Generating orbits for stable close encounter periodic solutions of the restricted problem

Details Generating orbits for stable close encounter periodic solutions of the restricted problem Generating orbits for stable close encounter periodic solutions of the restricted problem

Aug 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976aaas.confs....h&link_type=abstract

American Institute of Aeronautics and Astronautics and American Astronautical Society, Astrodynamics Conference, San Diego, Cali

Astronomy and Astrophysics

Astronomy

Elliptical Orbits, Encounters, Motion Stability, Orbit Calculation, Periodic Functions, Three Body Problem, Earth-Moon System, Kepler Laws, Numerical Stability, Orbit Perturbation

Scientific paper

Recently the second species periodic solutions of the restricted three-body problem have been investigated in the limiting case mu equals O. The term second species solution is due to Poincare and is basically a Keplerian elliptical orbit about the larger primary mass which, at some time, makes a close passage by the smaller attracting mass. Our new result is that for mu equals O, second species orbits are critical if and only if the Jacobi constant C has an extremum. This paper explains this new analytical result in some detail and related it to the previous numerical determinations of stability.

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