Post-New Horizons orbits and masses for the satellites of Pluto

We report on ephemerides for the satellites of Pluto based on the large set of astrometric measurements. Our orbit fit yielded the following masses: $GM_{Pluto}=869.0 \pm 0.9~km^3s^{-2}$, $GM_{Charon}=106.4 \pm 0.5~km^3s^{-2}$, $GM_{Nix}=1.41 \pm 0.52\times 10^{-3}~km^3s^{-2}$, $GM_{Hydra}=2.02 \pm 0.27\times 10^{-3}~km^3s^{-2}$, corresponding to the densities of $\rho_{Pluto}=1.852 \pm 0.004~g~cm^{-3}$, $\rho_{Charon}=1.710 \pm 0.009~g~cm^{-3}$, $\rho_{Nix}=0.83\pm 0.31~g~cm^{-3}$, $\rho_{Hydra}=1.22\pm 0.19~g~cm^{-3}$. Masses of Kerberos and Styx remain unconstrained, and it is unlikely that we will be able to measure them even if we obtain abundant 1 mas precision astrometry during the next 20 years. We summarize the results of orbit integration in terms of osculating and precessing ellipse mean elements. All satellites reside in near-circular orbits, and Kerberos and Styx have 0.4 deg and 0.3 deg inclinations with respect to Charon's orbit plane. We found that Charon's orbit pole can be approximated as: $RA=133.0065 + 0.003653T$ deg, $Dec=-6.2447+2.7\times10^{-5}T$, where $T$ is Julian centuries from the epoch J2000, based on 5000 years of orbit integration. The nodal regression periods for Kerberos and Hydra are $\sim$ 9 and $\sim$ 14 years respectively, and Hydra appears to have the apsidal precession with the similar period as the node.