As it makes its 248 year tour around the Sun, it turns out that Pluto (which has been downgraded to a dwarf planet), Charon (which has been upgraded from Pluto's moon to a binary dwarf planet partner of Pluto), and the four other moons of this "binary dwarf planet", do an elaborate six way dance.
This is tricky to model mathematically.
The lessons learned modeling this gravitationally bound system moons and dwarf planets, may provide useful tips for modeling other complex binary systems (of two stars, of a star and a black hole, or of a small star with a brown dwarf or maximally large planet system), which have planets.
Four small moons (Styx, Nix, Kerberos and Hydra) are at present known to orbit around the barycenter of Pluto and Charon, which are themselves considered a binary dwarf-planet due to their relatively high mass ratio.
The central, non-axisymmetric potential induces moon orbits inconvenient to be described by Keplerian osculating elements. Here, we report that observed orbital variations, may not be the result of orbital eccentricities or observational uncertainties, but may be due to forced oscillations caused by the central binary. We show, using numerical integration and analytical considerations, that the differences reported on their orbital elements, may well arise from this intrinsic behavior rather than limitations on our instruments.
Dionysios Gakis, Konstantinos N. Gourgouliatos, "Orbit determination of the moons of the Pluto-Charon system" arXiv:2202.13319 (February 27, 2022) (accepted for publication in Celestial Mechanics and Dynamical Astronomy).
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