Orbital parameters in Milky-Way-like potentials

We present and test a fast method for estimating these parameters using an application of the Sackel fudge, used previously for the estimation of action-angle variables.

We show that the method is highly accurate, to a level of <1% in eccentricity, over a large range of relevant orbits and in different Milky Way-like potentials, and demonstrate its validity by estimating the eccentricity distribution of the RAVE-TGAS data set and comparing it to that from orbit integration. Using the method, the orbital characteristics of the ~7 million Gaia DR2 stars with radial velocity measurements are computed with Monte Carlo sampled errors in ~116 hours of parallelised cpu time, at a speed that we estimate to be ~3 to 4 orders of magnitude faster than using numerical orbit integration.