Proving GPE considering 0 at earths surface

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SUMMARY

The discussion focuses on deriving the formula for gravitational potential energy (GPE) of a mass located at a distance from the Earth, using the Earth's surface as the reference point where potential is defined as zero. The formula for GPE is established as GPE = mgh, where h represents the height above the Earth's surface. The derivation involves calculating the potential difference between the Earth's surface and the point of interest, leading to the conclusion that GPE can be expressed as a constant multiplied by the difference in inverse radii, simplified under the assumption that height is much smaller than the Earth's radius.

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Can someone derive the formula to calculate the GPE of a mass which is away from the Earth by considering 0 potential at Earth's surface
 
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##GPE=mgh##
h is 0 at the surface of earth.
 
Miraj Kayastha said:
Can someone derive the formula to calculate the GPE of a mass which is away from the Earth by considering 0 potential at Earth's 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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