ch13-p080 - 80. (a) Since the volume of a sphere is 4R3/3,...

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80. (a) Since the volume of a sphere is 4 π R 3 /3, the density is total total 33 4 3 3 . 4 MM R R ρ ππ == When we test for gravitational acceleration (caused by the sphere, or by parts of it) at radius r (measured from the center of the sphere), the mass M which is at radius less than r is what contributes to the reading ( GM/r 2 ). Since M = (4 π r 3 /3) for r R then we can write this result as 3 total 3 total 23 3 4 43 M r G R GM r rR π §· ¨¸ ¨ ¸ ©¹ = when we are considering points on or inside the sphere. Thus, the value
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