celestial mechanics unit testing

Lang came in to New York to spend the day writing unit tests and functions (in that order, supposedly) for conversions between phase-space coordinates (position and velocity) and orbital elements (semi-major axis, eccentricity, inclination, longitude of the ascending node, argument of perihelion, and mean anomaly). We were able to pass the unit tests for most cases, but failed on a few edge cases where some of the angles become undefined. Rooting these issues out is not trivial. Also, there are some numerical instabilities which require analysis. I definitely feel like we are reinventing a wheel, but at the same time, we are learning a lot.

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