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# GEOP1 - Gravitational force exerted by point mass M on...

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Gravitational force exerted by point mass M on point mass m. F = GMm d 2 M m d F = ma A net force on an object m leads to its acceleration: F = mg When the force is gravity, the acceleration is written as g : g = GM d 2 The acceleration of m toward M is G=6.67x10 -11 m 3 kg -1 s -2

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Consider a hollow shell with radius R, but very thin Gravitational attraction of a shell (assuming uniform material) on mass m: F shell = GM shell m d 2 d is distance to shell center The same as if all the mass were concentrated at a point at the center What is g on the Earth’s surface? R This equation holds for any distance from the center, d R …some calculus…
Since observer is outside all smaller shells, same formula applies d Consider the Earth made of many hollow shells, each with the same center

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F sphere = F shell ! = Gm d 2 M shell ! = GmM sphere d 2 Force due to full sphere also acts as if all mass were concentrated into a point. Therefore, acceleration of gravity on the Earth’s surface is given by (to first order): g = GM E R E 2 For two planets of different sizes, made of the same material , which has the bigger surface gravity?
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