Critical generating orbits for second species periodic solutions of the restricted problem

Details Critical generating orbits for second species periodic solutions of the restricted problem Critical generating orbits for second species periodic solutions of the restricted problem

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..15..421h&link_type=abstract

Celestial Mechanics, vol. 15, Aug. 1977, p. 421-452.

Computer Science

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13

Earth Orbits, Orbital Mechanics, Periodic Functions, Three Body Problem, Collision Parameters, Computer Graphics, Elliptical Orbits, Jacobi Integral, Motion Stability, Orbit Calculation

Scientific paper

The second species periodic solutions of the restricted three body problem are investigated in the limiting case of second-body mass equal to zero. These orbits, called consecutive collision orbits by Henon and generating orbits by Perko, form an infinite number of continuous one-parameter families and are the true limit, for second-body mass approaching zero, of second species periodic solutions for second-body mass greater than zero. By combining a periodicity condition with an analytic relation for criticality, isolated members of several families are obtained which possess the unique property that the stability index jumps from plus-minus to minus-plus infinity at that particular orbit. These orbits are of great interest since, for small second-body mass values greater than zero, 'neighboring' orbits will then have a finite (but small) region of stability.

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