A History of Universal GravitationA History of Universal Gravitation

Realize that by the time Newton was a young man,Realize that by the time Newton was a young man,•An understanding that the Earth did something to make An understanding that the Earth did something to make objects fall or heavy (Greek word: gravitas) is mentioned objects fall or heavy (Greek word: gravitas) is mentioned in recorded history as far back as the 5in recorded history as far back as the 5 ththC C •Galileo had given us, more than 50 years earlier, the Galileo had given us, more than 50 years earlier, the idea that, in the absence of air, all objects fall at the idea that, in the absence of air, all objects fall at the same rate. same rate. •It was well established that the moon circled the Earth It was well established that the moon circled the Earth at about 60 Earth radii away.at about 60 Earth radii away.•An “circling” required a force… but what was it??An “circling” required a force… but what was it??

A History of Universal GravitationA History of Universal Gravitation

In 1665, In 1665,

the Great Plague was sweeping through Europe the Great Plague was sweeping through Europe

Cambridge University closed for 2 yearsCambridge University closed for 2 years

Newton went home to mother’s farm, WoolsthorpeNewton went home to mother’s farm, Woolsthorpe

Contemplated the question:Contemplated the question:

““Is the moon circling the Earth Is the moon circling the Earth

connected to the apple fallingconnected to the apple falling

from the tree?”from the tree?”

Is the moon circling the Earth connected to the apple falling Is the moon circling the Earth connected to the apple falling from the tree?from the tree?

If yes, he considered the inverse square “dilution of gravity” idea

says if moon is 60x’s further away,

then it should be affected by 1/602 the amount of gravity.

Since an object on Earth will fall 4.9m (≈5m) in 1 sec, then the moon should fall 1/602 of 4.9m

or 1.4mm in 1 secor 1.4mm in 1 sec

He couldn’t quite prove it completely without a few more bits of understanding… like calculus…

But 20 years later, when friend Edmund Halley asked, he got it together and published it as…

Universal GravitationUniversal Gravitation

Newton’s Universal Law of Gravitation: Newton’s Universal Law of Gravitation:

every object pulls on every other object with a every object pulls on every other object with a force of gravity that is proportional to the masses force of gravity that is proportional to the masses involved and inversely proportional to the square involved and inversely proportional to the square of the distance between their centers.of the distance between their centers.

So 3 main points: So 3 main points: all things pull on all things!

FG α each m

FG α 1/r2

So FSo FGG αα 1/r 1/r2 2 is an example of an inverse square lawis an example of an inverse square law

ISLs very common relationship in science / lifeISLs very common relationship in science / life

as objects get farther apart (r bigger), as objects get farther apart (r bigger),

strength gets A LOT strength gets A LOT smallersmaller, by the , by the squaresquare of r. of r.• paint sprayer

• light from a light bulb • electric force around a point charge

Universal GravitationUniversal GravitationTry some examples of ISL:Try some examples of ISL:

FFGG αα 1/r 1/r22

And remember,And remember, as r gets bigger, as r gets bigger,

FFGG gets A LOT gets A LOT smallersmaller, by the , by the squaresquare of r. of r.

Ex If objects twice as far apart, then how did Ex If objects twice as far apart, then how did FFGG change? change?

1. If 2r, then ___ 1. If 2r, then ___ FFGG

2. If 4r, then ___ F2. If 4r, then ___ FGG

3. If ⅓r, then ___F3. If ⅓r, then ___FGG

4. If ⅝4. If ⅝ r, then ___Fr, then ___FGG

Universal GravitationUniversal Gravitation

So, again, there’s 2 main relationships in UG: So, again, there’s 2 main relationships in UG:

FFGG αα each m (the 2 masses pulling on each other) each m (the 2 masses pulling on each other)

FFGG αα 1/r 1/r22 (the distance between those masses) (the distance between those masses)

But what’s the equation for UG? But what’s the equation for UG?

11stst let’s put the relationships together in one proportion: let’s put the relationships together in one proportion:

FFGG αα m m11mm22/r/r22

22ndnd to turn a proportion into an equation, we need a to turn a proportion into an equation, we need a constant of proportionality…for universal gravitation, it’sconstant of proportionality…for universal gravitation, it’s

official name is the universal gravitation constant, also official name is the universal gravitation constant, also

fondly referred to as “big G” and it has a value of fondly referred to as “big G” and it has a value of

G = 6.67 x 10G = 6.67 x 10-11-11 Nm Nm22/kg/kg22

note that’s a really small number!!note that’s a really small number!!

Universal GravitationUniversal Gravitation

Henry Cavendish’s ApparatusHenry Cavendish’s Apparatus

1798 - over 100 years later 1798 - over 100 years later

Universal GravitationUniversal Gravitation

So the equation So the equation

for Newton’s Universal Law of Gravitation is: for Newton’s Universal Law of Gravitation is:

FFGG = = Gm Gm11mm22/r/r2 2 where where

• m1 is the bigger or main mass

• m2 is the other mass involved

• r is the distance between their centers• and G = 6.67 x 10-11 Nm2/kg2

Now let’s try some calculations…Now let’s try some calculations…

Estimate to one sig fig, the force of gravity Estimate to one sig fig, the force of gravity between you & your partner: between you & your partner:

Use FG = Gm1m2/r2

m1 = 70 kg (about ½ your pounds)

m2 = 60 kg

r = .7 m

G = 6.67 x 10-11 Nm2/kg2

so Fso FGG = = small digit x 10 small digit x 10-6-6 N or N or

big digit x 10big digit x 10-7-7 N N

Either way, a very small! Either way, a very small!

FFGG between everyday size objects is between everyday size objects is

really really small since the value of G is so small since the value of G is so small. small.

Estimate the force of gravity between you & the Earth:Estimate the force of gravity between you & the Earth:

mm11 is mass of Earth is mass of Earth

m2 = your mass

r is radius of Earth r is radius of Earth

FFGG = between 500 to 1000 N = between 500 to 1000 N

But what have you just found?? But what have you just found??

Calculate your weight using Calculate your weight using FFgg = mg = mg

How do they compare? How do they compare?

Now calculate just GmNow calculate just Gmearthearth/r/rearthearth2 2 = =

That should make sense! That should make sense!

FFgg = = FFG G on the surface of a planeton the surface of a planet

mmyouyoug = Gmg = Gm11mmyouyou/r/r2 2

So gSo gplanetplanet = Gm = Gmplanetplanet/r/rplanetplanet22

Estimate the force of gravity between Earth & the moon:Estimate the force of gravity between Earth & the moon:mm11 is mass of Earth is mass of Earth mm22 is mass of moon is mass of moonr is distance to moon (do we need rr is distance to moon (do we need ree & r & rmm in there?) in there?)FFGG = about 2 x 10 = about 2 x 102020 N N

Estimate the force of gravity between the sun & the Estimate the force of gravity between the sun & the moon:moon:mm11 is mass of sun is mass of sun mm22 is mass of moon is mass of moonr is distance to sun r is distance to sun FFGG = about 4 x 10 = about 4 x 102020 N N

Which one’s bigger? What does that mean? Which one’s bigger? What does that mean? The moon is not truly a moon, but a binary (dwarf) planet!The moon is not truly a moon, but a binary (dwarf) planet!

We follow an orbital path along our combined CM, We follow an orbital path along our combined CM, which is inside the Earth’s radius since the earth is which is inside the Earth’s radius since the earth is 100’s more massive than the moon.100’s more massive than the moon.

One more fascinating revelation:One more fascinating revelation:

The big problem with Newton’s Universal Law of The big problem with Newton’s Universal Law of Gravitation was that masses are applying forces Gravitation was that masses are applying forces without having to touch each other.without having to touch each other.

So the first answer was to come up with the idea of a So the first answer was to come up with the idea of a force field – the space about an object in which it force field – the space about an object in which it can apply a force without touchingcan apply a force without touching

But then Albert Einstein came up with a different But then Albert Einstein came up with a different explanation:explanation:

Gravity should not be considered a force, but Gravity should not be considered a force, but an an effect of space itself. effect of space itself.

Einstein said to think of mass as altering the Einstein said to think of mass as altering the space around it, causing it to be warped or curved.space around it, causing it to be warped or curved.

Then bodies wouldn’t move toward a planet Then bodies wouldn’t move toward a planet because a “mystical” force of gravity was pulling on because a “mystical” force of gravity was pulling on them, but instead because they were following the them, but instead because they were following the curvature of space near the massive object. curvature of space near the massive object.

That’s a lot to ponder! That’s a lot to ponder!

Unifying the Fundamental ForcesUnifying the Fundamental ForcesAlmost since the major forces were discovered, there’s been a Almost since the major forces were discovered, there’s been a drive by physicist (now mostly theoretical physicist) to reduce drive by physicist (now mostly theoretical physicist) to reduce them to the least number possible.them to the least number possible.

In the 19In the 19thth C, the electric & magnetic forces where believed to C, the electric & magnetic forces where believed to have completely separate causes.have completely separate causes.

But when E&M turned out to have exactly the same source, But when E&M turned out to have exactly the same source, they were combined – a they were combined – a hugehuge deal at the time! deal at the time!

So by the mid 20th C, there were 4 fundamental forces:So by the mid 20th C, there were 4 fundamental forces:

1) gravity 2) electromagnetic 3) strong nuclear 4) weak nuclear 1) gravity 2) electromagnetic 3) strong nuclear 4) weak nuclear

More recently, weak nuclear was combined with EM, which puts More recently, weak nuclear was combined with EM, which puts us at 3. us at 3.

There is a real drive to find the single unifying theory that would There is a real drive to find the single unifying theory that would show all forces are manifestations of a single cause – show all forces are manifestations of a single cause –

GUT: grand unified theories.GUT: grand unified theories.

The most prominent of these today is called String Theory…The most prominent of these today is called String Theory…

Kepler’s Laws of Planetary MotionKepler’s Laws of Planetary Motion

Johannes Kepler Johannes Kepler German Astronomer 1571-1630 50 years before Newton’s

work on UL of G Thru careful analysis of

experimental data Worked out detailed

descriptions of the motion of the planets around the sun

Kepler’s Laws of Planetary MotionKepler’s Laws of Planetary Motion11st st Law: the path of each planet about the Sun is an Law: the path of each planet about the Sun is an ellipse with the Sun at one focus ellipse with the Sun at one focus

Kepler’s Laws of Planetary MotionKepler’s Laws of Planetary Motion

22ndnd Law: each planet moves so that an imaginary line Law: each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal drawn from the Sun to the planet sweeps out equal areas in equal period of timeareas in equal period of time

Kepler’s Laws of Planetary MotionKepler’s Laws of Planetary Motion

33rdrd Law: The ratio of the squares of any two planets Law: The ratio of the squares of any two planets revolving about the Sun is equal to the ratio of the cubes revolving about the Sun is equal to the ratio of the cubes of their mean distances from the Sun of their mean distances from the Sun

mean distance refers to half the length of the major (as opposed to minor) axis of the ellipse

minor axis

major axismajor axis

point of point of point of apogeepoint of apogee

perigeeperigee

2 useful equations from Kepler’s 32 useful equations from Kepler’s 3rdrd Law Law

eq’n 1:eq’n 1: TT1122 r r11

33 __________________________ _________ _________

TT2222

r r2233

where the T’s and r’s are for any 2 objects orbiting the where the T’s and r’s are for any 2 objects orbiting the same object in approximately circular motion same object in approximately circular motion

eq’n 2:eq’n 2: r r33orbiting orbiting GmGmorbitedorbited

________________ ____________________________ ____________

TT22orbitingorbiting

44ππ2 2

where the right side of the eq’n is a constant for any where the right side of the eq’n is a constant for any object,object,

so if a suspected orbiting object’s rso if a suspected orbiting object’s r33/T/T2 2 ratio equals the ratio equals the orbited object’s K (Kepler) constant, it is indeed orbiting orbited object’s K (Kepler) constant, it is indeed orbiting that object. that object.

Kepler’s Constant for the EarthKepler’s Constant for the Earth

Discoveries made thanks to Kepler’s Laws…Discoveries made thanks to Kepler’s Laws…

•Newton used measured perturbations in Saturn’s orbit to Newton used measured perturbations in Saturn’s orbit to support his idea that all objects pull on all objects… support his idea that all objects pull on all objects…

aka N’s UL of G!

Together with his 3 laws of motion, it was clear that heavenly bodies followed the same laws as Earth bound objects – a big deal to make that connection…

referred to as “Newton’s synthesis”

These (types of) laws known as causal laws…

•Others used measured perturbations in Others used measured perturbations in

Uranus’ orbit to predict the existence of Neptune 1846

Neptune’s orbit to predict the existence of Pluto 1930

A star’s wobble to predict existence of orbiting planets - mid 1990’s