# Gravitational Potential Energy

1. Aug 28, 2008

### J. Richter

Hi.

If I throw a stone straight upwards from the surface of the Earth, with the escape speed of 11,2 km/s, assuming that no air or other particles gets in the way, and waited for a very, very long time, the velocity of my stone (and the Earth in the opposite direction) would be almost 0, and the gravitational potential energy between my stone and the Earth would be almost 0 as well, according to the formula for gravitational potential energy.

However I used a lot of energy to throw that stone.
That energy I used to actually do some work, must be stored somehow, as it can’t disappear.

It is obvious, that the energy is stored in this “end” scenario itself.
If something far out there in space gave the stone a tiny little push towards the Earth, it would accelerate “backwards”, until it reaches 11,2 km/s, hit the surface of the Earth, and converts it’s kinetic energy to heat.

This kind of “stored” energy that the two masses have, when being far away from each other, to make it up for the loss of energy in my muscles after throwing the stone, appears to be different from the potential energy described in the formula for gravitational potential energy.

And that’s what confuses me.

If we can’t call this additional “stored” energy for potential energy between the masses, what can we call it then? And why does the formula for gravitational potential energy say that the resulting energy in this “throwing stone“ thought experiment is 0, when I actually did some work on the stone while throwing it?

That seems to be the same as saying, that the energy I used is lost forever.

2. Aug 28, 2008

### Staff: Mentor

Why do you think that? That "stored" energy is gravitational potential energy.

You have to compare the final energy of 0 to what you started with. Gravitational PE between two objects is given by:

$$-\frac{Gm_1m_2}{r}$$

It is negative for finite distances. Thus the work you did on the stone increases the total energy to 0.