# How is the equation for force by charge or by mass discovered?

It's a newbie question. How is the formula for force between two charges or gravitational force between two particles derived. Is it just intuition or is there any method used to derive these equations? For example I am not able to understand how is $r^2$ term of these formulas are taken.

Consider the gravitational force equation is not yet discovered. So what would be the steps someone need to reach in this formula?

• search for Hook ( and Newton ). This R² is proportionnal to a sphere surface centered on each center of mass or charge. It's a physical law , built from observations
– user46925
Commented Dec 31, 2015 at 9:39

Newtons law of gravitation is not just a speculation based on intuition. It is safe to say that $\frac{1}{r^2}$ law of gravitation is based on accurate experimental quantification by Kepler relating time period of orbit and semi major axis of the orbit goes by the rule Kepler's third law. I invite you to work out how the $\frac{1}{r^2}$ rule beautifully explains Kepler's relation.
Now Coulomb discovered his $\frac{1}{r^2}$ law by conducting extensive and presise experiments. Coulomb used a torsion balance and measure the forces between charged objects leading to his law. Read more about the experiment here.