Statistics – Applications
Scientific paper
Dec 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998dps....30.5525e&link_type=abstract
American Astronomical Society, DPS meeting #30, #55.P25; Bulletin of the American Astronomical Society, Vol. 30, p.1452
Statistics
Applications
Scientific paper
We discuss planar and off-plane orbit families associated with major circumbinary resonances in the restricted three-body problem, which has applications to protoplanetary disks and to the Kuiper Belt. Several families of off-plane orbits around a circular binary or star-planet system are stable, and are accessible to particles orbiting in a circumbinary or protoplanetary disk. The presence of vertical instabilities in the family of planar orbits which supports circumbinary disks suggests that disk particles can be excited into off-plane motion; additional instabilities exist in planar orbits associated with major resonances. We use a simple form of dissipation to mimic such effects gas drag and Poynting-Robertson drag, allowing disk particles to spiral slowly inwards. For mass ratios 0.02 <= mu <= 0.35 and binary eccentricity e < 0.01, the vertical resonance at r ~ 2.1a (3:1 commensurability) intercepts the majority of inward-drifting particles and excites them onto the stable off-plane orbits. For mu <= 0.01, the neighboring planar instability dominates, forcing most particles onto asymmetric planar resonance orbits. For typical star-planet mass-ratios (mu <= 0.001), neither of the outer resonances are strong enough to intercept a significant fraction of particles; most particles are then trapped by the 2:1 or 3:2 planar resonances. For moderately eccentric systems with e ~ 0.1 we find vertical excitation for particles on planar resonance orbits further out, branching from the main circumbinary orbits at the 4:1 commensurability. We discuss the resonance orbits for the mass ratio appropriate to the Neptune-Sun case and their relevance to understanding the orbital distribution of Kuiper Belt objects.
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