As many exoplaneteers know, parameterizing eccentric gravitational two-body orbits (ellipses or Kepler orbits) for inferences (MCMC sampling or, alternatively, likelihood optimizations) is not trivial. One non-triviality is that there are combinations of parameters that are very-nearly degenerate for certain kinds of observations. Another is that when the eccentricity gets near zero (as it does for many real systems), some of the orientation parameters become unconstrained (or unidentifiable or really non-existent). Today Adrian Price-Whelan (Flatiron) was hacking on this with the thought that the time or phase of maximum radial velocity (with respect to the observer) and the time or phase of minimum radial velocity could be used as a pair of parameters that give stable, well-defined combinations of phase, eccentricity, and ellipse orientation (when that exists). We spent an inordinate amount of time in the company of trig identities.
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