Upper estimates of the distances between bodies in the restricted three-body problem

Details Upper estimates of the distances between bodies in the restricted three-body problem Upper estimates of the distances between bodies in the restricted three-body problem

Feb 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977pazh....3...82g&link_type=abstract

Pis'ma v Astronomicheskii Zhurnal, vol. 3, Feb. 1977, p. 82-85. In Russian.

Astronomy and Astrophysics

Astronomy

Astrometry, Celestial Mechanics, Solar System, Three Body Problem, Center Of Gravity, Distance, Hill Method, Motion Stability

Scientific paper

An analytical method for improving upper estimates of the distances between bodies in the restricted three-body problem is proposed for the case where the constant of the energy integral is negative and sufficient conditions for absolute Hill stability of the motion of the fixed pair of bodies are satisfied. A theorem concerning conditional boundedness of the motion is proven, and some problems involving the sun, Jupiter, and Saturn as well as the sun, earth, and Jupiter are evaluated as examples. The theorem is used to show that if the sun-earth separation were ever to equal 0.1 AU, the distance of Jupiter from their center of mass would still be less than 12.96 AU.

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