# Gravitational Potential Energy with reference point at infinity?

1. Dec 8, 2012

### Tommy1995

So, the gravitational potential energy of a mass "X" from the sun is, let's say, 100joules.

Why is it that when we take the gravitational potential energy of the mass from the reference point of infinity that the gravitational potential energy is -100joules?

I understand the negative symbol but it amazes me that the mass would still have the exact same value of 100.

2. Dec 8, 2012

### K^2

It's not. You are misunderstanding something. If it's -100J from reference at infinity, it doesn't mean it's 100J with reference at the surface. At the surface, you have -MmG/R from infinity. So if you are distance r away, the energy with reference to surface is MmG/R-MmG/r.

3. Dec 8, 2012

### Tommy1995

Aaaahh I see K^2, thanks!!!

But you see how u said, "So if you are distance r away, the energy with reference to surface is MmG/R-MmG/r." What would be the different values of "R" and "r"? I'd like help to know how you can calculate the values of Potential energy from a reference point such as the surface of a planet.

I made up my own thought experiment, finding the potential energy of a 10kg ball at distance 100m from the earth's surface and found the Gravitational potential energy to be 1000J using the formula W=FS. It was totally different to the Ep found using the formula "-Gmm/r" to find the Ep from infinity... So I have another question, how did they derive "Ep=-Gmm/r" ? It seems I don't quite understand how it calculates the work needed to move an object from an extremely large distance to a point X in space :/

Thanks again for helping me clear up my misunderstandings!

4. Dec 8, 2012

### K^2

That's what these are for. R is radius of the planet. r is position at which you want potential energy, also from center of the planet. M is mass of the planet, and m is mass of the body whose potential you want.

5. Dec 8, 2012

### Tommy1995

Thanks again K^2! :D

Btw what is GMm/R finding?