Universal Universal GravitationGravitation

Wait a minute, Doc, are you trying to tell me that my Wait a minute, Doc, are you trying to tell me that my mother has got the hots for me?mother has got the hots for me?

Precisely.Precisely.

Whoa, this is heavy.Whoa, this is heavy.

There's that word again; "heavy". Why are There's that word again; "heavy". Why are things so heavy in the future? Is there a things so heavy in the future? Is there a problem with the earth's gravitational pull?problem with the earth's gravitational pull?

TopicsTopics

IntroductionIntroduction Kepler’s LawsKepler’s Laws Universal GravitationUniversal Gravitation Planetary and Satellite MotionPlanetary and Satellite Motion Different Views: Newton v. EinsteinDifferent Views: Newton v. Einstein

A little history…A little history…

Ancient GreeceAncient Greece Things rose or fell according to what they Things rose or fell according to what they

werewere Smoke risesSmoke rises Objects fallObjects fall

Gave birth to the termsGave birth to the terms Levity Levity (lightweight)(lightweight) Gravity Gravity (heavy)(heavy)

StargazingStargazing

Always the popular past time, early humans Always the popular past time, early humans noticed that celestial bodies moved in regular noticed that celestial bodies moved in regular patternspatterns Planet = “wanderer”Planet = “wanderer”

Tycho Brahe (1546-1601)Tycho Brahe (1546-1601) ExtremelyExtremely detailed measurements of planetary detailed measurements of planetary

motionmotion Built first observatory (an entire island! Built first observatory (an entire island! ~Hven)~Hven) Had precise instruments constructedHad precise instruments constructed

Johannes KeplerJohannes Kepler

One of Brahe’s assistants and a brilliant One of Brahe’s assistants and a brilliant mathematicianmathematician

Used Used heliocentric heliocentric (sun-centered) model and (sun-centered) model and Brahe’s measurements to discover basic Brahe’s measurements to discover basic descriptions for the behavior of every planet descriptions for the behavior of every planet and satellite (moons, comets, etc.)and satellite (moons, comets, etc.) ““fatal” blow to church-enforced geocentric fatal” blow to church-enforced geocentric

descriptiondescription Verified Copernicus’ ideasVerified Copernicus’ ideas

Those 3 descriptions are now known as…Those 3 descriptions are now known as…

Kepler’s Laws of Kepler’s Laws of Planetary MotionPlanetary Motion First LawFirst Law

The paths of the planets are The paths of the planets are ellipsesellipses, with the sun at , with the sun at one focus.one focus.

Kepler’s Laws of Kepler’s Laws of Planetary MotionPlanetary Motion

12

2

2

2

b

y

a

x

Kepler’s Laws of Kepler’s Laws of Planetary MotionPlanetary Motion

Second LawSecond Law An imaginary line from the sun to a planet An imaginary line from the sun to a planet

sweeps out equal areas in equal time sweeps out equal areas in equal time intervals.intervals.

Kepler’s Laws of Kepler’s Laws of Planetary MotionPlanetary Motion Third LawThird Law

The square of the ratio of the periods of any two The square of the ratio of the periods of any two planets revolving about the sun is equal to the cube of planets revolving about the sun is equal to the cube of the ratio of their average distances from the sunthe ratio of their average distances from the sun

32

B

A

B

A

r

r

T

T

T = Period

r = average distance from the sun

Kepler’s Laws of Kepler’s Laws of Planetary MotionPlanetary Motion

Notice that the first two laws pertain to Notice that the first two laws pertain to individualindividual planets or satellites planets or satellites

The third law relates the motion of The third law relates the motion of differentdifferent planets or satellites! planets or satellites!

The falling appleThe falling apple

About 45 years after KeplerAbout 45 years after Kepler Isaac Newton saw an apple fall, and also Isaac Newton saw an apple fall, and also

observed the moon in the daytime skyobserved the moon in the daytime sky What’s keeping the moon from flying off into What’s keeping the moon from flying off into

space?space? Force that makes the apple fall must be Force that makes the apple fall must be

causing the moon to continually “fall” toward causing the moon to continually “fall” toward EarthEarth

Universal GravitationUniversal Gravitation

If the planets travel in ellipses, then the If the planets travel in ellipses, then the distance between the planets and the sun distance between the planets and the sun changes. changes.

If this distance changes, then the amount If this distance changes, then the amount

of force on the planet from the sun must of force on the planet from the sun must changechange

A universal forceA universal force

He named this force He named this force gravitygravity, and he said , and he said it existed between it existed between every single objectevery single object! !

The amount of force depends on:The amount of force depends on: How massive the objects areHow massive the objects are

More mass = more forceMore mass = more force

The distance between the objectsThe distance between the objects Closer together = more forceCloser together = more force

Inverse Square LawInverse Square Law

Inverse relationship Inverse relationship between gravitational between gravitational force and the force and the square square ofof the distance the distance between two objectsbetween two objects

The sign means The sign means “proportional to”“proportional to”

2

1

dF

Law of Universal Law of Universal GravitationGravitation

mm11 and m and m2 2 = masses of two objects= masses of two objects

d = distance between objects’ d = distance between objects’ centers of centers of massmass

G = gravitational constant G = gravitational constant 6.7 x 10 6.7 x 10 -11-11 N N·m·m22/kg/kg22

221

d

mmGF

Revolutionary IdeaRevolutionary Idea

We can use the Law of Universal Gravitation to figure We can use the Law of Universal Gravitation to figure out how long it takes a satellite to complete its orbit out how long it takes a satellite to complete its orbit around the sun.around the sun.

mmss = mass of the sun = mass of the sun This can be modified to orbit anything (i.e. moon This can be modified to orbit anything (i.e. moon

around sun)!around sun)!

sGm

rT

3

2

SatellitesSatellites

221

r

mmGF

r

mvF

2

AND

Set them equal to each other…

r

Gmv E

Gravitational FieldGravitational Field

Friction – block on an inclined planeFriction – block on an inclined plane Normal force – standing on the groundNormal force – standing on the ground

Both are contact forcesBoth are contact forces

How can the sun exert a force on Earth, How can the sun exert a force on Earth, even though we’re millions of miles even though we’re millions of miles away?away?

Newton’s IdeasNewton’s Ideas

Great for explaining planetary motionGreat for explaining planetary motion

Gave us accurate, precise method for Gave us accurate, precise method for predictionspredictions

Couldn’t answer the question “Couldn’t answer the question “how?”how?”

Faster than Superman…Faster than Superman…

Newton said that gravitational forces Newton said that gravitational forces permeated instantly…permeated instantly… Suppose the sun disappeared…Suppose the sun disappeared…

Einstein said that gravitational effects Einstein said that gravitational effects would take time to feelwould take time to feel

Einstein’s IdeasEinstein’s Ideas

Gravity is not a force, but a “bend” in Gravity is not a force, but a “bend” in spacespace

More massive bodies will cause a greater More massive bodies will cause a greater bendbend

Tested and “true”Tested and “true”

Both of Einstein’s theories have been Both of Einstein’s theories have been tested time and time again, and have tested time and time again, and have been extremely accurate in their been extremely accurate in their predictionspredictions

New discoveries may necessitate New discoveries may necessitate revision of his theories, nonetheless!revision of his theories, nonetheless!