Mathematics – Probability
Scientific paper
Dec 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995aas...18711605m&link_type=abstract
American Astronomical Society, 187th AAS Meeting, #116.05; Bulletin of the American Astronomical Society, Vol. 27, p.1448
Mathematics
Probability
Scientific paper
Orbital resonances --- both, mean motion resonances as well as secular resonances --- are essential to understanding the present-day dynamical behavior of objects in the Kuiper Belt. Furthermore, during the formation and subsequent dynamical evolution of the outer planets, the region beyond the orbit of Neptune and up to approximately 50 AU would have been swept by strong resonant perturbations from the giant planets, particularly Neptune. Previous work [Malhotra 1995, AJ 110:420] has indicated that the mass in the Kuiper Belt would have been gravitationally sculpted into a highly non-uniform distribution, with most of the Kuiper Belt objects being swept into narrow zones of long-term stable orbits at mean motion resonances with Neptune. The resonance sweeping process would have excited the orbital eccentricities in the Kuiper Belt to moderately high values, e ~ 0.1-0.3. I have determined the locations, widths, and capture cross sections of these resonance zones and have studied the dynamical properties of resonant orbits. The short term ( ~ 10(5) yr) dynamics of resonance-trapped objects is determined primarily by Neptune's perturbations alone, but the long term dynamics is sensitive to the secular perturbations of all the giant planets as well as weak higher-order mean motion resonances. If the majority of Kuiper Belt objects do indeed reside in the narrow stable libration zones at Neptune resonances, then an important observational consequence is that detection probability for KB objects is highly non-uniform in ecliptic longitude. A comparison of theory with current observations will be presented.
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