Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

Details Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

May 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27...27k&link_type=abstract

Celestial Mechanics, vol. 27, May 1982, p. 27-38.

Mathematics

5

Elliptical Orbits, Jupiter (Planet), Orbital Mechanics, Saturn (Planet), Solar Orbits, Three Body Problem, Circular Orbits, Equations Of Motion, Mass Ratios, Numerical Stability, Orbit Calculation, Stellar Motions, Periodicity, Orbits, Sun, Jupiter, Saturn, Three Body Problem, Data, Eccentricity, Equations Of Motion, Mathematical Models, Diagrams

Scientific paper

A systematic approach to generate periodic orbits in the elliptic restricted problem of three bodies is introduced. The approach is based on (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to periodic orbits in the elliptic restricted problem. Two families of periodic orbits of the elliptic restricted problem are found by this approach. The mass ratio of the primaries of these orbits is equal to that of the Sun-Jupiter system. The sidereal mean motions between the infinitesimal body and the smaller primary are in a 2:5 resonance, so as to approximate the Sun-Jupiter-Saturn system. The lineaar stabilities of these periodic orbits are studied as functions of the eccentricities of the primaries and of the infinitesimal body. The results show that both stable and unstable periodic orbits exist in the elliptic restricted problem that are close to the actual Sun-Jupiter-Saturn system. However, the periodic orbit closest to the actual Sun-Jupiter-Saturn system is (linearly) stable.

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