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Universal Gravitation
Chapter 9 - Gravity
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Universal Law of Gravity
Universal Gravitational Constant, G
Gravity and Distance – Inverse Square Laws
Weight and Weightlessness
Ocean Tides
Gravitational Fields
Einstein's Theory of Gravitation
Black Holes
Universal Gravitation
Physics 1100 – Spring 2012
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Newton’s Law of Universal Gravitation
• From the Orbits of the planets, Newton deduced inverse square
law of attraction.
Gm
m
Gm
1
F ~ M M 1/rm22
FF
22
dd
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2
2
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Cavendish Measurement of Gravity
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Calculation of G
F = GM1M2/r2
Newton’s Law of Universal Gravitation
G = 6.67410-11 m3/(kg·s2)
Earth: M = 5.9761024 kg; r = 6,378,000 m  a = 9.80 m/s2
a1 = F/M1 = GM2/r2  acceleration of mass #1 due to mass #2
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Inverse Square Laws
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Gravity as Inverse Square Law
Physics 1100 – Spring 2012
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Weight and Weightlessness
• Weight
• the force due to gravity on an object
• Weight = Mass  Acceleration of Gravity
• W=mg
• Weightlessness - a conditions wherein gravitational pull
appears to be lacking
– Examples:
• Astronauts
• Falling in an Elevator
• Skydiving
• Underwater
Physics 1100 – Spring 2012
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Weight and Weightlessness
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Gravity Questions
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Did the Moon exert a gravitational force on the Apollo astronauts?
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What kind of objects can exert a gravitational force on other objects?
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The constant G is a rather small number. What kind of objects can
exert strong gravitational forces?
Physics 1100 – Spring 2012
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Gravity Questions
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If the distance between two objects in space is doubled, then what
happens to the gravitational force between them?
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What is the distance is tripled?
…is quadrupled?
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What if the mass of one of the object is doubled?
…tripled?
…quadrupled?
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Tidal forces (Moon & Sun)
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Gravity Fields
Physics 1100 – Spring 2012
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Class Problem
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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 orbit
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General Relativity
Einstein Upsets the Applecart
Einstein’s Theory of Gravitation
• Einstein perceived a gravitational field as a geometrical warping
of 4-D space and time.
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Mattress Example
• Imagine 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
surface
• If they get close to each other, they sense these dimples and
are “attracted” to each other
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Bowling Balls on a Mattress
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The 3 “Classic” Tests of General Relativity
• Precession of Mercury’s orbit
• Deflection of starlight (gravitational lensing)
• Gravitational Redshift - Clocks run slower and slower in more
and more intense grativational fields.
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Black Holes
Copyright – A. Hobart
BLACK HOLES
• 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.
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