Analysis of radial velocity variations in multiple planetary systems

By studying multiple extrasolar planetary systems, it is possible to obtain constraints for planetary masses and orbital inclinations using the detection of mutual perturbations. An analysis of precise radial velocity measurements might reveal these planet-planet interactions and yield a more accurate view of such planetary systems. As in generic data modelling problems, a fit to radial velocity data series has a set of unknown parameters of which parametric derivatives have to be known by both the regression methods and the estimations for the uncertainties. In this paper, an algorithm is described that aids the computation of such derivatives when planetary perturbations are not neglected. The application of the algorithm is demonstrated for the planetary systems of HD 73526, HD 128311 and HD 155358. In addition to the functions related to radial velocity analysis, the actual implementation of the algorithm contains functions that compute spatial coordinates, velocities and barycentric coordinates for each planet. These functions aid the joint analysis of multiple transiting planetary systems, transit timing and/or duration variations or systems where the proper motion of the host star is also measured involving high precision astrometry. The practical implementation related to the above-mentioned problems features functions that make these types of investigation simple and effective.