Abstracts Category : Other

On the orbits and the early in-situ formation of Pluto'ssmall satellites

by Man-yin Woo

The formation of Pluto's small satellites Styx,Nix, Keberos and Hydra remains a mystery. Their orbits arenearly circular, near mean-motion resonances (MMR) and nearlycoplanar with Charon's orbit. One scenario suggests that they allformed close to their current locations from a disk of debris,which was ejected from the Charon-forming impact before the tidalevolution of Charon. The validity of this scenario is tested byperforming N-body simulations with Pluto-Charon evolving tidallyfrom an initial orbit at a few Pluto radii with initialeccentricity e C = 0 or 0.2. After tidal evolution, thefree eccentricities e free of the test particles arecompared with the current eccentricities of the four smallsatellites. The only case with e free matching with theeccentricities of the current satellites are those not affected byMMR during the tidal evolution in a model with constant Q andinitial e C = 0.2 that is damped down rapidly, where Q isthe effective tidal dissipation function. However, the survivingtest particles not affected by resonance do not have strongpreference to be in or near 4:1, 5:1 and 6:1 MMR with Charon. Analternative scenario may be needed to explain the formation of thefour small satellites. Inspired by the circumbinary nature ofthe orbits of the small satellites, a better understanding anddescription of circumbinary orbits is sought. By applying FastFourier transformation (FFT) to the cylindrical distance betweencircumbinary object and the center of mass of the binary as afunction of time R(t), the free eccentricity e free, theforced eccentricity e forced, and the forced oscillationterms of an orbits around a binary can be extracted. An analytictheory for the osculating Keplerian semi-major axis a oscand eccentricity e osc of an orbit around a circular binaryis also derived, in terms of e free and the forcedoscillation terms. From the analytic solution, the termsresponsible for the large variations of a osc and eosc are identified. Due to the large variations in the osculatingelements and the fact that the mean of e osc can besignificantly different from e free, it is more suitable touse e free, which can be determined by FFT, to describe acircumbinary orbit. The Laplace-like three-body resonancebetween Styx, Nix and Hydra is also studied. By repeating thesimulations of , but with a smaller time step of 3000s, none of the cases are found to have the three-body resonantangle = 3l S - 5l N + 2l H inpurely librating state within the measurable range of the masses ofthe satellites, where l S, l N and l H arethe true longitudes of Styx, Nix and Hydra, respectively. We alsosearch for (1) the libration of other three-body resonant angleswhen is circulating, and (2) the libration of two-bodyresonant angles that combine to give when islibrating.