How do you derive the equation for gravitational potential energy?

Answer 1

GPE=M*G*H

It means Gravitational potential energy=Mass* Gravity( which is always 9.8)* Height thanx ;)

* * * * *

The value of the force of gravity is approximately 9.8 on the surface of the earth. For simplicity it is assumed that it is 9.8 anywhere on the surface of the earth even though it is known to vary.

Answer 2

For situations near surface of the Earth: Ug = mgΔy where m is the mass of the object, g is the acceleration due to gravity, and Δy is the change in distance. For general situations involving a two-body system, Ug = Gm1m2/r where G is the universal gravitational constant, m1 and m2 are the mass of the two objects in question, and r is the distance between the objects.

Answer 3

You could integrate the force f= GmM/r^2, E= integral fdr = - GmM/r + constant.

Another derivation is to recognize the essential variable in Nature the Energy-moment. The energy-moment = GmM for masses and zcqQ for charges. Potential Energy is the slope of the energy-moment.