## How to derive the formula for Gravitational Potential Energy?

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) ?

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

 Quote by Tommy1995 How did scientists derive the formula -GMm/r=Ep
not "G"...

Mentor

## How to derive the formula for Gravitational Potential Energy?

 Quote by Tommy1995 How did scientists derive the formula -GMm/r=Ep
They used integral calculus.

$$PE_{grav} = - \int^r_\infty {F_{grav} dr^\prime} = - \int^r_\infty {\left( -\frac{GmM}{{r^\prime}^2} \right) dr^\prime} = - \frac{GmM}{r}$$
 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'...al_gravitation
 Thanks ya'll!