Sphere with gravitational pull at the center

Question

I'm wondering whats the easiest way to apply gravity at the center of a sphere (much like a planet) I'm thinking that ODE would be the best library to use? But not sure on how to implement it to apply the gravity at the center of the sphere.

Answer 1

All you need is :

a = F/m = -GM r/r^3

where r is the radial vector for the mass m from the Sphere of mass M and G is the Gravitational constant.

You don't necessarily need much of a library to integrate this. You can just compute acceleration for each time step. The only point is that you get a much better result (E.g. closed orbits!) if for each step you first compute an approximate new position, then compute the acceleration for the location at mid-point of the timestep and then use that to determine the new position and velocity.