Force of Gravity Between Earth and Moon

How would you make a computer simulation of the solar system that is based on gravitational forces between the planets—if you want the planets to move in a way that the real planets do, due to the gravitational and inertial forces between them?

Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This is the equation for universal gravitation:

${\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},}$

where F is the gravitational force acting between two objects, m₁ and m₂ are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.

Data

Gravitational Formula

Expressed another way: