# Question about the Derivation of the Gravitational Law

The derivation of the law have been put up in the forums but I have a question regarding its derivation.

I understood everything from the assumptions to the application of Newton's Third Law, but I got stocked at this step:

$$\frac{m}{k} = \frac{M}{k'}$$.

This is similar to

$$\frac{C}{M} = \frac{c}{m} = \frac{k}{4 \pi^2}$$

at this site, http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml.

According to the same site, the next step requires the force to be squared. Why is this so? Is it merely to acquire the force ##F## between the two bodies? Aren't there any other ways to calculate the force other than multiplication?