A database of planar axisymmetric periodic orbits for the Solar system

  • Ricardo L. RestrepoEmail author
  • Ryan P. Russell
Original Article


A multiple grid search strategy is implemented to generate a broad database of axisymmetric three-body periodic orbits for planets and main planetary satellites in the Solar system. The periodic orbit search is performed over 24 pairs of bodies that are well approximated by the circular restricted three-body problem (CR3BP), resulting in approximately 3 million periodic solutions. The periodic orbit generation is implemented in a two-level grid search scheme. First, a global search is applied to each CR3BP system in order to capture the global structure of most existing families, followed by a local grid search, centered around a few fundamental families, where useful, highly sensitive periodic orbits emerge. A robust differential corrector is implemented with a full second-order trust region method in order to efficiently converge the highly sensitive solutions. The periodic orbit database includes solutions that (1) remain in the vicinity of the secondary only; (2) circulate the primary only via inner or outer resonances; and (3) connect both resonance types with orbits bound to the secondary, approximating heteroclinic connections that leads to natural escape/capture mechanisms. The periodic solutions are characterized and presented in detail using a descriptive nomenclature. Initial conditions, stability indices, and other dynamical parameters that allow for the solution characterization are computed and archived. The data and sample scripts are made available online.


Periodic orbits Circular restricted three-body problem Dynamical system theory Stability Solar system dynamics 


Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.The University of Texas at AustinAustinUSA

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