A database of planar axisymmetric periodic orbits for the Solar system
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.
KeywordsPeriodic 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.
- Broucke, R.A.: Periodic orbits in the restricted three-body with Earth–Moon masses. Technical report 32-1168, JPL, Caltech (1968)Google Scholar
- Dichmann, D.J., Doedel, E.J., Paffenroth, R.C.: The computation of periodic solutions of the 3-body problem using the continuation software AUTO. In: International Conference on Libration Points Orbits and Applications, Aiguablava, Spain (2002)Google Scholar
- Haapala, A.F., Vaquero, M., Pavlak, T.A., Howell, K.C., Folta, D.C.: Trajectory selection strategy for tours in the Earth–Moon system. In: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, Hilton Head, SC (2013)Google Scholar
- Hénon, M.: Generating families in the restricted three-body problem. In: Lecture Notes in Physics, vol. 52. Springer, Berlin (1997)Google Scholar
- Keller, H.B.: Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems. Springer, Berlin (1986)Google Scholar
- Lam, T., Whiffen, G.J.: Exploration of distant retrograde orbits around Europa. In: 15th AAS/AIAA Space Flight Mechanics Conference, Copper Mountain, CO (2005)Google Scholar
- Lo, M.W., Parker, J.S.: Unstable resonant orbits near Earth and their applications in planetary missions. In: AIAA/AAS Conference, vol. 14, Providence, RI (2004)Google Scholar
- Ocampo, C.A., Rosborough, G.W.: Transfer trajectories for distant retrograde orbiters of the Earth. In: Proceedings of the 3rd Annual Spaceflight Mechanics Meeting, vol. 82, No. 2, pp. 1177–1200 (1993)Google Scholar
- Pellegrini, E., Russell, R.P.: A multiple-shooting differential dynamic programming algorithm. In: AAS/AIAA Space Flight Mechanics Meeting, Paper AAS 17-453, San Antonio (2017)Google Scholar
- Restrepo, R.L., Russell, R.P.: Patched periodic orbits: a systematic strategy for low-energy transfer design. In: AAS/AIAA Astrodynamics Specialist Conference, AAS 17-695, Stevenson, WA (2017)Google Scholar