I haven't seen a lot of contributions (yet) in this domain, but I think Julia is uniquely suited to astrodynamics problems. SGP4.jl [1] is a wrapper of the python-sgp4 package, which allows a user to propagate satellites using the Simplified General Perturbations model via two-line element sets (TLEs). Interplanetary.jl [2] is a collection of code initially written for a class I took involving interplanetary navigation and guidance. Feedback is very much appreciated -- these are my first two open source contributions!
[1] https://github.com/crbinz/SGP4.jl [2] https://github.com/crbinz/Interplanetary.jl
