# ch13 - Chapter 13 Gravitation In this chapter we will...

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Chapter 13 Gravitation In this chapter we will explore the following topics: -Newton’s law of gravitation that describes the attractive force between two point masses and its application to extended objects -The acceleration of gravity on the surface of the earth, above it, as well as below it. -Gravitational potential energy -Kepler’s three laws on planetary motion -Satellites (orbits, energy , escape velocity) (13-1)

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m 1 m 2 Newton realized that the force which holds the moon it its orbit is of the same nature with the force that makes an apple drop near the surface of th Newton's L e earth. aw of Newto Gravitat n concl ion uded that the earth attracts both apples as well as the moon but also that every object in the universe attracts every other object. The tendency of objects to move towards each other is known as gravitation. Newton formulated a force law known as Every particle any other particle with a gravitational force that has the following char Newton's law of gravitat acteristics: attracts ion. 1. 1 2 1 2 2 The force acts along the line that connects the two particles 2. Its magnitude is given by the equation: Here and are the masses of the two particles, is their separation and i m m F G m m r G r = 11 2 2 s the gravitational constant. Its value is: 6.67 10 N.m / G kg - = × 1 2 2 m m F G r = (13-2)
m 1 m 2 F 12 F 21 r 12 1 2 21 2 1 12 21 The gravitational force exerted on by is equal in magnitude to the force exerted on by but opposite in direction. The two forces obey Newton's third law: 0 F m m F F m m F + = r r 1 2 1 2 Newton proved that a uniform shell attarcts a particle that is outside the shell as if the shell's mass N were ote: concetrated at the shell center If the particle is inside the shell, the m m F G r = net force is zero Consider the force F the earth (radius R, mass M) exerts on an apple of mass m. The earth can be thought of as consisting of concentric shells. Thus from the apple's point of view the earth behaves li 2 ke a point mass at the earth center The magnitude of the force is given by the equation: mM F G R = (13-3) m 1 m 2 r F 1 m 2 m 1 1 2 2 m m F G r =

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m 1 dm r dF r The net gravitational force exerted by a group of particles is equal to the vect Gravitat or sum o ion and the Principle of Su f the contribution from each perposition particle. 1 1 2 3 12 13 1 1 12 13 2 3 1 For example the net force exerted on by and is equal to: Here and are the forces exerted on by and , respectively. In general the force exerted
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ch13 - Chapter 13 Gravitation In this chapter we will...

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