Mathematics – Probability
Scientific paper
Mar 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993lpi....24..869l&link_type=abstract
In Lunar and Planetary Inst., Twenty-Fourth Lunar and Planetary Science Conference. Part 2: G-M p 869-870 (SEE N94-16173 03-91)
Mathematics
Probability
1
Celestial Mechanics, Charon, Neptune (Planet), Orbital Resonances (Celestial Mechanics), Pluto (Planet), Uranus (Planet), Orbital Elements, Stability, Time Measurement
Scientific paper
Pluto and Charon are most likely the remnants of a large number of objects that existed in the Uranus-Neptune region at early epochs of the solar system. Numerical integrations have shown that, in general, such objects were ejected from the planetary region on timescales of approximately 107 years after Neptune and Uranus reached their current masses. It is thought that the Pluto-Charon system survived to current times without being dynamically removed in this way because it is trapped in a set of secular and mean motion resonances with Neptune. The best-known Pluto-Neptune orbit coupling is the 3:2 mean motion resonance discovered almost 30 years ago by C. Cohen and E. Hubbard. These workers showed that the resonance angle, delta is equivalent to 3(lambdaP) - 2(lambdaN) - omega-barP where omega-barP is the longitude of perihelion of the Pluto-Charon system, and lambdaN and lambdaP are the mean longitude of Neptune and Pluto-Charon respectively, librates about 180 deg with an amplitude, Adelta, of 76 deg. A numerical simulation project to map out the stability region of the 3:2 resonance is reported. The results of these simulations are important to understanding whether Pluto's long-term heliocentric stability requires only the 3:2 resonance, or whether it instead requires one or more of the other Pluto-Neptune resonances. Our study also has another important application. By investigating stability timescales as a function of orbital elements, we gain insight into the fraction of orbital phase space which the stable 3:2 resonance occupies. This fraction is directly related to the probability that the Pluto-Charon system (and possibly other small bodies) could have been captured into this resonance.
Alan Stern S.
Levison Harold F.
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