EFFICIENT FITTING OF MULTIPLANET KEPLERIAN MODELS TO RADIAL VELOCITY AND ASTROMETRY DATA

We describe a technique for solving for the orbital elements of multiple planets from radial velocity ( RV) and/or astrometric data taken with 1 m s(-1) and mu as precision, appropriate for efforts to detect Earth-massed planets in their stars' habitable zones, such as NASA's proposed Space Interferometry Mission. We include details of calculating analytic derivatives for use in the Levenberg-Marquardt (LM) algorithm for the problems of fitting RV and astrometric data separately and jointly. We also explicate the general method of separating the linear and nonlinear components of a model fit in the context of an LM fit, show how explicit derivatives can be calculated in such a model, and demonstrate the speed up and convergence improvements of such a scheme in the case of a five-planet fit to published RV data for 55 Cnc.