Astronomy and Astrophysics – Astronomy
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.0604d&link_type=abstract
American Astronomical Society, DDA meeting #40, #6.04; Bulletin of the American Astronomical Society, Vol. 41, p.899
Astronomy and Astrophysics
Astronomy
Scientific paper
Long-term numerical integrations have revealed an orbital instability of Uranus’ tiny inner moons that might result in collisions on a timescale as short as 4-100 million years (Martin and Lissauer, Icarus 125, 1-12, 1997). To understand this possibly chaotic system's behavior on shorter timescales, we have numerically integrated and fit accurate orbital elements to the moons’ positions over durations of up to 10,000 years. Three of the moons -- Bianca, Cressida, and Desdemona -- experience closely coupled orbital variations. Bianca and Cressida are strongly affected by a nearby 16:15 inner Lindblad resonance (ILR), while Cressida's and Desdemona's present orbits place them very near to a 47:46 ILR. From spectral analysis of the time series of orbital elements of the satellites, we see clear interactions among a number of small moons at dynamically significant periodicities, including the libration periods of the critical arguments of these two resonances. The magnitude of the orbital variations is highly sensitive to the satellites’ masses. Assuming nominal satellite masses based on a density of 1 g cm-3 and volumes photometrically estimated by Karkoschka (Icarus 151, 51-68, 2001), we infer quasi-periodic hundred meter variations in the semi-major axes of the satellites from our numerical integrations. Increasing the assumed masses by only a factor of two results in much stronger and more irregular interactions, as also evident in the increased ergodicity of surfaces of section of the critical arguments of resonance, suggesting that the satellite system may be just below the limit of chaotic behavior. Ongoing longer duration numerical integrations, including the full suite of small Uranian satellites, will enable us to explore the dynamical interactions of this complex system in more detail. This work was supported by the National Science Foundation, the Jerome A. Schiff Fund, and the Wilson/Birney Fund.
Dawson Rebekah I.
French Richard G.
Showalter Robert M.
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