# How to derive the formula for Gravitational Potential Energy?

1. Dec 9, 2012

### Tommy1995

How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?

2. Dec 9, 2012

### DiracPool

Experimental observation and number fudging to find the constant of proportionality G.

3. Dec 9, 2012

not "G"...

4. Dec 9, 2012

### Staff: Mentor

They used integral calculus.

$$PE_{grav} = - \int^r_\infty {F_{grav} dr^\prime} = - \int^r_\infty {\left( -\frac{GmM}{{r^\prime}^2} \right) dr^\prime} = - \frac{GmM}{r}$$

5. Dec 9, 2012

### dipole

Newton's law of graviation is emperical - it can't be derived from some other fundamental law or set of equations. This is the case with all the basic laws of physics - nature is the way it is.

If you want to read more about the history try here and related pages:

http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

6. Dec 9, 2012

### Tommy1995

Thanks ya'll!