Kepler Solver

The heart of this package is being able to take a set of Keplerian elements and output relative positions, velocities, etc. The Kepler solver used to go from mean anomaly to eccentric anomaly is a tweaked version copied from AstroLib.jl.

From AstroLib.jl:

Many different numerical methods exist to solve Kepler's equation. This function implements the algorithm proposed in Markley (1995) Celestial Mechanics and Dynamical Astronomy, 63, 101 (DOI:10.1007/BF00691917). This method is not iterative, requires only four transcendental function evaluations, and has been proved to be fast and efficient over the entire range of elliptic motion 0≤e≤10.

On my laptop, this solves for a single eccentric anomaly in just 47 ns. Since it is implemented in pure Julia, there is no overhead from calling into a C or Cython compiled function and no need for vectorization.