# Deriving the Formula for Gravitational Potential Energy

1. Dec 31, 2009

### blackwing1

Hey guys,
Do any of you happen to know how to derive the formula for General gravitational potential energy (not the mgh one) without using calculus? Thanks.

Just in case you guys want to know, I'm trying to derive the equation for this: http://xkcd.com/681_large/. I've got most of it, but I didn't know the formula for escape velocity so I searched it up and it led up to the formula for General Gravitational E_P. I haven't learned calculus yet, but I would still like to know how to derive it. Thanks. :D

2. Dec 31, 2009

### Yuqing

The escape energy is given by
$$E_{e} = \frac{GMm}{r}$$
where M is the planet mass, m is the object mass and r is the radius of the planet.

They set the energy raised in constant Earth's gravity equal to the escape energy.

$$mgh = \frac{GMm}{r}$$
$$h = \frac{GM}{gr}$$

The first equation given is derived using calculus. I have seen a way of deriving it using the graph of the function and geometric means but it is not as meaningful as the calculus derivation.

3. Dec 31, 2009

Thanks. :D