Abstract
The second species periodic solutions of the restricted three body problem are investigated in the limiting case of μ=0. These orbits, called consecutive collision orbits by Hénon and generating orbits by Perko, form an infinite number of continuous one-parameter families and are the true limit, for μ→0, of second species periodic solutions for μ>0. 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 indexk jumps from ±∞ to ∓∞ at that particular orbit. These orbits are of great interest since, for small μ>0, ‘neighboring’ orbits will then have a finite (but small) region of stability.
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Hitzl, D.L., Hénon, M. Critical generating orbits for second species periodic solutions of the restricted problem. Celestial Mechanics 15, 421–452 (1977). https://doi.org/10.1007/BF01228610
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DOI: https://doi.org/10.1007/BF01228610