I'm playing with orbits in a simple 2-d game where a ship flies around in space and is attracted to massive things. The ship's velocity is stored in a vector and acceleration is applied to it every frame as appropriate given Newton's law of universal gravitation. The point masses don't move (there's only 1 right now) so I would expect an elliptical orbit. Instead, I see this: I've tried with nearly circular orbits, and I've tried making the masses vastly different (a factor of a million) but I always get this rotated orbit. Here's some (D) code, for context: void accelerate(Vector delta) { velocity = velocity + delta; // Velocity is a member of the ship class. } // This function is called every frame with the fixed mass. It's a // method of the ship's. void fall(Well well) { // f=(m1 * m2)/(r**2) // a=f/m // Ship mass is 1, so a = f. float mass = 1; Vector delta = well.position - loc; float rSquared = delta.magSquared; float force = well.mass/rSquared; accelerate(delta * force * mass); }