Universal GravitationUniversal Gravitation

2Physics 1100 – Spring 2012

Chapter 9 - GravityChapter 9 - Gravity

• Universal Law of GravityUniversal Law of Gravity• Universal Gravitational Constant, GUniversal Gravitational Constant, G• Gravity and Distance – Inverse Square LawsGravity and Distance – Inverse Square Laws• Weight and WeightlessnessWeight and Weightlessness• Ocean TidesOcean Tides• Gravitational FieldsGravitational Fields• Einstein's Theory of GravitationEinstein's Theory of Gravitation• Black HolesBlack Holes• Universal Gravitation Universal Gravitation

3Physics 1100 – Spring 2012

221

d

mGmF

Newton’s Law of Universal GravitationNewton’s Law of Universal Gravitation

• From the Orbits of the planets, Newton deduced inverse square From the Orbits of the planets, Newton deduced inverse square law of attraction. law of attraction.

221

d

mGmF FF ~ ~ MM11MM22//rr22

4Physics 1100 – Spring 2012

Cavendish Measurement of GravityCavendish Measurement of Gravity

5Physics 1100 – Spring 2012

Calculation of GCalculation of G

FF = = GMGM11MM22//rr22

a1 = F/M1 = GM2/r2 acceleration of mass #1 due to mass #2

G = 6.67410-11 m3/(kg·s2)Earth: M = 5.9761024 kg; r = 6,378,000 m a = 9.80 m/s2

Newton’s Law of Universal Gravitation

6Physics 1100 – Spring 2012

Inverse Square LawsInverse Square Laws

7Physics 1100 – Spring 2012

Gravity as Inverse Square LawGravity as Inverse Square Law

8Physics 1100 – Spring 2012

Weight and WeightlessnessWeight and Weightlessness

• Weight Weight • the force due to gravity on an object

• Weight = Mass Acceleration of Gravity

• W = m g

• Weightlessness Weightlessness - a conditions wherein gravitational pull - a conditions wherein gravitational pull appearsappears to be lacking to be lacking– Examples:

• Astronauts

• Falling in an Elevator

• Skydiving

• Underwater

9Physics 1100 – Spring 2012

Weight and WeightlessnessWeight and Weightlessness

10Physics 1100 – Spring 2012

Gravity QuestionsGravity Questions

• Did the Moon exert a gravitational force on the Apollo astronauts?Did the Moon exert a gravitational force on the Apollo astronauts?

• What kind of objects can exert a gravitational force on other objects?What kind of objects can exert a gravitational force on other objects?

• The constant G is a rather small number. What kind of objects can The constant G is a rather small number. What kind of objects can exert exert strongstrong gravitational forces? gravitational forces?

11Physics 1100 – Spring 2012

Gravity QuestionsGravity Questions

• If the distance between two objects in space is doubled, then what If the distance between two objects in space is doubled, then what happens to the gravitational force between them?happens to the gravitational force between them?

• What is the distance is tripled?What is the distance is tripled?• ……is quadrupled?is quadrupled?

• What if the mass of one of the object is doubled?What if the mass of one of the object is doubled?• ……tripled?tripled?• ……quadrupled?quadrupled?

12Physics 1100 – Spring 2012

Tidal forces (Moon & Sun)Tidal forces (Moon & Sun)

13Physics 1100 – Spring 2012

Gravity FieldsGravity Fields

14Physics 1100 – Spring 2012

Class ProblemClass Problem

• If the sun suddenly collapsed to If the sun suddenly collapsed to become a black hole, the earth become a black hole, the earth wouldwould

a) leave the solar system in a a) leave the solar system in a straight-line path spiral straight-line path spiral b) spiral into the black holeb) spiral into the black holec) undergo a major increase in tidal c) undergo a major increase in tidal forcesforcesd) continue to circle in its usual orbit d) continue to circle in its usual orbit

General Relativity General Relativity Einstein Upsets the ApplecartEinstein Upsets the Applecart

16Physics 1100 – Spring 2012

Einstein’s Theory of GravitationEinstein’s Theory of Gravitation

• Einstein perceived a gravitational field as a geometrical warping Einstein perceived a gravitational field as a geometrical warping of 4-D space and time.of 4-D space and time.

17Physics 1100 – Spring 2012

Mattress ExampleMattress Example

• Imagine 2 bowling balls on a mattress, ignore for the moment Imagine 2 bowling balls on a mattress, ignore for the moment the “gravitational” interaction between themthe “gravitational” interaction between them

• As they roll around on the mattress, they make dimples in its As they roll around on the mattress, they make dimples in its surfacesurface

• If they get close to each other, they sense these dimples and If they get close to each other, they sense these dimples and are “attracted” to each otherare “attracted” to each other

18Physics 1100 – Spring 2012

Bowling Balls on a MattressBowling Balls on a Mattress

19Physics 1100 – Spring 2012

The 3 “Classic” Tests of General RelativityThe 3 “Classic” Tests of General Relativity

• Precession of Mercury’s orbit Precession of Mercury’s orbit

• Deflection of starlight (gravitational lensing)Deflection of starlight (gravitational lensing)

• Gravitational Redshift - Clocks run slower and slower in more Gravitational Redshift - Clocks run slower and slower in more

and more intense grativational fields.and more intense grativational fields.

Black HolesBlack Holes

Copyright – A. Hobart

21Physics 1100 – Spring 2012

• If a massive star shrinks enough so

that the escape velocity is equal to or

greater than the speed of light, then it

has become a black hole.

• Light cannot escape from a black

hole.

BLACK HOLESBLACK HOLES