Gravity

Orbits and Gravitational simulations using OpenGL and C.

The Algorithm

Firstly, the program calculates the gravitational force between all the celestial bodies by using this formula:

$F = G \frac{Mm}{r^2}$

by using this other formula, the force formula:

the program can get the acceleration of a body:

$a = \frac{F}{m}$

$a = \frac{GM}{r^2}$

now, apply this acceleration to this movement equation:

$x_{i + 1} = x_i + v \Delta t + \frac{1}{2}a \Delta t^2$

Example: