# Proving GPE considering 0 at earths surface

by Miraj Kayastha
Tags: earths, gravitational energy, proving, surface
 P: 52 Can someone derive the formula to calculate the GPE of a mass which is away from the earth by considering 0 potential at earths surface
 PF Gold P: 816 ##GPE=mgh## h is 0 at the surface of earth.
PF Gold
P: 11,341
 Quote by Miraj Kayastha Can someone derive the formula to calculate the GPE of a mass which is away from the earth by considering 0 potential at earths surface
Assume a point mass for the Earth. Use the standard definition for potential (this looks like homework so you can easily find it yourself) then write down the potential at the Earth's surface and the Potential for the point of interest. The difference will be the difference.
The answer will be a constant times (1/R1 - 1/R2),
which can be re-written (with R2 - R1 on the top) and then you substitute h = R2 - R1.
Then you assume h << R and then you can eliminate some terms to give mgh. (Where g is the value at the surface)

You can do this!

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