# Gravitational potential energy - problem

1. Aug 9, 2007

### zinc79

Hello. I'm new. I was looking around on the web a bit to find an answer to my problem, and I came across these forums.

Gravitational force = -GMm/(r^2)

Gravitational force between a small mass (m) and the earth (M) is zero at a distance of infinity. Any distance smaller than infinity gives a negative value. When the distance is minimum, the force is mathematically minimum but actually the largest in magnitude. When the distance is infinite, the force is mathematically largest but actually the least in magnitude.

But what is gravitational potential energy? Is it work done due to gravitational force in moving a mass from a distance (r) to an infinite distance? Is it work done due to gravitational force in moving a mass from a an infinite distance to a distance (r)? Or is it simply the work done due to gravitational force in moving the mass from one point to another?

Now, I'll deal with a case when I move a mass (m) from a distance (r1) to an infinite distance from the earth (r2)

The gravitational potential energy, as I have learnt, is simply the integration the the gravitational force. This comes out as GMm[(1/r2) - (1/r1)]. This is where I have the problem. If the mass gains height, i.e. moves away from the earth, then r1 is small and r2 is large, and because of this the gravitational potential energy turns out negative! Isn't it supposed to be a GAIN in potential energy? Isn't the change supposed to give a positive value? If not, then why? Work is being done ON the object to raise it, right?

2. Aug 9, 2007

### mgb_phys

Gravitational potential energy is the energy something has because of it's position in a graviy field. The change is simply the change from it's original position - the total GPE would be compared to it's potential at an infinite distance but that isn't usually very useful.

The negative sign in the force is beacuse it is attractive, you have to be a little careful with the sign conventiona, see-
http://en.wikipedia.org/wiki/Gravitational_potential_energy#Gravitational_potential_energy

3. Aug 9, 2007

### Staff: Mentor

Careful. To calculate the change in gravitational PE you must integrate the force needed to lift the object over the distance r1 to r2. That force is upward and equals +GMm/(r^2). So if you calculate the work done by that force, which is the work done ON the object, you'll find that the change in gravitational PE in raising a mass will be positive, as you suspect.

4. Aug 11, 2007

### zinc79

Re:

I get you Doc Al, but wikipedia says that "Gravitational potential energy is the work of gravitational force", and well, it is a popular source... I'm still confused...

5. Aug 11, 2007

### Staff: Mentor

I wouldn't lean too heavily upon wiki as a source. Don't you have a textbook? Here's a reliable discussion of gravitational PE: Gravitational Potential Energy.

6. Aug 11, 2007

### rootX

from my personal expierence it's all just nonsense. It really doesn't mean anything. Because they analyze lot of problems with gravitational force in them, so they name the work done by gravitational force "gravitional potential enery".

Yes, it is work done due to gravitational force while moving an object from A to B.

Edit: While solving your problems, ignoring gravitational potential energy may help you (it always helped me!)

7. Aug 11, 2007

### rootX

oops, i missed this part

see the potential curve well( that would explain why it's more negative)

Yes, work is being done on the object to raise it,
but assuming that the object had some initial v at the start,
then after reaching the height the v would be reduced..

and so the system is losing its kinetic energy..