Periodic planetary-type orbits of the general 4-body problem with an application to the satellites of Jupiter

Details Periodic planetary-type orbits of the general 4-body problem with an application to the satellites of Jupiter Periodic planetary-type orbits of the general 4-body problem with an application to the satellites of Jupiter

Jan 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a....93..204h&link_type=abstract

Astronomy and Astrophysics, vol. 93, no. 1-2, Jan. 1981, p. 204-211.

Astronomy and Astrophysics

Astrophysics

8

Celestial Mechanics, Four Body Problem, Galilean Satellites, Orbital Mechanics, Planetary Orbits, Natural Satellites, Orbit Perturbation, Orbital Elements, Orbital Resonances (Celestial Mechanics), Jupiter, Satellites, Orbits, Four Body Problem, Resonance, Motion, Data, Evolution, Parameters, Eccentricities, Perturbations, Periodicity, Analysis

Scientific paper

Several families of periodic orbits of the general four-body problem are computed numerically. The periodic orbits are of the planetary type, i.e., one body is the more massive one and the masses of the other three bodies are small but not negligible. It is indicated that there exists an infinite number of such families which are separated by resonant orbits. Each family has a part with nearly circular orbits and a part with nearly elliptic orbits, with an almost constant resonance. These results have been applied to the Galilean satellites of Jupiter, which have the resonance 1:2:4. Four resonant branches of families of periodic orbits exist, with nearly elliptic orbits, with the resonance 1:2:4, which differ in phase only. One of these branches has the observed phase, and is the only branch with stable orbits, the periodic orbits of the other three branches being unstable. One particular periodic orbit of the former branch is very close to the observed motion of the Galilean satellites.

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