Star Apocalypse is the reinvention of the 4X genre. The game is a real time game of intergalactic civilization, using the computation power of modern computers to run advanced simulations on cultural, technological and societal interaction and development.
This is the prototype we used to optimize orbital motion. It features very simple mechanics to simulate a 'simplified' orbital motion method. It can simulate fairly realistic orbits. The upside is that it is one of the keys to our very low resources consumption. The downside is it can't simulate very elliptical orbits. The formula used to this can be found on wikipedia under orbital motion.