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Motion of two planets with periods commensurable in the ratio 2∶1 solutions of the hori auxiliary system

Abstract

It is shown that the Hori auxiliary system for the motion of two planets, whose motions around the Sun have commensurable periods in the ratio 2 : 1, is completely integrable and, an intermediate orbit that includes the effects of the resonance is obtained. The difficulties of classifying some solutions as librations or circulations are discussed.

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Sessin, W., Ferraz-Mello, S. Motion of two planets with periods commensurable in the ratio 2∶1 solutions of the hori auxiliary system. Celestial Mechanics 32, 307–332 (1984). https://doi.org/10.1007/BF01229087

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Keywords

  • Auxiliary System
  • Intermediate Orbit
  • Commensurable Period