On the Orbits and Masses of the Satellites of the Pluto-Charon System

(Abridged) The orbits of the recently discovered satellites of Pluto, S/2005 P2 and S/2005 P1, are significantly non-Keplerian, even if P2 and P1 have negligible masses, because the mass ratio of Charon-Pluto is ~0.1. We present an analytic theory with P2 and P1 treated as test particles. This analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods and that the periapse and ascending node precess at nearly equal rates in opposite directions for P2 and P1. The deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. We also present direct numerical orbit integrations with different assumed masses for P2 and P1 within the ranges allowed by the albedo uncertainties. If the albedos are as high as that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. There is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and its prograde periapse precession with a period of 5300 days should be easily detectable. If the albedos are as low as that of comets, the large inferred masses induce significant variations in the epicyclic eccentricities and/or periapse longitudes on the 400-500-day timescales, due to the proximity of P2 and P1 to the 3:2 mean-motion commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400- 500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future