Families of periodic orbits in the general three-body problem for the sun-Jupiter-Saturn mass-ratio and their stability

Details Families of periodic orbits in the general three-body problem for the sun-Jupiter-Saturn mass-ratio and their stability Families of periodic orbits in the general three-body problem for the sun-Jupiter-Saturn mass-ratio and their stability

Nov 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..45..207d&link_type=abstract

Astrophysics and Space Science, vol. 45, Nov. 1976, p. 207-233.

Astronomy and Astrophysics

Astrophysics

15

Jupiter (Planet), Motion Stability, Orbital Mechanics, Saturn (Planet), Solar Orbits, Three Body Problem, Celestial Mechanics, Mass Ratios, Periodic Functions, Tables (Data), Variational Principles, Vertical Motion

Scientific paper

Several families of planar planetary-type periodic orbits in the general three-body problem, in a rotating frame of reference, for the sun-Jupiter-Saturn mass-ratio are found and their stability is studied. It is found that the configuration in which the orbit of the smaller planet is 'inside' the orbit of the larger planet is, in general, more stable. We also develop a method to study the stability of a planar periodic motion with respect to vertical perturbations. Planetary periodic orbits with the orbits of the two planets not close to each other are found to be vertically stable. There are several periodic orbits that are stable in the plane but vertically unstable and vice versa. It is also shown that a vertical critical orbit in the plane can generate a monoparametric family of three-dimensional periodic orbits.

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