How to derive the formula for Gravitational Potential Energy?

[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) ?

 

[DiracPool]

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.

 

[Tommy1995]

How did scientists derive the formula -GMm/r=Ep

not "G"...

 

[jtbell]

How did scientists derive the formula -GMm/r=Ep

They used integral calculus.

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

 

[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

 

[Tommy1995]

Thanks ya'll!