Physics homework help?

Question

I'm in astrophysics and I have to justify Ug=mgh from Ug=-(GmM)/r

Note that the g next to the U is a subscript because its gravitational potential energy.

the "m" and the "M" are just mass subscript 1 and mass subscript 2.

Does anyone know how to derive mgh from the other thing?

Answer 1

Previous knowledge:

mg = F

U = Fr (radius is distance in this situation: fd=U)

Fg=GmM/r^2

Now plug Fg=GmM/r^2 into U=Fr to get:

U= (GmM/r^2) * r

r's cancell:

U=GmM/r