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didi_plus · Jan 10, 2012, 02:21 AM

If I want to calculate the potential energy at the earth's center.. what's the rule?

ebaines · Jan 10, 2012, 07:28 AM

Potential energy in a the earth's gravitational field is PE= -GMm/r, where M is the earth's mass. For a point that is inside the earth the value for M is the mass of the sphere below that point, so for a point at the center of the earth M=0. But r = 0 as well, so this looks like an eqaution that has 0 divided by 0, so undefined. However, we can substitute $M=\rho \frac 4 3 \pi r^3$ , so potential energy becomes:

$<br /> PE= \frac {-G\rho \frac 4 3 \pi r^3m} r = -G\rho \frac 4 3 \pi r^2m<br />$

which is 0 at r=0.