Short-term dynamical interactions among extrasolar planets

We show that short-term perturbations among massive planets in multiple pla net systems can result in radial velocity variations of the central star th at differ substantially from velocity variations derived assuming the plane ts are executing independent Keplerian motions. We discuss two fitting meth ods that can lead to an improved dynamical description of multiple planet s ystems. 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 are allowed to vary according to a simple model for resonant interactions between the planets. Both of these methods can determine the true masses fo r the planets by eliminating the degeneracy inherent in fits that assume in dependent Keplerian motions. We apply our fitting methods to the sin i GJ 8 76 radial velocity data and argue that the mass factors for the two planets are likely in the 1.25-2.0 range.