Mathematics – Dynamical Systems
Scientific paper
Mar 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..35..289k&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 35, March 1985, p. 289-303. NSF-NASA-supported research.
Mathematics
Dynamical Systems
Jupiter (Planet), Orbit Calculation, Saturn (Planet), Solar Orbits, Three Body Problem, Approximation, Equations Of Motion, Planetary Mass, Tables (Data), Planets, Jupiter, Sun, Saturn, Three Body Problem, Orbits, Periodicity, Celestial Mechanics, Eccentricity, Mass, Dynamics, Evolution, Theoretical Studies
Scientific paper
Two families of symmetric periodic orbits of the planar, general, three-body problem are presented. The masses of the three bodies include ratios equal to the sun-Jupiter-Saturn system and the periods of the orbits of Jupiter and Saturn are in a 2:5 resonance. The (linear) stability of the orbits are studied in relation to eccentricity and mass variations. The generation of the two families of periodic orbits follows a systematic approach and employs (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to the elliptic restricted problem and from the circular and elliptic problems to the general problem through bifurcation phenomena relating the three dynamical systems. The approach also provides insight into the evolutionary process of periodic orbits continued from the restricted problems to the general problem.
Kwok Johnny H.
Nacozy Paul E.
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