Orekit, a low level space dynamics library written in Java, has gained widespread recognition since it was released under an open-source license in 2008.
Low level space dynamics library
Orekit aims at providing accurate and efficient low level components for the development of flight dynamics applications. It is designed to be easily used in very different contexts, from quick studies up to critical operations.
As a library, Orekit provides basic elements (orbits, dates, attitude, frames, ...) and various algorithms to handle them (conversions, propagations, pointing, ...).
Free (open-source) software
Orekit is freely available both in source and binary formats, with all related documentation and tests.
Orekit is distributed under the Apache License version 2.0, a well known business-friendly license. This means anybody can use it to build any application, free or not. There are no strings attached to user code.