Why can the major planets have their satellites moving in direct and retrograde orbits as well?

Details Why can the major planets have their satellites moving in direct and retrograde orbits as well? Why can the major planets have their satellites moving in direct and retrograde orbits as well?

Apr 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991apmam..12..339w&link_type=abstract

Applied Mathematics and Mechanics (English Edition) (ISSN 0253-4827), vol. 12, April 1991, p. 339-343.

Mathematics

Natural Satellites, Orbital Mechanics, Planetary Orbits, Three Body Problem, Circular Orbits, Jacobi Integral, Kinetic Energy, Motion Stability

Scientific paper

The stability of planetary satellites is investigated theoretically in the framework of the circular restricted three-body problem, applying the Jacobian integral to establish a stability testing function. The derivation of the method is briefly outlined, and numerical results for the major planets are presented in tables. It is shown that both direct and retrograde orbits can be stable and coexist around one central body because the relative kinetic energy is the same. The boundary surface of the stability region is found to be a nearly oblate ellipsoid.

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