A Pluto-Charon Sonata V. Long-term Stability of the HST State Vector

We analyze a new set of 275 n-body calculations designed to place limits on the masses of the small circumbinary satellites in the Pluto-Charon system. Together with calculations reported in previous papers, we repeat that a robust upper limit on the total mass of the four satellites is roughly $9.5 \times 10^{19}$ g. For satellite volumes derived from New Horizons, this mass limit implies a robust upper limit on the bulk densities of Nix and Hydra, $\lesssim 1.7$ g cm$^{-3}$, that are comparable to the bulk density of Charon. Additional calculations demonstrate that satellite systems with mass $\lesssim 8.25 \times 10^{19}$ g are robustly stable over the current age of the Sun. The bulk densities of Nix and Hydra in these lower mass systems are clearly smaller than the bulk density of Charon. These new n-body results enable accurate measurements of eccentricity and inclination for Nix, Kerberos, and Hydra that agree well with orbital elements derived from numerical calculations with new HST and New Horizons state vectors. With these new state vectors, Styx has a 37% larger eccentricity and an 85% smaller inclination, which makes it more prone to gravitational perturbations from Nix.