Problem A.l : Journey to Proxima Centauri (a Points)

The diameter of the Sun is 1.39 million kilometres and the Earth is 8.3 light minutes fur away.

Proxima Centauri is the nearest star - it has a dista nce of 4.24 light years to our Sun.

(a) How long does it take to travelto Proxima Centauriwith

(i) an airplane (920 km/h)or(ii) with the Voyoger I space probe (17 km/s).

(b) Let the Sun have the size of a tennis batt (diameter: 6.7 cm): How far away is the Earth and

how far away is Proxima Centauri on this scale?

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Problem A.2 z Orbit of the Solar System (4 Points)

The Milky Way has a diameter of about 15O,O0O light years. Our solar system is locate d 27,OOO

light years from the center of the Milky Way and orbits the center with a speed of 220 km/s.

(a) How long does it take for the solar system to circte the center of the Milky Way?

(b) The earth has formed about 4.5 biltion years ago. How often has the earth circled the center?

MilkLl

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=

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Problem A.3 : Distance to Arcturus (4 Points)

The stellar parallax of the starArcturus in the constellation Bocites was measures with 0.09'.

(a) Catcutate the distance (in parsec) between Arcturus and the Earth.

(b) How long does it take to send a light message from Earth to Arcturus?

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Problem A.4 : From Earth to Mars (a Points)

For a special mission to Mars you need to know the smallest distance between Earth and Mars.

However, you have lost your astronomy book and you could onty find these values:

Distance Earth to Sun: 149.6 mitlion km

Orbital period Earth: 1.00 years

Orbital period Mars: 1.88 years

By using these values and assuming that Mars and Earth move an circutar orbits, calculate the

smallest possible distance between Earth and Mars.

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Problem B.l : New Star (6 Points)

You have discovered a new star in the Mitky Way: Your new star is red and has 3/5 the temper:a-

ture of our Sun. The new star emits a total power that is 100,000 times greater than the power

emitted by our Sun.

(a) Determine the spectraltype (i.e. spectral ctassification) of the new star.

(b) How many times bigger is the radius of the new star compared to the radius of our Sun?

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Problem 8,2 z Moon Satellite (6 Points)

TheMoonhasamass olM :7.3-7022 kg,aradiusof .R : T.T.T06mandarotationperiodofT : 27.3 days. Scientists are ptanning to place a satellite around the Moon that always remains

above the same position (geostationary).

(a) Calculate the distance from the Moon's surface to this satetlite.

(b) Explain if such a Moon sateltite is possibte in reatity.

u

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T

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s\on \not lne sqttlllP't- \^rt\\

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-" | (-z,i-re,+:o)'(b,otxto-uI7.3 xtola kg.

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he$tnt' flo- fl = gb,ro?,,|Jl,bn l, ?oo)000/)

0.*+^q a sate\tite {or tha- noon ir

lossib\e b'V tt 'u\\ nDt

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Problem 8.3 : Binary Star System (6 Points)

You are the captain of a spaceship that is circling through a binary star system. Due to the gravi-

tational forces and the rocket engines, the orbit of your spaceship looks like that:

The position of your spaceship (in AU) at the time t (in days) is given by:

r:Ssin(t) a:sin(2t) z:0

(a) How long does it take your spaceship to circle the orbit once?

(b) Find an equation that calcutates the velocity u(t) of you.rpacethip at a given time t.(c) The two stars are positioned at the points (4, 0, 0) and (-4,0, 0): What is the distance of your

spaceship to the stars at the time t : t?

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sin

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Problem 8.4: Asteroid Collision (6 Points)

A warning system has calculated that two asteroids witl cotlide not far from Earth any time soon.

The smaller asteroid has the mass ?n and moves with the velocity u-. The bigger asteroid has the

mass M : 3rn and the vetocity of uy : iu*.They cottide at an angte of a : 60" and turn into a

single heavy asteroid (inelastic collision):

Ma

(a) Calculate the velocity of the single object after the collision.

(b) Determine the angle 0 after the collision.

1el :

3rn = Vl

t{*,' = *V*

D

v'Vt sin GO' :

\r\r m (ilr+vn) \i cos $[trr n -) ,/t s\n p

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Answer fottowing questions related to this article:

(a) Why is it difficulty for LyC rodiation to escape galaxies with high star formation rates?

l+ contqrnS larga orno&n+s.O| \neu+rul hydrog*lr nhrr-&r otaslnrArs

*he es.ape of LyA p6ldiahort'

(b) What is the difference between the density- bounded medium and the picket fence model?

gsveth fi;; rn€druwu arv i;rnouna€d 'Q iio+.opip ,qq'wrlh l,oal.colume densrly of

Mh?#trki*iil;trffi #lufllr#ffi ,*ffil:W*Wvs hr g'tli'#ilin

the spectratshape of the perforoted siell mode/ (se6 a#cle: figure 1, right box).' .€t*Pe'tn +his modej , LgoA.hnc shapa ilormv{c on'rts csntrql p*\( *nrf ,W*F.+{nt*9lur4caur,rsrl Sfrlhi\,n<s ) ,,..ffniol,r is suPenwposr) pnthB c,hanro|<rni{lr d'o*W'WWofrl-a {t^"+ "dnnrcr3ss fttd, aph calty *rrrat< gae'

(d) What is the SunburstArc and how was it discovered? ^ ,

l+soi,er,;J qa\axyttndt d1"-;*;;;,iA es'"p" $r Lyrn ancx pholons )roryn a

pe,nfol-41-ecr .il,sd.d'",rn, ll rios'rcpd€d Dy fuwta 0l.6l arrcl'tdas itbcorord _bYi la-a-1

frnarar-hprmogrrrg aF l}s lensrDl'chxt{$nwu,gb ifs eun/atn/ -7r)'dovr6t6 c'f{+d tn nTi|/{O,

(e)When did the scientist observe-[he object and which instruments did they use?

Ihe s.Jerrtsts abser\te[ *ns \prrse/ qalaXq On *he 24+h af May 2411 nslnq ttreM a gd\an E-chel dlet CVta3 e) sp*r;Ug F6'pA allaot,u 0h +fie Ma3 eltan -tYfltaadl+*escnpe,

(f) What is the redshift of the SunburstArc and how was it determined from the data?

Itrysc,ttirh;t's o\€,lorh.rn+-d *VrB redsUift af the Sr.rnDun* Fro bdtqd ar'*lr,fuid€/ -p*+ tn$rared p'neliLCnep) cpegfrwrn by fif+inq astnqte Gqustqnptofll.i {otnar,' oFtt'}n.S*^r *-y e{Yrrsslpp lrne l+Be+a c,nd HFlphor, "

Problem CJ l/.he Sunburst Arc (10 Points)

This problem requires you to read following recently pubtished scientific article:

The Sunburst Arc: Direct Lymon o escope obserued in the brightest known lensed golaxy,

T.E. Rivera-Thorsen, H. Dahle, M. Gronke, M. Bayliss, J.R. Rigby, R. Simcoe, R. Bordoloi, M. Turner, and G. Furesz,

Astronomy & Astrophysics 608, (20I7). 1-;nk: https://iaac.space/doc/Pre-Final-Article-20l7-sunburst-Arc.pdf

G) Exptain the difference between the right and the left diagram in figure 4 (see articte).

l{ shouts *heu c.onpnrmn }f+he shafe o$*he oe.nlnal qg1R _[et{.le/, l}hlpha onl

*t*.e^^p?*/*o drnoril*c 0[ iYf-] W1*,0* til* sgnifrcants avhountsaFrB-trhnz-l

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*han LyA.

Answer foltowing questions related to this article:

(a) What are the cunent methods to determine the dark matter density I radialvelocity and what

are the disadvantages of these methods? l+ is dVfennin*a f-..p 'lhv. Gglaalib folahoro 4flO,Mensursd*'lqlJ"egtr*.ff

a$,"ii:ilT,rilr"$Jffi lf#ffi Y*EJip?'r,nXYJffi ?",,direcJ.ror' otboutlrvrt{uodsa.e, not#;r;;iy ;s"a' i;th"+ uo+tr t,rse *heqsYumpiron at"enrrrltun"rn {rno+Jytruri".'in;v<]

ne""thed s*eodY lsto#e "(b) Explain the new method. for measuring dark matter density that is proposed in the article.

thw u."d {fu*"rng preoston nadial ,/docl*.ty rleaqlre.f^"ftttpi tl.ru rc"=te.natrr.n a[ rrrtiv'idual

S"Urury* -ffi ft {'. Wm ?'fl'#,frIff*J lW ls?ll#ffi F, fiff {,["

aalo,firg?iiii:ffi?l,ntlY$Jr contribution to rhe accereration: show that the dark matrer den-

Problem C.2 z Dark Matter (10 Points)

This problem requires you to read following recently published scientific article:

Probing Dark Matter Using Precision Meosurements ofStellar Accelerations.A. Ravi, N. Langellier, D.F. Phillips, M. Buschmann, B.R. Safdi, R.L. Walsworth,

arXiv:1812.07578, (2018). Link: https://iaac.space/doc/Pre-Final-Article-2018-1812.07578.pdf

sity is given by pnm x

(d) How much does the vetocity of the stars change during the lifetime of a human (80 years)?

40 LnA

. (e) What is important for measuring stellar acceferations and which instrumentS tan be used?

\ts r*pjrt"nl +o rnbqs,rrs st€lb,l^ ,;rLAi"+rii-Vet",^.g if ^,titrtlp;r;.,ltnn,^e

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(f) Explain the curves of the four diagrams in figure 2 (see article). . r

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