On the Perko timing condition for second species orbits in the restricted problem

Details On the Perko timing condition for second species orbits in the restricted problem On the Perko timing condition for second species orbits in the restricted problem

Jan 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977a%26a....54...47h&link_type=abstract

Astronomy and Astrophysics, vol. 54, no. 1, Jan. 1977, p. 47-55.

Astronomy and Astrophysics

Astrophysics

3

Dynamic Stability, Earth-Moon System, Orbit Calculation, Three Body Problem, Collision Parameters, Convergence, Kepler Laws, Periodic Variations

Scientific paper

The general timing condition originally derived by Henon (1968) for so-called consecutive-collision orbits in the restricted three-body problem is derived again, and the timing condition introduced by Perko (1974) for second-species periodic generating orbits in the limiting case of mu equals 0 is examined. It is shown that Perko's timing condition is just a special case of the Henon condition. Some sample computer plots of second-species generating orbits are provided to illustrate the wide variety of possible orbits. Recent results concerning the stability of such consecutive-collision orbits are briefly reviewed.

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