Slingshot

Every body pulls the probe with Newton's inverse-square law. The game advances in fixed steps of 1/240 of a second using velocity Verlet, the same family of integrators used in real orbit simulations, so orbits stay stable instead of slowly spiraling.

Planets and stars move on fixed, precomputed paths, which keeps the dotted prediction exact: what you see before launch is what will happen. In the Lagrange level the view rotates with the planet, which is how astronomers usually draw L4 and L5.