := 273.16 *kelvin; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1361/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1362/2950
watertriplepressure := 611.73 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1363/2950
platinummelttemp := (1769.0+273.15) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1364/2950
waterfreezetemp := 273.15 *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1365/2950
waterboiltemp := 373.15 *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1366/2950
#celsius := waterfreeze + kelvin. fahrenheit := celsius * (5/9) + 32;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1367/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1368/2950
caloriethermo := 4.184 *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1369/2950
calorieintl := 4.1868 *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1370/2950
calorie := calorieintl;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1371/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1372/2950
#weapons kiloton is by convention 10^(12) calories.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1373/2950
kiloton := 10^(12) * calorie;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1374/2950
mageaton := 10^(3) * kiloton;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1375/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1376/2950
rankine := (5/9) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1377/2950
standardatmosphere := 101325 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1378/2950
standardgravity := 9.80665 *meter/second^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1379/2950
vsoundair := 331.4 *meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1380/2950
specheatair := 1010 *joule/kg/kelvin: #at const pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1381/2950
densityair := 1.21 * kg/meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1382/2950
vsoundwater := 1496.7 *meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1383/2950
densitywater := 1000*kg/meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1384/2950
specheatwater := 4190 *joule/kg/kelvin; #at const pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1385/2950
heatfusionwater := 333 * kilo*joule/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1386/2950
heatvapwater := 2260* kilo*joule/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1387/2950
indexrefwater := 1.33; #at 589 nm
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1388/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1389/2950
resistivitysilver := 1.587 * 10^(-8) * ohm * meter; #at 293 Kelvin
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1390/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1391/2950
radgeosync := 42200 * kilo * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1392/2950
vescapeearth := 11200 * meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1393/2950
muearth := 8.0*10^(22) *joule/tesla; #magnetic dipole moment
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1394/2950
efieldearth := 150 * volt/meter; #down. At earth's surface. mean.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1395/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1396/2950
suntemp := 5780*kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1397/2950
sunluminosity := 3.846 * 10^(26) * joule/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1398/2950
solarconst := evalf(sunluminosity / (4*Pi*astronomicalunit^2));#varies 2%
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1399/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1400/2950
mmilkyway := 2.2*10^(41) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1401/2950
moceans := 1.4 *10^(21) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1402/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1403/2950
velocorbitalgalaxy := 220 * km/second; #of solar system round milkyway galaxy
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1404/2950
velocwrtcosmicbackground := 369.3 * km/second; #+-2.5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1405/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1406/2950
disttocenterofmilkyway := 8.0 * mega * parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1407/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1408/2950
distproximacentauri := 4.22 * c*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1409/2950
#**Alpha Centauri system:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1410/2950
#Separation between Alpha Centauri A and B varies from 11 to 35 AU;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1411/2950
#they take 80 years to orbit around each other.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1412/2950
#Proxima Centauri is currently 13,000 AUs from A and B; no orbital
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1413/2950
#parameters of it are known.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1414/2950
# A B proxima sun
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1415/2950
# 5800K 5300K 2700K 5800K
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1416/2950
# 4.35 4.35 4.22 0 lightyears away
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1417/2950
# Yellow Orange Red Yellow
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1418/2950
distandromedagalaxy := 2*10^(22) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1419/2950
distlargemagellaniccloud := 55*kilo*parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1420/2950
distvirgocluster := 20*mega*parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1421/2950
disttouniverseedge := 10^(26) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1422/2950
distearthmoon := 384404 *km; #+3 cm per year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1423/2950
periodmoon := 27 *solarday: #??? +2 milliseconds/century
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1424/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1425/2950
distsunmercury := .38 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1426/2950
distsunvenus := .72 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1427/2950
distsunearth := 1.0 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1428/2950
distsunmars := 1.52 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1429/2950
distsunjupiter := 5.20 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1430/2950
distsunsaturn := 9.5 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1431/2950
distsunuranus := 19.2 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1432/2950
distsunneptune := 30.0 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1433/2950
distsunpluto := 39.5 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1434/2950
#pluto has 1 satellite "charon" with about .1 its mass;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1435/2950
#it has day 6.38 earth days.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1436/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1437/2950
#radiusearth := 6371.006 *km:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1438/2950
radiusearth := 6378.140 *km:#equatorial
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1439/2950
radiusmoon := 1738 *km;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1440/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1441/2950
radiusmercury := .38 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1442/2950
radiusvenus := .96 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1443/2950
radiusmars := .53 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1444/2950
radiusjupiter := 10.8 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1445/2950
radiussaturn := 9.0 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1446/2950
radiusuranus := 4.1 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1447/2950
radiusneptune := 3.85 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1448/2950
radiuspluto := 1137 *km: #+-8
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1449/2950
radiussun := 695990 *km: #equatorial
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1450/2950
radiussunschwarzschild := 2.95325008 * km;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1451/2950
radiusmilkyway := 15 * kilo *parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1452/2950
thicknessmilkyway := 1 * kilo *parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1453/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1454/2950
mmercury := .33022 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1455/2950
mvenus := 4.8690 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1456/2950
mearth := 5.97370 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1457/2950
mmoon := .073483 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1458/2950
mmars := .64191 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1459/2950
mjupiter := 1898.8 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1460/2950
msaturn := 568.50 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1461/2950
muranus := 86.625 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1462/2950
mneptune := 102.78 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1463/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1464/2950
msun := 1.98892 * 10^(30) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1465/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1466/2950
hubnum := .5: #could be anywhere .2 to 1.0
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1467/2950
hubbleconst := 70*hubnum*km/second/(mega*parsec);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1468/2950
#http://ucsu.colorado.edu/~lisle/main.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1469/2950
#``The cosmological implications of Hipparcus''
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1470/2950
#direct trig parallax distance measurement to nearby Cepheids with
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1471/2950
#Hipparcus satellite. Leads to 10% revision of Hubble constant, now
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1472/2950
#about 60 km/s/Mpc.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1473/2950
#another place claims 60-80 is the range; I'm going with it.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1474/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1475/2950
criticaldensity := 3*hubbleconst^2/(8*pi*G); #needed to close theuniverse
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1476/2950
#matter density is supposed to be .2 to 1.0 times this
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1477/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1478/2950
entropydensityofuniverse := 2899.3 * (2.853/2.728)^3 * kb / cc;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1479/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1480/2950
tempuniversebackground := 2.853 * kelvin; #plus or minus .002
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1481/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1482/2950
lightyear := c*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1483/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1484/2950
#various rough estimates of universe-quantities on Misner-Thorne- Wheeler p738:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1485/2950
#max radius 19*10^9 lightyear
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1486/2950
#time start to max 3*10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1487/2950
#time bang to crunch 6*10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1488/2950
#age now 10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1489/2950
#radius now 13*10^9 lightyear note: larger than age
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1490/2950
#volume now 3.83*10^79 meter^3
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1491/2950
#density at maximum 5*10^(-30) * gram/cc
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1492/2950
#rate of increase of radius now .66 lightyear/year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1493/2950
#amount of matter 5.68*10^(53) kg
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1494/2950
#baryon number 3.39*10^(80)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1495/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1496/2950
#MTW 29.6p796
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1497/2950
#density of universe now is <10^(-28) g/cc and >2*10^(-31) g/cc
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1498/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1499/2950
#MTW when universe about 10^5 years old, density was 10^(-20) g/ccand temp 3000K
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1500/2950
#and then:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1501/2950
#1. radiation ceased to domaine, now matter
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1502/2950
#2. universe became transparent
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1503/2950
#3. hydrogen atoms began to form (no longer ionized perpetually)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1504/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1505/2950
#------------------fundamental constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1506/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1507/2950
#these constants suffice to define the planck units:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1508/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1509/2950
#speed of light in vacuum exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1510/2950
c := 299792458 * meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1511/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1512/2950
#boltzmann constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1513/2950
kb := 1.3806503 * 10^(-23) *joule/kelvin; #1700 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1514/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1515/2950
#permittivity & permeability of vacuum
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1516/2950
mu0 := evalf(4*Pi*1.0 * 10^(-7)) *henry/meter; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1517/2950
eps0 := 1/(c^2 * mu0); #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1518/2950
#eps0 := 8.854187817 * 10^(-12) *farad/meter
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1519/2950
#mu0*eps0*c^2=1
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1520/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1521/2950
#newton gravitational constant (force = G*m1*m2/r^2)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1522/2950
G := 6.673 * 10^(-11) *newton*meter^2/kg^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1523/2950
#+- .010; huge relative uncert .0015
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1524/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1525/2950
#coulomb law constant (force = coulombconst * q1*q2/r^2)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1526/2950
coulombconst := 1/ (4 * pi *eps0);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1527/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1528/2950
#planck's constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1529/2950
h := 6.62606876 * 10^(-34) *joule*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1530/2950
hbar := 1.054571596 * 10^(-34) *joule*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1531/2950
#hbar = evalf(h/(2*Pi)):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1532/2950
#78 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1533/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1534/2950
#------------planck length, mass, time, charge:--------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1535/2950
#These are the fundamental units of
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1536/2950
#length, mass, time, charge, temperature
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1537/2950
#in a unit system where c=G=hbar=kb=1 and
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1538/2950
#where coulombconst*qplanck^2 = G*mplanck^2.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1539/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1540/2950
lplanck := sqrt(hbar*G/c^3);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1541/2950
mplanck := sqrt(hbar*c/G);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1542/2950
tplanck := sqrt(hbar*G/c^5);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1543/2950
qplanck := evalf(sqrt(4*Pi*hbar*c*eps0));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1544/2950
#qplanck / qe = 1/sqrt(alpha), reciprocal sqrt of fine structureconstant!
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1545/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1546/2950
tempplanck := (mplanck*c^2)/kb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1547/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1548/2950
# lplanck := 1.616048609*10^(-35) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1549/2950
# tplanck := 5.390557920*10^(-44) *second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1550/2950
# mplanck := 2.176714074*10^(-8) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1551/2950
# qplanck := 1.875546788*10^(-18) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1552/2950
# tempplanck := 1.416957021*10^(32) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1553/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1554/2950
# qplanck = 11.7062 charge quanta = sqrt(137).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1555/2950
# mplanck = 2.389527889 * 10^(22) electron masses.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1556/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1557/2950
#------other fundamental constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1558/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1559/2950
#charge of proton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1560/2950
qe := 1.602176462 * 10^(-19) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1561/2950
#39 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1562/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1563/2950
#atomic mass unit
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1564/2950
amu := 10^(-3) * kg/mole;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1565/2950
#amu := 1.66053873*10^(-27) *kg: #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1566/2950
#mole is number of carbon-12 atoms in 12 grams, amu is
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1567/2950
#1/12 mass of a carbon-12 atom.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1568/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1569/2950
#rest mass of electron, proton, neutron, muon, deuteron, alpha particle
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1570/2950
#me := 9.10938188 * 10^(-31) *kg: #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1571/2950
me := 5.48579903 * 10^(-4) * amu; # +- .00000013
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1572/2950
me := .510998902 * mega * ev/c^2; #40 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1573/2950
#failed excited lepton searches: e >86 GeV, muon >=86 GeV, tau>72 GeV
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1574/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1575/2950
mp := 1.67262158* 10^(-27) *kg; #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1576/2950
mp := 938.271998 * mega * ev / c^2; #40 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1577/2950
mp := 1.00727646688 * amu; # .13ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1578/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1579/2950
mpbyme := 1836.1526675; #2.1ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1580/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1581/2950
#mn := 1.6749286 * 10^(-27) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1582/2950
mn := 1.008664904 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1583/2950
# +-.000000014
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1584/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1585/2950
#mmu := 1.8835327*10^(-28) *kg:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1586/2950
mmu := .113428913 * amu: # +- .000000017
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1587/2950
mmu := 105.658389 * mega * ev/c^2; #+-.000034 (1998 value)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1588/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1589/2950
mdeuteron := 3.3435860 * 10^(-27) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1590/2950
mdeuteron := 1875.612762 * mega * ev/c^2; #40 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1591/2950
mtriton := 3.015500 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1592/2950
m3he := 3.014932 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1593/2950
malpha := me / (1.37093354 * 10^(-4));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1594/2950
#malpha := 4.001505 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1595/2950
mpi := 135.0 * mega*ev/c^2; #mass of pi
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1596/2950
mpi0 := 139.6 * mega*ev/c^2; #mass of pi_0^{+-}
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1597/2950
mtau := 1777.05 * mega * ev / c^2; #+.29, -.26 (1998 value)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1598/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1599/2950
#heavy lepton searches supposedly go up to 81.5GeV now with 95% conf
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1600/2950
#nothing charged there. Ackerstaff Euro Phys J C1 (1998) 45
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1601/2950
#also 95% conf nothing uncharged below 69GeV
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1602/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1603/2950
mquarku := 3.25 * mega * ev/c^2; #charge +2/3 (1.5 to 5)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1604/2950
mquarkd := 6 * mega * ev/c^2; #charge -1/3 #??? wrong way ??? (3to 9)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1605/2950
mquarks := 115 * mega * ev/c^2; #charge -1/3 (60 to 170)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1606/2950
mquarkc := 1.25 * giga * ev/c^2; #charge +2/3 (1.25 +-.15)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1607/2950
mquarkb := 4.25 * giga * ev/c^2; #charge -1/3 (4.25 +- .15)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1608/2950
mquarkt := 174.3 * giga * ev/c^2; #charge +2/3. 174.3+-5.1
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1609/2950
#all quarks spin 1/2, baryon # 1/3, RGB or anti-RGB color.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1610/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1611/2950
mw := 80.41 * giga * ev/c^2; #+-.4 Gev. Charge +-1. Spin 1. W boson.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1612/2950
mz := 91.187 * giga * ev/c^2; #+-.031 Gev. Charge 0. Spin 1. Z boson.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1613/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1614/2950
#particle mean lifetimes
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1615/2950
meanlifemu := 2.19703 * micro * second;#uncert .00004
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1616/2950
meanlifetau := .2900 * pico * second; #+-.0012
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1617/2950
meanlifen := 888.6 * second; #+- 3.5 second
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1618/2950
#meanlifep > 10^31 years for some investigated modes
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1619/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1620/2950
#Bohr magneton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1621/2950
bohrmag := qe*hbar/(2*me);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1622/2950
#bohrmag = mue/1.001159652:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1623/2950
#bohrmag := 9.2740154 * 10^(-24) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1624/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1625/2950
#Nuclear magneton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1626/2950
nucmag := qe*hbar/(2*mp);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1627/2950
#nucmag := 5.0507866*10^(-27) * joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1628/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1629/2950
#magnetic moment of electron, proton, neutron, muon, deuteron
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1630/2950
#mue := 9.2847701 * 10^(-24) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1631/2950
#mue := 1.001159652193 * bohrmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1632/2950
# +- .000000000010
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1633/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1634/2950
#mup := 1.41060761 * 10^(-26) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1635/2950
mup := 2.792847386 * nucmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1636/2950
# +- .000000063
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1637/2950
;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1638/2950
#mun := 9.6623707 * 10^(-27) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1639/2950
mun := 1.91304275 * nucmag; #has negative sign, incidentally
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1640/2950
# +-.00000045
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1641/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1642/2950
mumu := 4.4904514 * 10^(-26) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1643/2950
mudeuteron := 4.3307375 * 10^(-27) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1644/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1645/2950
#------------"atomic units":--------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1646/2950
#mass me
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1647/2950
#charge qe
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1648/2950
#action hbar
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1649/2950
#length rbohr
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1650/2950
#energy hartree
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1651/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1652/2950
#Bohr radius (estimate, for hydrogen atom)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1653/2950
rbohr := evalf(4*Pi*eps0*hbar^2/(me*qe^2));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1654/2950
#rbohr := 5.29177208 * 10^(-11) *meter: #3.7ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1655/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1656/2950
#hartree energy unit, about 27 ev
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1657/2950
#hartree := 2*rydberg*h*c := 4.3598 * 10^(-18) *joule:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1658/2950
hartree := hbar^2 / (me*rbohr^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1659/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1660/2950
atomictimeunit := hbar / hartree;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1661/2950
atomicvelocityunit := rbohr / atomictimeunit; #about c/137
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1662/2950
atomicforceunit := hartree / rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1663/2950
atomicmomentumunit := hbar / rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1664/2950
atomiccurrentunit := qe / atomictimeunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1665/2950
atomicefieldunit := hartree/(qe*rbohr);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1666/2950
atomicpotentialunit := hartree/qe;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1667/2950
atomicedipoleunit := qe*rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1668/2950
atomicmagfieldunit := hbar / (qe*rbohr^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1669/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1670/2950
atomicmagdipoleunit := 2*bohrmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1671/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1672/2950
#------derived constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1673/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1674/2950
#magnetic flux quantum
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1675/2950
phi0 := h/(2*qe);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1676/2950
#phi0 := 2.06783461 * 10^(-15) *weber
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1677/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1678/2950
#alpha = fine structure constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1679/2950
#alpha := 1/137.0359895;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1680/2950
alpha := evalf(qe^2 / (4*Pi*eps0*hbar*c));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1681/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1682/2950
#stefan-boltzmann constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1683/2950
sigmasb := evalf(Pi^2*kb^4/(60*hbar^3*c^2));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1684/2950
#sigmasb := 5.670400*10^(-8) *watt/meter^2/kelvin^4; #7000 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1685/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1686/2950
#first radiation constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1687/2950
c1radiation := evalf(2*Pi*h*c^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1688/2950
#c1radiation := 3.7417749 * 10^(-16) watt/meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1689/2950
c2radiation := h*c/kb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1690/2950
#c2radiation := 0.01438769 *meter*kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1691/2950
#The max intensity lambda in blackbody radiation is
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1692/2950
#wienconst*T*cm/kelvin, where
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1693/2950
wienconst := c2radiation / 4.965114231;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1694/2950
#wienconst := 0.2897756 *cm/kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1695/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1696/2950
#rydberg (approx hydrogen waves per meter, infinite mass nuc)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1697/2950
rydberg := me*c*alpha^2/(2*h);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1698/2950
#rydberg := 10973731.56834(24) /meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1699/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1700/2950
#classical electron radius
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1701/2950
#re := 2.817940285 * 10^(-15) *meter; #11 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1702/2950
re := alpha^2 * rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1703/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1704/2950
#compton wavelengths of electron, proton, neutron, muon
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1705/2950
e_compton := h/(me*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1706/2950
p_compton := h/(mp*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1707/2950
n_compton := h/(mn*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1708/2950
mu_compton := h/(mmu*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1709/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1710/2950
fermicouplingconst := 1.16639 * 10^(-5) / (giga * ev)^2; #9000 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1711/2950
sinsquaredweakmixingangle := 0.23124; #.001 relative uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1712/2950
#codata says .2235 +- .0023
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1713/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1714/2950
strongcouplingconst := .119;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1715/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1716/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1717/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1718/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1719/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1720/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1721/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1722/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1723/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1724/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1725/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1726/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1727/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1728/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1729/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1730/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1731/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1732/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1733/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1734/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1735/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1736/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1737/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1738/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1739/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1740/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1741/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1742/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1743/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1744/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1745/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1746/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1747/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1748/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1749/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1750/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1751/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1752/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1753/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1754/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1755/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1756/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1757/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1758/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1759/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1760/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1761/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1762/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1763/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1764/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1765/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1766/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1767/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1768/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1769/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1770/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1771/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1772/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1773/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1774/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1775/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1776/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1777/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1778/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1779/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1780/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1781/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1782/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1783/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1784/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1785/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1786/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1787/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1788/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1789/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1790/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1791/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1792/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1793/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1794/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1795/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1796/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1797/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1798/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1799/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1800/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1801/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1802/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1803/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1804/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1805/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1806/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1807/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1808/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1809/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1810/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1811/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1812/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1813/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1814/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1815/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1816/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1817/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1818/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1819/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1820/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1821/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1822/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1823/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1824/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1825/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1826/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1827/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1828/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1829/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1830/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1831/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1832/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1833/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1834/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1835/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1836/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1837/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1838/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1839/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1840/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1841/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1842/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1843/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1844/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1845/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1846/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1847/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1848/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1849/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1850/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1851/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1852/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1853/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1854/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1855/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1856/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1857/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1858/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1859/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1860/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1861/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1862/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1863/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1864/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1865/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1866/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1867/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1868/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1869/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1870/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1871/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1872/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1873/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1874/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1875/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1876/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1877/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1878/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1879/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1880/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1881/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1882/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1883/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1884/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1885/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1886/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1887/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1888/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1889/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1890/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1891/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1892/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1893/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1894/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1895/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1896/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1897/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1898/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1899/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1900/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1901/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1902/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1903/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1904/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1905/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1906/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1907/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1908/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1909/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1910/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1911/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1912/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1913/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1914/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1915/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1916/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1917/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1918/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1919/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1920/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1921/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1922/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1923/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1924/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1925/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1926/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1927/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1928/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1929/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1930/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1931/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1932/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1933/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1934/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1935/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1936/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1937/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1938/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1939/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1940/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1941/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1942/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1943/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1944/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1945/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1946/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1947/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1948/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1949/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1950/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1951/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1952/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1953/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1954/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1955/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1956/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1957/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1958/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1959/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1960/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1961/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1962/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1963/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1964/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1965/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1966/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1967/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1968/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1969/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1970/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1971/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1972/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1973/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1974/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1975/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1976/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1977/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1978/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1979/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1980/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1981/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1982/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1983/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1984/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1985/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1986/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1987/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1988/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1989/2950
Error, invalid function arguments
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1990/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1991/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1992/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1993/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1994/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1995/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1996/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1997/2950
Ovde se vidi da i Maple moze da radi sa koeficijentima srazmernosti. Prema tpme Maple biva mocniji
od Mathcada
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1998/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 1999/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2000/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2001/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2002/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2003/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2004/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2005/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2006/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2007/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2008/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2009/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2010/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2011/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2012/2950
> m:=me;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2013/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2014/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2015/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2016/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2017/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2018/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2019/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2020/2950
Examples
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2021/2950
Define the coordinates and covariant metric for the Schwarzschild metric:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2022/2950
> with(tensor):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2023/2950
> coords:=[t, r, theta,phi]:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2024/2950
g:=array (symmetric, sparse, 1..4, 1..4):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2025/2950
g[1,1]:=(1-2*m/r): g[2,2]:=-1/g[1,1]: g[3,3]:=-r^2: g[4,4]:=-r^2*sin(theta)^2:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2026/2950
metric:=create([-1,-1], eval(g));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2027/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2028/2950
> metric := TABLE([index_char = [-1, -1], compts =linalg['eigenvalues'](matrix([[1-2*m/r, 0, 0, 0], [0, -1/(1-2*m/r),0, 0], [0, 0, -r^2, 0], [0, 0, 0, -r^2*sin(theta)^2]]))]);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2029/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2030/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2031/2950
Compute the curvature (without the print option)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2032/2950
> tensorsGR(coords,metric,contra_metric,det_met, C1, C2, Rm, Rc, R,G, C):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2033/2950
Error, invalid input: tensorsGR expects its 1st argument, coord, to be of type list(name), but received [t,
0.5100000000e-10, theta, phi]
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2034/2950
Use displayGR to show that it is a vacuum solution of the Einstein field equations:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2035/2950
> displayGR(Einstein,G);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2036/2950
`type/tensor_type` : ".6673000000e-10*meter^3/kg/second^2" is not a table.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2037/2950
Error, (in displayGR) Einstein tensor, 0.6673000000e-10*meter^3/(kg*second^2), has invalid input:
%1 expects its %-2 argument, %3, to be of type %4, but received %5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2038/2950
Use displayGR to show the nonzero Christoffel symbols of the first kind:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2039/2950
> displayGR(Christoffel1,C1);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2040/2950
`type/tensor_type` : "C1" is not a table.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2041/2950
Error, (in displayGR) Christoffel symbols of the 1st kind, C1, has invalid input: %1 expects its %-2
argument, %3, to be of type %4, but received %5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2042/2950
Display everything using display_allGR :
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2043/2950
> display_allGR (coords,metric,contra_metric, det_met, C1, C2, Rm,Rc, R, G, C);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2044/2950
Error, invalid input: display_allGR expects its 1st argument, coord, to be of type list(name), but
received [t, 0.5100000000e-10, theta, phi]
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2045/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2046/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2047/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2048/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2049/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2050/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2051/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2052/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2053/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2054/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2055/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2056/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2057/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2058/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2059/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2060/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2061/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2062/2950
Iz mase elektrona naci klasicni radijus elektrona pomocu koeficijenta srazmernosti. Maple je to gore
uradio.Iz bekerela je nadjena masa elektrona.Treci primer :iz slozene formule naci masu sunca pomocu
koeficijenta srazmernosti.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2063/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2064/2950
> #------UNITS, PHYSICAL CONSTANTS, AND DATA----
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2065/2950
#-------Warren D. Smith 1998-------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2066/2950
#This useful file causes MAPLE to know about
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2067/2950
#fundamental physical constants, useful data, and units.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2068/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2069/2950
#I feel cgs, emu, esu units are an abomination.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2070/2950
#If you want to have no units, go totally dimensionless
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2071/2950
#(for example, the Planck units). If you want to have units,
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2072/2950
#use SI. The cgs, emu, esu systems are a silly halfassed attempt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2073/2950
#to have it both ways and get rid of some units and keep others.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2074/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2075/2950
# The present file features conversion factors to random non-SI
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2076/2950
#units like foot, horsepower, pound, ounce. The entire group
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2077/2950
#of units is known to it, so all quantities are dimensioned
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2078/2950
#automatically. Meter, second, coulomb, kelvin, and kg are
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2079/2950
#my fundamental units. (Arguably kelvin is not needed.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2080/2950
#Also for radiation dose units, I use the "disintegration", e.g.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2081/2950
#disintegration/second.)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2082/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2083/2950
# I have so far been unable to stomach the "candela".
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2084/2950
#The old definition was...
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2085/2950
#candle = 1/60 the luminous intensity of 1 cm^2 of a Blackbody atthe
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2086/2950
#melting Temperature of platinum (2042.15 kelvin) = 1.6437 *watt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2087/2950
#= meter^2 / 600000 * sigmasb * platinummelttemp^4;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2088/2950
#a candela is the light intensity from a candle (now redefined
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2089/2950
#as "1/683 watt per steradian" of 555nm wavelength light (which theeye
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2090/2950
#is maximally sensitive to).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2091/2950
#Note, this seems to be a lot smaller than the old defn.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2092/2950
#Huh? Then lumen = candela*steradian = 1/683 *watt;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2093/2950
#lux = lumen/meter^2 = 1/683 *watt/meter^2; candlepower = candela.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2094/2950
#Yuk!
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2095/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2096/2950
#I also hate the "radian" and "steradian"; they should be
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2097/2950
#dimensionless, in my view.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2098/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2099/2950
# Finally, decibels and bels are another abomination.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2100/2950
# decibels = 10*bels = 10*log10(Intensity/ReferenceIntensity);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2101/2950
#and for use in auditory work, one uses
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2102/2950
#ReferenceIntensity = 1 phon = 10^(-16) *watt/cm^2/sec at 1000*hertz.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2103/2950
#Idiotic - haven't these guys heard of scientific notation to dealwith
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2104/2950
#logarithms?
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2105/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2106/2950
# This MAPLE code does not know about precision (usually the
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2107/2950
#last 2 digits of our numbers are imprecise). My values
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2108/2950
#are CODATA values plus miscellaneous sources like
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2109/2950
#CRC handbook. If you really care about errors you have to know
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2110/2950
#about the correlations among the errors in the
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2111/2950
#fundamental constants (many errors are highly correlated)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2112/2950
#and that would require a lot of extra software, which I
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2113/2950
#didn't feel like trying to write.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2114/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2115/2950
#Update 1999:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2116/2950
#PJ Mohr BN Taylor
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2117/2950
#CODATA recommended values of the fundamental physical constants 1998
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2118/2950
#J Phys Chem Ref Data 28 (1999)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2119/2950
#finally came out
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2120/2950
#http://physics.nist.gov/cgi-bin/cuu/
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2121/2950
# http://physics.nist.gov/PhysRefData/contents.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2122/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2123/2950
#The 1998 CODATA
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2124/2950
#Recommended Values of the Fundamental Physical
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2125/2950
#Constants, Web Version 3.0," available at
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2126/2950
#http://physics.nist.gov/constants (National Institute of
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2127/2950
#Standards and Technology, Gaithersburg, MD 20899,
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2128/2950
#release date 23 July 1999).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2129/2950
#http://physics.nist.gov/cuu/Constants/index.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2130/2950
#http://physics.nist.gov/constants
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2131/2950
#http://www.codata.org/
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2132/2950
#http://pdg.lbl.gov/1998/astrorpp.ps
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2133/2950
#these sites very recommended - can now download any correlationcoeff too
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2134/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2135/2950
#A detailed description of the data and its analysis that led tothese
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2136/2950
#values will be published by early 2000 in the Journal of Physical
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2137/2950
#and Chemical Reference Data.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2138/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2139/2950
#"Review of particle properties", Phys Rev D50 (1994) 1-.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2140/2950
#PRD 54 (July 1996) 1-720.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2141/2950
#C.Caso et al.: Review of particle physics, Europ. Phys. J. C3 (1998)1-.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2142/2950
#http://pdg.lbl.gov
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2143/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2144/2950
#---------units (and data):---------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2145/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2146/2950
#prefixes:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2147/2950
zepto := 10^(-21);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2148/2950
atto := 10^(-18);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2149/2950
femto := 10^(-15);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2150/2950
pico := 10^(-12);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2151/2950
nano := 10^(-9);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2152/2950
micro := 10^(-6);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2153/2950
milli := 10^(-3);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2154/2950
centi := 10^(-2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2155/2950
kilo := 10^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2156/2950
mega := 10^6;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2157/2950
giga := 10^9;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2158/2950
tera := 10^12;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2159/2950
peta := 10^15;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2160/2950
exa := 10^18;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2161/2950
zetta := 10^21;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2162/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2163/2950
joule := meter^2 * kg / second^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2164/2950
watt := joule/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2165/2950
mole := 6.02214199 * 10^(23); #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2166/2950
ampere := coulomb/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2167/2950
hertz := 1/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2168/2950
newton := meter*kg/second^2; #force
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2169/2950
pascal := newton/meter^2; #pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2170/2950
poise := pascal*second; #absolute viscosity
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2171/2950
stokes := meter^2 /second; #kinematic viscosity
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2172/2950
volt := watt/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2173/2950
farad := coulomb/volt;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2174/2950
ohm := volt/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2175/2950
mho := 1/ohm;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2176/2950
siemens := 1/ohm;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2177/2950
weber := volt*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2178/2950
tesla := weber/meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2179/2950
henry := weber/ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2180/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2181/2950
sipole := meter*coulomb/second; #my own unit of magentic monopolecharge
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2182/2950
#One SIpole is the amount of magnetic charge that would
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2183/2950
#experience a force of 1 Newton if placed in a 1 Tesla magnetic
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2184/2950
#field.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2185/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2186/2950
becquerel := disintegration/second; #radioactivity unit
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2187/2950
gray := joule/kg; #for measuring absorbed radiation dose
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2188/2950
#a sievert is the amount of radiation equivalent in health effect to1 gray
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2189/2950
#of some kind of standard type of radiation.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2190/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2191/2950
minute := 60*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2192/2950
hour := 60*minute;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2193/2950
solarday := 24*hour; #increases 1 millisecond/century
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2194/2950
starday := 86164.09 * second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2195/2950
year := 365.24219879 *solarday;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2196/2950
month := year/12;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2197/2950
century := 100*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2198/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2199/2950
denier := kg/meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2200/2950
dyne := 10^(-5) *newton;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2201/2950
erg := 10^(-7) *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2202/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2203/2950
gauss := 10^(-4) * tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2204/2950
maxwell := 10^(-8) *weber;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2205/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2206/2950
horsepower := 746 * watt; #several definitions exist 735 to 746watt.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2207/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2208/2950
jansky := 10^(-26) * watt * second / meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2209/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2210/2950
oersted := 7.957747 * ampere/meter; #says CRC handbook
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2211/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2212/2950
parsec := cot(1 * angularsecond) * astronomicalunit;#3.085678*10^(16) *meter; 3.26*lightyear
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2213/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2214/2950
lb := .45359237 *kg; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2215/2950
poundmass := lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2216/2950
ounce := lb/16;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2217/2950
shortton := 2000 *lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2218/2950
longton := 2240 *lb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2219/2950
grain := lb/7000;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2220/2950
slug := 14.59390 *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2221/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2222/2950
lbf := 4.4482216152605 * newton; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2223/2950
poundforce := lbf;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2224/2950
psi := lbf/inch^2; #6895*pascal
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2225/2950
torr := 133.322 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2226/2950
mmhg := torr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2227/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2228/2950
liter := 10^(-3) *meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2229/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2230/2950
sverdrup := 10^6 *meter^3/second; #volume flux. Used in oceanography.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2231/2950
kayser := 1/(centi*meter); #used in spectroscopy
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2232/2950
cc := (centi*meter)^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2233/2950
micron := 10^(-6) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2234/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2235/2950
metricton := 10^3 *kg; #also "tonne"
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2236/2950
#electron-volt
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2237/2950
ev := 1.602176462 * 10^(-19) *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2238/2950
km := 10^3 *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2239/2950
mm := 10^(-3) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2240/2950
cm := 10^(-2) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2241/2950
astronomicalunit := 149597900 *km: #earth-sun distance
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2242/2950
nauticalmile := 1852*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2243/2950
#nauticalmile := 6076.115486*foot:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2244/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2245/2950
angstrom := 10^(-10) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2246/2950
barn := 10^(-28) *meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2247/2950
fermi := 10^(-15) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2248/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2249/2950
bar := 10^(5) *pascal:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2250/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2251/2950
abampere := ampere/10;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2252/2950
abcoulomb := coulomb/10;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2253/2950
statampere := 3.335641 * 10^(-10) *ampere;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2254/2950
statcoulomb := 3.335641 * 10^(-10) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2255/2950
curie := 3.7*10^(10) *becquerel;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2256/2950
roentgen := 2.58 * 10^(-4) *coulomb/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2257/2950
rad := 10^(-2) *gray;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2258/2950
remunit := 10^(-2) *sievert;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2259/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2260/2950
pi := evalf(Pi);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2261/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2262/2950
radian := 1;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2263/2950
revolution := evalf(2*Pi*radian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2264/2950
angulardegree := evalf(Pi/180 *radian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2265/2950
angularminute := angulardegree/60;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2266/2950
angularsecond := angularminute/60;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2267/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2268/2950
fullsphere := evalf(4*Pi*steradian);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2269/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2270/2950
knot := nauticalmile/hour;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2271/2950
hectare := 10^4 *meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2272/2950
angstrom := 10^(-10)*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2273/2950
inch := 2.54 * 10^(-2)*meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2274/2950
foot := 12*inch;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2275/2950
yard := 3*foot;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2276/2950
printerpoint := 0.13837 *inch; #or is it inch/72? close
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2277/2950
mile := 5280*foot:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2278/2950
acre := mile^(2) /640; #acre := 43560 *foot^2
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2279/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2280/2950
usgallon := 231 * inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2281/2950
brgallon := 277.420 *inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2282/2950
quart := usgallon/4;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2283/2950
pint := quart/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2284/2950
cup := pint/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2285/2950
gill := cup/2; #british cups, pints, gills are each a bit bigger
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2286/2950
fluidounce := cup/8;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2287/2950
tablespoon := fluidounce/2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2288/2950
teaspoon := tablespoon/3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2289/2950
boardfoot := 144 *inch^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2290/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2291/2950
gram := 10^(-3) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2292/2950
carat := .2 *gram;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2293/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2294/2950
btu := 1.055056 * 10^(3) * joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2295/2950
ustherm := 1.054804 * 10^(8) *joule; #used by US natural gasindustry
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2296/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2297/2950
watertripletemp := 273.16 *kelvin; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2298/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2299/2950
watertriplepressure := 611.73 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2300/2950
platinummelttemp := (1769.0+273.15) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2301/2950
waterfreezetemp := 273.15 *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2302/2950
waterboiltemp := 373.15 *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2303/2950
#celsius := waterfreeze + kelvin. fahrenheit := celsius * (5/9) + 32;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2304/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2305/2950
caloriethermo := 4.184 *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2306/2950
calorieintl := 4.1868 *joule;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2307/2950
calorie := calorieintl;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2308/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2309/2950
#weapons kiloton is by convention 10^(12) calories.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2310/2950
kiloton := 10^(12) * calorie;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2311/2950
mageaton := 10^(3) * kiloton;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2312/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2313/2950
rankine := (5/9) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2314/2950
standardatmosphere := 101325 *pascal;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2315/2950
standardgravity := 9.80665 *meter/second^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2316/2950
vsoundair := 331.4 *meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2317/2950
specheatair := 1010 *joule/kg/kelvin: #at const pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2318/2950
densityair := 1.21 * kg/meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2319/2950
vsoundwater := 1496.7 *meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2320/2950
densitywater := 1000*kg/meter^3;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2321/2950
specheatwater := 4190 *joule/kg/kelvin; #at const pressure
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2322/2950
heatfusionwater := 333 * kilo*joule/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2323/2950
heatvapwater := 2260* kilo*joule/kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2324/2950
indexrefwater := 1.33; #at 589 nm
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2325/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2326/2950
resistivitysilver := 1.587 * 10^(-8) * ohm * meter; #at 293 Kelvin
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2327/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2328/2950
radgeosync := 42200 * kilo * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2329/2950
vescapeearth := 11200 * meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2330/2950
muearth := 8.0*10^(22) *joule/tesla; #magnetic dipole moment
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2331/2950
efieldearth := 150 * volt/meter; #down. At earth's surface. mean.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2332/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2333/2950
suntemp := 5780*kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2334/2950
sunluminosity := 3.846 * 10^(26) * joule/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2335/2950
solarconst := evalf(sunluminosity / (4*Pi*astronomicalunit^2));#varies 2%
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2336/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2337/2950
mmilkyway := 2.2*10^(41) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2338/2950
moceans := 1.4 *10^(21) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2339/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2340/2950
velocorbitalgalaxy := 220 * km/second; #of solar system round milkyway galaxy
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2341/2950
velocwrtcosmicbackground := 369.3 * km/second; #+-2.5
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2342/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2343/2950
disttocenterofmilkyway := 8.0 * mega * parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2344/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2345/2950
distproximacentauri := 4.22 * c*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2346/2950
#**Alpha Centauri system:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2347/2950
#Separation between Alpha Centauri A and B varies from 11 to 35 AU;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2348/2950
#they take 80 years to orbit around each other.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2349/2950
#Proxima Centauri is currently 13,000 AUs from A and B; no orbital
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2350/2950
#parameters of it are known.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2351/2950
# A B proxima sun
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2352/2950
# 5800K 5300K 2700K 5800K
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2353/2950
# 4.35 4.35 4.22 0 lightyears away
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2354/2950
# Yellow Orange Red Yellow
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2355/2950
distandromedagalaxy := 2*10^(22) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2356/2950
distlargemagellaniccloud := 55*kilo*parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2357/2950
distvirgocluster := 20*mega*parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2358/2950
disttouniverseedge := 10^(26) * meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2359/2950
distearthmoon := 384404 *km; #+3 cm per year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2360/2950
periodmoon := 27 *solarday: #??? +2 milliseconds/century
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2361/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2362/2950
distsunmercury := .38 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2363/2950
distsunvenus := .72 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2364/2950
distsunearth := 1.0 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2365/2950
distsunmars := 1.52 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2366/2950
distsunjupiter := 5.20 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2367/2950
distsunsaturn := 9.5 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2368/2950
distsunuranus := 19.2 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2369/2950
distsunneptune := 30.0 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2370/2950
distsunpluto := 39.5 * astronomicalunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2371/2950
#pluto has 1 satellite "charon" with about .1 its mass;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2372/2950
#it has day 6.38 earth days.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2373/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2374/2950
#radiusearth := 6371.006 *km:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2375/2950
radiusearth := 6378.140 *km:#equatorial
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2376/2950
radiusmoon := 1738 *km;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2377/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2378/2950
radiusmercury := .38 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2379/2950
radiusvenus := .96 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2380/2950
radiusmars := .53 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2381/2950
radiusjupiter := 10.8 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2382/2950
radiussaturn := 9.0 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2383/2950
radiusuranus := 4.1 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2384/2950
radiusneptune := 3.85 * radiusearth;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2385/2950
radiuspluto := 1137 *km: #+-8
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2386/2950
radiussun := 695990 *km: #equatorial
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2387/2950
radiussunschwarzschild := 2.95325008 * km;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2388/2950
radiusmilkyway := 15 * kilo *parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2389/2950
thicknessmilkyway := 1 * kilo *parsec;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2390/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2391/2950
mmercury := .33022 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2392/2950
mvenus := 4.8690 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2393/2950
mearth := 5.97370 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2394/2950
mmoon := .073483 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2395/2950
mmars := .64191 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2396/2950
mjupiter := 1898.8 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2397/2950
msaturn := 568.50 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2398/2950
muranus := 86.625 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2399/2950
mneptune := 102.78 * 10^(24) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2400/2950
mpluto := 1.27 * 10^(22) * kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2401/2950
msun := 1.98892 * 10^(30) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2402/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2403/2950
hubnum := .5: #could be anywhere .2 to 1.0
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2404/2950
hubbleconst := 70*hubnum*km/second/(mega*parsec);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2405/2950
#http://ucsu.colorado.edu/~lisle/main.html
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2406/2950
#``The cosmological implications of Hipparcus''
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2407/2950
#direct trig parallax distance measurement to nearby Cepheids with
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2408/2950
#Hipparcus satellite. Leads to 10% revision of Hubble constant, now
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2409/2950
#about 60 km/s/Mpc.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2410/2950
#another place claims 60-80 is the range; I'm going with it.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2411/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2412/2950
criticaldensity := 3*hubbleconst^2/(8*pi*G); #needed to close theuniverse
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2413/2950
#matter density is supposed to be .2 to 1.0 times this
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2414/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2415/2950
entropydensityofuniverse := 2899.3 * (2.853/2.728)^3 * kb / cc;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2416/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2417/2950
tempuniversebackground := 2.853 * kelvin; #plus or minus .002
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2418/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2419/2950
lightyear := c*year;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2420/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2421/2950
#various rough estimates of universe-quantities on Misner-Thorne- Wheeler p738:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2422/2950
#max radius 19*10^9 lightyear
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2423/2950
#time start to max 3*10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2424/2950
#time bang to crunch 6*10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2425/2950
#age now 10^10 year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2426/2950
#radius now 13*10^9 lightyear note: larger than age
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2427/2950
#volume now 3.83*10^79 meter^3
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2428/2950
#density at maximum 5*10^(-30) * gram/cc
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2429/2950
#rate of increase of radius now .66 lightyear/year
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2430/2950
#amount of matter 5.68*10^(53) kg
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2431/2950
#baryon number 3.39*10^(80)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2432/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2433/2950
#MTW 29.6p796
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2434/2950
#density of universe now is <10^(-28) g/cc and >2*10^(-31) g/cc
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2435/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2436/2950
#MTW when universe about 10^5 years old, density was 10^(-20) g/ccand temp 3000K
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2437/2950
#and then:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2438/2950
#1. radiation ceased to domaine, now matter
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2439/2950
#2. universe became transparent
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2440/2950
#3. hydrogen atoms began to form (no longer ionized perpetually)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2441/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2442/2950
#------------------fundamental constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2443/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2444/2950
#these constants suffice to define the planck units:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2445/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2446/2950
#speed of light in vacuum exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2447/2950
c := 299792458 * meter/second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2448/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2449/2950
#boltzmann constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2450/2950
kb := 1.3806503 * 10^(-23) *joule/kelvin; #1700 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2451/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2452/2950
#permittivity & permeability of vacuum
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2453/2950
mu0 := evalf(4*Pi*1.0 * 10^(-7)) *henry/meter; #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2454/2950
eps0 := 1/(c^2 * mu0); #exact
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2455/2950
#eps0 := 8.854187817 * 10^(-12) *farad/meter
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2456/2950
#mu0*eps0*c^2=1
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2457/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2458/2950
#newton gravitational constant (force = G*m1*m2/r^2)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2459/2950
G := 6.673 * 10^(-11) *newton*meter^2/kg^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2460/2950
#+- .010; huge relative uncert .0015
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2461/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2462/2950
#coulomb law constant (force = coulombconst * q1*q2/r^2)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2463/2950
coulombconst := 1/ (4 * pi *eps0);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2464/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2465/2950
#planck's constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2466/2950
h := 6.62606876 * 10^(-34) *joule*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2467/2950
hbar := 1.054571596 * 10^(-34) *joule*second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2468/2950
#hbar = evalf(h/(2*Pi)):
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2469/2950
#78 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2470/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2471/2950
#------------planck length, mass, time, charge:--------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2472/2950
#These are the fundamental units of
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2473/2950
#length, mass, time, charge, temperature
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2474/2950
#in a unit system where c=G=hbar=kb=1 and
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2475/2950
#where coulombconst*qplanck^2 = G*mplanck^2.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2476/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2477/2950
lplanck := sqrt(hbar*G/c^3);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2478/2950
mplanck := sqrt(hbar*c/G);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2479/2950
tplanck := sqrt(hbar*G/c^5);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2480/2950
qplanck := evalf(sqrt(4*Pi*hbar*c*eps0));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2481/2950
#qplanck / qe = 1/sqrt(alpha), reciprocal sqrt of fine structureconstant!
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2482/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2483/2950
tempplanck := (mplanck*c^2)/kb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2484/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2485/2950
# lplanck := 1.616048609*10^(-35) *meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2486/2950
# tplanck := 5.390557920*10^(-44) *second;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2487/2950
# mplanck := 2.176714074*10^(-8) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2488/2950
# qplanck := 1.875546788*10^(-18) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2489/2950
# tempplanck := 1.416957021*10^(32) *kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2490/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2491/2950
# qplanck = 11.7062 charge quanta = sqrt(137).
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2492/2950
# mplanck = 2.389527889 * 10^(22) electron masses.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2493/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2494/2950
#------other fundamental constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2495/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2496/2950
#charge of proton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2497/2950
qe := 1.602176462 * 10^(-19) *coulomb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2498/2950
#39 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2499/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2500/2950
#atomic mass unit
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2501/2950
amu := 10^(-3) * kg/mole;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2502/2950
#amu := 1.66053873*10^(-27) *kg: #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2503/2950
#mole is number of carbon-12 atoms in 12 grams, amu is
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2504/2950
#1/12 mass of a carbon-12 atom.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2505/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2506/2950
#rest mass of electron, proton, neutron, muon, deuteron, alpha particle
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2507/2950
#me := 9.10938188 * 10^(-31) *kg: #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2508/2950
me := 5.48579903 * 10^(-4) * amu; # +- .00000013
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2509/2950
me := .510998902 * mega * ev/c^2; #40 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2510/2950
#failed excited lepton searches: e >86 GeV, muon >=86 GeV, tau>72 GeV
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2511/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2512/2950
mp := 1.67262158* 10^(-27) *kg; #79 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2513/2950
mp := 938.271998 * mega * ev / c^2; #40 ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2514/2950
mp := 1.00727646688 * amu; # .13ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2515/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2516/2950
mpbyme := 1836.1526675; #2.1ppb uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2517/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2518/2950
#mn := 1.6749286 * 10^(-27) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2519/2950
mn := 1.008664904 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2520/2950
# +-.000000014
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2521/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2522/2950
#mmu := 1.8835327*10^(-28) *kg:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2523/2950
mmu := .113428913 * amu: # +- .000000017
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2524/2950
mmu := 105.658389 * mega * ev/c^2; #+-.000034 (1998 value)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2525/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2526/2950
mdeuteron := 3.3435860 * 10^(-27) *kg;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2527/2950
mdeuteron := 1875.612762 * mega * ev/c^2; #40 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2528/2950
mtriton := 3.015500 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2529/2950
m3he := 3.014932 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2530/2950
malpha := me / (1.37093354 * 10^(-4));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2531/2950
#malpha := 4.001505 * amu;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2532/2950
mpi := 135.0 * mega*ev/c^2; #mass of pi
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2533/2950
mpi0 := 139.6 * mega*ev/c^2; #mass of pi_0^{+-}
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2534/2950
mtau := 1777.05 * mega * ev / c^2; #+.29, -.26 (1998 value)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2535/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2536/2950
#heavy lepton searches supposedly go up to 81.5GeV now with 95% conf
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2537/2950
#nothing charged there. Ackerstaff Euro Phys J C1 (1998) 45
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2538/2950
#also 95% conf nothing uncharged below 69GeV
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2539/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2540/2950
mquarku := 3.25 * mega * ev/c^2; #charge +2/3 (1.5 to 5)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2541/2950
mquarkd := 6 * mega * ev/c^2; #charge -1/3 #??? wrong way ??? (3to 9)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2542/2950
mquarks := 115 * mega * ev/c^2; #charge -1/3 (60 to 170)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2543/2950
mquarkc := 1.25 * giga * ev/c^2; #charge +2/3 (1.25 +-.15)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2544/2950
mquarkb := 4.25 * giga * ev/c^2; #charge -1/3 (4.25 +- .15)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2545/2950
mquarkt := 174.3 * giga * ev/c^2; #charge +2/3. 174.3+-5.1
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2546/2950
#all quarks spin 1/2, baryon # 1/3, RGB or anti-RGB color.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2547/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2548/2950
mw := 80.41 * giga * ev/c^2; #+-.4 Gev. Charge +-1. Spin 1. W boson.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2549/2950
mz := 91.187 * giga * ev/c^2; #+-.031 Gev. Charge 0. Spin 1. Z boson.
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2550/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2551/2950
#particle mean lifetimes
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2552/2950
meanlifemu := 2.19703 * micro * second;#uncert .00004
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2553/2950
meanlifetau := .2900 * pico * second; #+-.0012
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2554/2950
meanlifen := 888.6 * second; #+- 3.5 second
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2555/2950
#meanlifep > 10^31 years for some investigated modes
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2556/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2557/2950
#Bohr magneton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2558/2950
bohrmag := qe*hbar/(2*me);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2559/2950
#bohrmag = mue/1.001159652:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2560/2950
#bohrmag := 9.2740154 * 10^(-24) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2561/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2562/2950
#Nuclear magneton
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2563/2950
nucmag := qe*hbar/(2*mp);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2564/2950
#nucmag := 5.0507866*10^(-27) * joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2565/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2566/2950
#magnetic moment of electron, proton, neutron, muon, deuteron
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2567/2950
#mue := 9.2847701 * 10^(-24) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2568/2950
#mue := 1.001159652193 * bohrmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2569/2950
# +- .000000000010
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2570/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2571/2950
#mup := 1.41060761 * 10^(-26) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2572/2950
mup := 2.792847386 * nucmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2573/2950
# +- .000000063
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2574/2950
;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2575/2950
#mun := 9.6623707 * 10^(-27) *joule/tesla:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2576/2950
mun := 1.91304275 * nucmag; #has negative sign, incidentally
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2577/2950
# +-.00000045
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2578/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2579/2950
mumu := 4.4904514 * 10^(-26) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2580/2950
mudeuteron := 4.3307375 * 10^(-27) *joule/tesla;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2581/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2582/2950
#------------"atomic units":--------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2583/2950
#mass me
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2584/2950
#charge qe
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2585/2950
#action hbar
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2586/2950
#length rbohr
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2587/2950
#energy hartree
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2588/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2589/2950
#Bohr radius (estimate, for hydrogen atom)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2590/2950
rbohr := evalf(4*Pi*eps0*hbar^2/(me*qe^2));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2591/2950
#rbohr := 5.29177208 * 10^(-11) *meter: #3.7ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2592/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2593/2950
#hartree energy unit, about 27 ev
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2594/2950
#hartree := 2*rydberg*h*c := 4.3598 * 10^(-18) *joule:
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2595/2950
hartree := hbar^2 / (me*rbohr^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2596/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2597/2950
atomictimeunit := hbar / hartree;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2598/2950
atomicvelocityunit := rbohr / atomictimeunit; #about c/137
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2599/2950
atomicforceunit := hartree / rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2600/2950
atomicmomentumunit := hbar / rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2601/2950
atomiccurrentunit := qe / atomictimeunit;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2602/2950
atomicefieldunit := hartree/(qe*rbohr);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2603/2950
atomicpotentialunit := hartree/qe;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2604/2950
atomicedipoleunit := qe*rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2605/2950
atomicmagfieldunit := hbar / (qe*rbohr^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2606/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2607/2950
atomicmagdipoleunit := 2*bohrmag;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2608/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2609/2950
#------derived constants:-----------------
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2610/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2611/2950
#magnetic flux quantum
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2612/2950
phi0 := h/(2*qe);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2613/2950
#phi0 := 2.06783461 * 10^(-15) *weber
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2614/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2615/2950
#alpha = fine structure constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2616/2950
#alpha := 1/137.0359895;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2617/2950
alpha := evalf(qe^2 / (4*Pi*eps0*hbar*c));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2618/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2619/2950
#stefan-boltzmann constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2620/2950
sigmasb := evalf(Pi^2*kb^4/(60*hbar^3*c^2));
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2621/2950
#sigmasb := 5.670400*10^(-8) *watt/meter^2/kelvin^4; #7000 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2622/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2623/2950
#first radiation constant
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2624/2950
c1radiation := evalf(2*Pi*h*c^2);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2625/2950
#c1radiation := 3.7417749 * 10^(-16) watt/meter^2;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2626/2950
c2radiation := h*c/kb;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2627/2950
#c2radiation := 0.01438769 *meter*kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2628/2950
#The max intensity lambda in blackbody radiation is
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2629/2950
#wienconst*T*cm/kelvin, where
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2630/2950
wienconst := c2radiation / 4.965114231;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2631/2950
#wienconst := 0.2897756 *cm/kelvin;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2632/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2633/2950
#rydberg (approx hydrogen waves per meter, infinite mass nuc)
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2634/2950
rydberg := me*c*alpha^2/(2*h);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2635/2950
#rydberg := 10973731.56834(24) /meter;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2636/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2637/2950
#classical electron radius
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2638/2950
#re := 2.817940285 * 10^(-15) *meter; #11 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2639/2950
re := alpha^2 * rbohr;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2640/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2641/2950
#compton wavelengths of electron, proton, neutron, muon
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2642/2950
e_compton := h/(me*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2643/2950
p_compton := h/(mp*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2644/2950
n_compton := h/(mn*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2645/2950
mu_compton := h/(mmu*c);
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2646/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2647/2950
fermicouplingconst := 1.16639 * 10^(-5) / (giga * ev)^2; #9000 ppb
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2648/2950
sinsquaredweakmixingangle := 0.23124; #.001 relative uncert
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2649/2950
#codata says .2235 +- .0023
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2650/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2651/2950
strongcouplingconst := .119;
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2652/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2653/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2654/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2655/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2656/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2657/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2658/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2659/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2660/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2661/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2662/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2663/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2664/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2665/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2666/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2667/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2668/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2669/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2670/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2671/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2672/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2673/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2674/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2675/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2676/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2677/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2678/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2679/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2680/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2681/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2682/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2683/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2684/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2685/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2686/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2687/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2688/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2689/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2690/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2691/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2692/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2693/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2694/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2695/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2696/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2697/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2698/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2699/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2700/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2701/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2702/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2703/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2704/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2705/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2706/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2707/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2708/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2709/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2710/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2711/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2712/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2713/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2714/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2715/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2716/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2717/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2718/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2719/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2720/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2721/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2722/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2723/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2724/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2725/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2726/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2727/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2728/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2729/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2730/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2731/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2732/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2733/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2734/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2735/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2736/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2737/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2738/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2739/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2740/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2741/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2742/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2743/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2744/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2745/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2746/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2747/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2748/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2749/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2750/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2751/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2752/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2753/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2754/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2755/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2756/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2757/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2758/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2759/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2760/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2761/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2762/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2763/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2764/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2765/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2766/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2767/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2768/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2769/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2770/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2771/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2772/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2773/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2774/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2775/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2776/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2777/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2778/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2779/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2780/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2781/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2782/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2783/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2784/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2785/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2786/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2787/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2788/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2789/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2790/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2791/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2792/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2793/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2794/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2795/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2796/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2797/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2798/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2799/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2800/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2801/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2802/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2803/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2804/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2805/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2806/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2807/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2808/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2809/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2810/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2811/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2812/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2813/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2814/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2815/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2816/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2817/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2818/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2819/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2820/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2821/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2822/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2823/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2824/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2825/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2826/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2827/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2828/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2829/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2830/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2831/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2832/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2833/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2834/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2835/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2836/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2837/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2838/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2839/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2840/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2841/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2842/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2843/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2844/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2845/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2846/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2847/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2848/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2849/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2850/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2851/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2852/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2853/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2854/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2855/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2856/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2857/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2858/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2859/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2860/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2861/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2862/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2863/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2864/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2865/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2866/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2867/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2868/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2869/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2870/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2871/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2872/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2873/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2874/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2875/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2876/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2877/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2878/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2879/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2880/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2881/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2882/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2883/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2884/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2885/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2886/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2887/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2888/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2889/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2890/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2891/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2892/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2893/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2894/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2895/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2896/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2897/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2898/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2899/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2900/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2901/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2902/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2903/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2904/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2905/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2906/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2907/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2908/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2909/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2910/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2911/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2912/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2913/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2914/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2915/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2916/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2917/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2918/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2919/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2920/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2921/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2922/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2923/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2924/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2925/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2926/2950
Error, invalid function arguments
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2927/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2928/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2929/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2930/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2931/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2932/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2933/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2934/2950
Ovde se vidi da i Maple moze da radi sa koeficijentima srazmernosti. Prema tpme Maple biva mocniji
od Mathcada
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2935/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2936/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2937/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2938/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2939/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2940/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2941/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2942/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2943/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2944/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2945/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2946/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2947/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2948/2950
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2949/2950
>
8/14/2019 Opsta teorija relativnostich18mws
http://slidepdf.com/reader/full/opsta-teorija-relativnostich18mws 2950/2950
>