10_1425_web_Lec_11_Gravitation

10_1425_web_Lec_11_Gravitation - Gravitation Physics 1425...

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Gravitation Physics 1425 Lecture 11 Michael Fowler, UVa
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The Inverse Square Law Newton’s idea : the centripetal force keeping the Moon circling the Earth is the same gravitational force that pulls us to the ground. BUT : the Moon’s centripetal acceleration is only 1/3600 of g ! The Moon is 60 times further from the Earth’s center than we are. SO: this suggests the gravitational pull from the Earth decreases with distance from the Earth’s center as 1/ r 2 .
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Gravitational Attraction is Proportional to Mass The gravitational force causes everything to fall with the same acceleration : For downward motion F grav = ma = mg That is, F / m has the same value for all masses. Conclusion: F m : the gravitational force on a mass is proportional to the mass.
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Clicker Question Does the Moon attract the Earth gravitationally? A. No B. Yes, but with a much weaker force than the Earth attracts the Moon. C. Yes, with the same force the Earth attracts the Moon.
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So why doesn’t the Earth go round the Moon ? The moon’s mass is about 1% of the Earth’s mass. In fact, the Moon’s attraction does cause the Earth to go in a circle—both Earth and Moon circle their common center of mass (which is inside the Earth!) We’ll discuss this more later.
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Gravitational Attraction is Proportional to Both Masses We’ve already seen, from Galileo’s observation of equal downward acceleration and Newton’s Second Law, that the Earth attracts an object with a force proportional to the object’s mass . But from Newton’s Third Law , the attractions are equal and opposite —symmetric. Therefore, the attraction is also proportional to the Earth’s mass.
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Law of Universal Gravitation The story so far: For two masses m 1 , m 2 at a distance r apart, the gravitational attraction between them is proportional to 1/ r 2 It is also proportional to both m 1 and m 2 . Therefore it must have the form where G is some constant.
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This note was uploaded on 12/07/2011 for the course PHYSICS 1425 taught by Professor Michaelfowler during the Spring '10 term at UVA.

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10_1425_web_Lec_11_Gravitation - Gravitation Physics 1425...

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