The origin of the Kirkwood gaps - A mapping for asteroidal motion near the 3/1 commensurability

Details The origin of the Kirkwood gaps - A mapping for asteroidal motion near the 3/1 commensurability The origin of the Kirkwood gaps - A mapping for asteroidal motion near the 3/1 commensurability

Mar 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982aj.....87..577w&link_type=abstract

Astronomical Journal, vol. 87, Mar. 1982, p. 577-593.

Astronomy and Astrophysics

Astronomy

170

Asteroids, Astronomical Maps, Eccentric Orbits, Equations Of Motion, Solar Orbits, Three Body Problem, Hamiltonian Functions, Jupiter (Planet), Mars (Planet), Numerical Integration, Orbit Calculation, Asteroids, Origin, Kirkwood Gaps, Mapping, Motion, Techniques, Data, Eccentricity, Hypotheses, Mars Crossers, Distribution, Perturbations, Formation, Width, Inclinations, Time Dependency, Mathematical Models, Resonance

Scientific paper

A mapping of the phase space onto itself with the same low-order resonance structure as the 3/1 commensurability in the planar-elliptic restricted three-body problem is obtained. This mapping is about 1,000 times faster than the usual method of numerically integrating the averaged equations of motion. It exhibits some surprising behavior that might provide a key to the origin of the Kirkwood gaps. It is noted that a test asteroid placed in the gap may evolve for a million years with low eccentricity (less than 0.05) and then suddenly jump to large eccentricity (greater than 0.3), becoming a Mars crosser. The removal of the asteroid by a close encounter with Mars would then be possible. As a first test of this hypothesis, a distribution of 300 test asteroids in the area of the 3/1 commensurability was evolved for two million years. When the Mars crossers are removed, the distribution of initial conditions reveals a gap at the location of the 3/1 Kirkwood gap.

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