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Therefore, x is r, in general.
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The U that you want for gravitation looks like this.
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So, gravitational potential energy
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for problems arbitrarily far from the center of this mass,
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not near just the surface of the Earth
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but wherever you go, in any gravitational problem,
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this is U.
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You can check that if you took this U,
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here's what I'm telling you guys to do.
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If you're really care.
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Did I miss something?
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No. Let's see.