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Chapter_13_Part_2

# Chapter_13_Part_2 - More on Universal Gravitation The...

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More on Universal Gravitation

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The Gravitational Field A gravitational field exists at every point in space When a particle of mass m is placed at a point where the gravitational field is , the particle experiences a force The field exerts a force on the particle g r g = m F g r r
The Gravitational Field, 2 The gravitational field is defined as The gravitational field is the gravitational force experienced by a test particle placed at that point divided by the mass of the test particle The presence of the test particle is not necessary for the field to exist The source particle creates the field g m F g r r g r

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The Gravitational Field, 3 The gravitational field vectors point in the direction of the acceleration a particle would experience if placed in that field The magnitude is that of the freefall acceleration at that location
The Gravitational Field, final The gravitational field describes the “effect” that any object has on the empty space around itself in terms of the force that would be present if a second object were somewhere in that space 2 ˆ g GM m r = = - F g r r r

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Gravitational Potential Energy The gravitational force is conservative The change in gravitational potential energy of a system associated with a given displacement of a member of the system is defined as the negative of the work done by the gravitational force on that member during the displacement ( 29 = - = - f i r f i r U U U F r dr
Gravitational Potential Energy, cont As a particle moves from A to B, its gravitational potential energy changes by U

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Gravitational Potential Energy for the Earth Choose the zero for the gravitational potential energy where the force is zero – This means U i = 0 where r i = – This is valid only for rs ° ° R E and not valid for r < R E U is negative because of the choice of U i ( ) E GM m U r r = -
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