Short-Term Dynamical Interactions Among Extrasolar Planets

We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are executing independent Keplerian motions. We discuss two alternate fitting methods which can lead to an improved dynamical description of multiple planet systems. In the first method, the osculating orbital elements are determined via a Levenberg-Marquardt minimization scheme driving an N-body integrator. The second method is an improved analytic model in which orbital elements such as the periods and longitudes of periastron are allowed to vary according to a simple model for resonant interactions between the planets. Both of these methods can potentially determine the true masses for the planets by eliminating the sin(i) degeneracy inherent in fits that assume independent Keplerian motions. As more radial velocity data is accumulated from stars such as GJ876, these methods should allow for unambiguous determination of the planetary masses and relative inclinations.