Computer Science
Scientific paper
Oct 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983icar...56...51w&link_type=abstract
Icarus (ISSN 0019-1035), vol. 56, Oct. 1983, p. 51-74.
Computer Science
272
Asteroids, Eccentric Orbits, Numerical Integration, Orbit Calculation, Three Body Problem, Hamiltonian Functions, Liapunov Functions, Orbital Elements, Trajectory Analysis, Jupiter, Gaps, Kirkwood Gap, Origin, Eccentricity, Three-Body Problem, Trajectories, Characteristics, Calculations, Mapping, Zones, Motion, Asteroids, Data, Parameters, Techniques
Scientific paper
The sudden eccentricity increases discovered by Wisdom (1982) are reproduced in numerical integrations of the planar ecliptic restricted three-body problem, verifying that this phenomenon is real. Mapping derivations are qualitatively reviewed and the maximum Liapunov characteristic exponent and its importance for determining the character of a trajectory are explained. The results of a number of calculations of this exponent using the differential equations for the unaveraged three-body problem are shown and compared to equivalent calculations using a mapping. In all cases the two approaches agree whether the orbits are chaotic or quasiperiodic. The mappings are used to trace out the chaotic zone near the 3/1 commensurability, both in the planar-ecliptic problem and in the three-dimensional elliptic problem. The outer boundary of the chaotic zone coincides with the boundary of the 3/1 Kirkwood gap in the actual distribution of asteroids within the errors of the asteroid orbital elements.
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