Celestial Mechanics and Dynamical Astronomy

, Volume 127, Issue 3, pp 331–341 | Cite as

On the covering of a Hill’s region by solutions in the restricted three-body problem

Original Article

Abstract

We consider two classical celestial-mechanical systems: the planar restricted circular three-body problem and its simplification, the Hill’s problem. Numerical and analytical analyses of the covering of a Hill’s region by solutions starting with zero velocity at its boundary are presented. We show that, in all considered cases, there always exists an area inside a Hill’s region that is uncovered by the solutions.

Keywords

Gyroscopic forces Hill’s problem Restricted three-body problem Hill’s region Numerical results 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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