Universal Gravitation

2Physics 1100 – Spring 2012 Chapter 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 GravitationUniversal Gravitation

3Physics 1100 – Spring 2012 Newton’s Law of Universal Gravitation From the Orbits of the planets, Newton deduced inverse square law of attraction.From the Orbits of the planets, Newton deduced inverse square law of attraction. F ~ M 1 M 2 /r 2

4Physics 1100 – Spring 2012 Cavendish Measurement of Gravity

5Physics 1100 – Spring 2012 Calculation of G F = GM 1 M 2 /r 2 F = GM 1 M 2 /r 2 a 1 = F/M 1 = GM 2 /r 2  acceleration of mass #1 due to mass #2 G =  m 3 /(kg·s 2 ) Earth: M =  kg; r = 6,378,000 m  a = 9.80 m/s 2 Newton’s Law of Universal Gravitation

6Physics 1100 – Spring 2012 Inverse Square Laws

7Physics 1100 – Spring 2012 Gravity as Inverse Square Law

8Physics 1100 – Spring 2012 Weight and Weightlessness WeightWeight the force due to gravity on an object Weight = Mass  Acceleration of Gravity W = m g Weightlessness - a conditions wherein gravitational pull appears to be lackingWeightlessness - a conditions wherein gravitational pull appears to be lacking –Examples: Astronauts Falling in an Elevator Skydiving Underwater

9Physics 1100 – Spring 2012 Weight and Weightlessness

10Physics 1100 – Spring 2012 Gravity 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 exert strong gravitational forces?The constant G is a rather small number. What kind of objects can exert strong gravitational forces?

11Physics 1100 – Spring 2012 Gravity Questions If the distance between two objects in space is doubled, then what happens to the gravitational force between them?If the distance between two objects in space is doubled, then what 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)

13Physics 1100 – Spring 2012 Gravity Fields

14Physics 1100 – Spring 2012 Class Problem If the sun suddenly collapsed to become a black hole, the earth would a) leave the solar system in a straight-line path spiral b) spiral into the black hole c) undergo a major increase in tidal forces d) continue to circle in its usual orbitIf the sun suddenly collapsed to become a black hole, the earth would a) leave the solar system in a straight-line path spiral b) spiral into the black hole c) undergo a major increase in tidal forces d) continue to circle in its usual orbit

General Relativity Einstein Upsets the Applecart

16Physics 1100 – Spring 2012 Einstein’s Theory of Gravitation Einstein perceived a gravitational field as a geometrical warping of 4-D space and time.Einstein perceived a gravitational field as a geometrical warping of 4-D space and time.

17Physics 1100 – Spring 2012 Mattress Example Imagine 2 bowling balls on a mattress, ignore for the moment the “gravitational” interaction between themImagine 2 bowling balls on a mattress, ignore for the moment the “gravitational” interaction between them As they roll around on the mattress, they make dimples in its surfaceAs they roll around on the mattress, they make dimples in its surface If they get close to each other, they sense these dimples and are “attracted” to each otherIf they get close to each other, they sense these dimples and are “attracted” to each other

18Physics 1100 – Spring 2012 Bowling Balls on a Mattress

19Physics 1100 – Spring 2012 The 3 “Classic” Tests of General Relativity Precession of Mercury’s orbitPrecession of Mercury’s orbit Deflection of starlight (gravitational lensing)Deflection of starlight (gravitational lensing) Gravitational Redshift - Clocks run slower and slower in more and more intense grativational fields.Gravitational Redshift - Clocks run slower and slower in more and more intense grativational fields.

Black 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 HOLES