OrbitLib was created from course material from university upper-division aerospace engineering courses. In addition to games, OrbitLib can help out with most first-semester orbital mechanics and space flight dynamics homework.
OrbitLib does not require any outside third-party dependencies nor does it force developers to framework their games and applications in a particular way.
Numerical analysis, orbital prediction, matrix transformations, Stumpff functions... Whatever it is, OrbitLib gets the hard parts done for you so you can focus on the mission.