What is gravitational potential energy? Why it varies inversely with the negative square of the distance

Why do you think it's a negative square of the distance? I guess any beginner textbook will answer your question. Copy/paste your question into a Google search tool and see the answer.

Actually, it varies as the negative inverse of the distance, not the inverse square of the distance.

Are you asking why is it's negative? It has to do with how the formula is obtained - by integrating the force of gravity over the distance the object rises:


\Delta PE = \int _{d_1} ^{d_2} \frac {G m_1 m_2} {r^2} dr = G m_1 m_2 ( \frac 1 {d_1} - \frac 1 {d_2} )


What's important is that the change in PE is positive as the object rises (i.e. for d_2 > d_1 )..