# Deriving gravitational potential energy (by bringing mass from infinity to r)

1. Sep 23, 2014

### Miraj Kayastha

I understand the derivation of gravitational potential energy when an object is moved away from earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from infinity to r is equal to (magnitude of F) times (dr) times (cos 0) and I get a positive gravitational potential energy?

Can somebody show me the derivation of gpe considering a mass brought from infinity to r with detailed explanation (especially the signs)?

2. Sep 23, 2014

### xAxis

Integrating F*dr from infinity to r gives you the work done. In the infinity the energy of system was 0. The work done gives you the change in kinetic energy. Since you got positive result, Ep + Ek = 0, therefor potential energy must be negative.
So everything is OK

3. Sep 24, 2014

### Miraj Kayastha

I did not get my answer from that. I need the derivation

4. Sep 24, 2014

### Staff: Mentor

What are you taking as your force F? What direction does it have?