Abstract
Starting from 80 families of low-energy fast periodic transfer orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), we obtain by analytical continuation 11 periodic orbits and 25 periodic arcs with similar properties in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their stability parameters and minimal distances to the Earth and Moon. The periods of these orbits are between 2.5 and 5 synodic months, their energies are among the lowest possible to achieve an Earth–Moon transfer, and they show a diversity of circumlunar trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close approaches to the last.
Similar content being viewed by others
References
Andreu, M.A.: The quasi-bicircular problem. Ph.D Thesis, Dept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona. Available on-line at http://www.maia.ub.es/dsg/1998/9801mangel_e.ps.gz (1998)
Andreu M.A.: Dynamics in the center manifold around L2 in the quasi-bicircular problem. Celest. Mech. Dynam. Astron. 84(2), 105–133 (2002)
Andreu M.A.: Preliminary study on the translunar halo orbits of the real Earth–Moon system. Celest. Mech. Dynam. Astron. 86(2), 107–130 (2003)
Arnold V.I., Kozlov V.V., Neishtadt A.I.: Mathematical aspects of classical and celestial mechanics. In: Arnold, V.I. (eds) Dynamical Systems III, 2nd edn, pp. 1–286. Springer-Verlag, Berlin (1993)
Bollt E., Meiss J.D.: Targeting chaotic orbits to the Moon through recurrence. Phys. Lett. A 204, 373–378 (1995)
Bolotin S., MacKay R.S.: Nonplanar second species periodic and chaotic trajectories for the circular restricted three-body problem. Celest. Mech. Dynam. Astron. 94(4), 433–449 (2006)
Broucke, R.A.: Periodic orbits in the elliptic restricted three-body problem. NASA Tech. Report 32-1360. (1969)
Bruno A.D., Varin V.P.: On families of periodic solutions of the restricted three-body problem. Celest. Mech. Dynam. Astron. 95(1–4), 27–54 (2006)
Devaney R.L.: An introduction to Chaotic Dynamical Systems. Addison Wesley, New York (1989)
Hénon M.: Generating Families in the Restricted Three Body Problem. Springer-Verlag LNP M52, Berlin (1997)
Leiva A.M., Briozzo C.B.: Fast periodic transfer orbits in the Sun–Earth–Moon quasi-bicircular problem. Celest. Mech. Dynam. Astron. 91(3–4), 357–372 (2005)
Leiva A.M., Briozzo C.B.: Control of chaos and fast periodic transfer orbits in the Earth–Moon CR3BP. Acta Astron. 58, 379–386 (2006a)
Leiva, A.M., Briozzo, C.B.: The Earth–Moon CR3BP: a full Atlas of low-energy fast periodic transfer orbits. arXiv.org astro-ph/0612386 (2006b)
Llibre J., Paşca D.: Periodic orbits of the planar collision restricted 3-body problem. Celest. Mech. Dynam. Astron. 96(1), 19–29 (2006)
Ott E., Grebogi C., Yorke J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)
Perdios E.A.: The manifolds of families of 3D periodic orbits associated to Sitnikov motions in the restricted three-body problem. Celest. Mech. Dynam. Astron. 99(2), 85–104 (2007)
Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P.: Numerical Recipes, 2nd edn. Cambridge University Press, New York (1992)
Ross, S., Koon, W.S., Lo, M.W, Marsden, J.E.: Design of a Multi-Moon Orbiter. AAS 03-143 (2003)
Schroer C.G., Ott E.: Targeting in Hamiltonian systems that have mixed regular/chaotic phase spaces. Chaos 7(4), 512–519 (1997)
Simó C., Gómez G., Jorba À., Masdemont J.: The bicircular model near the triangular libration points of the RTBP. In: Roy, A.E., Steves, B.A. (eds) From Newton to Chaos, pp. 343–370. Plenum Press, New York (1995)
Szebehely V.: Theory of Orbits. Academic Press, New York (1967)
Verhulst F.: Nonlinear Differential Equations and Dynamical Systems. Springer-Verlag, Berlin (1990)
Yagasaki K.: Computation of low energy Earth-to-Moon transfers with moderate flight time. Physica D 197, 313–331 (2004a)
Yagasaki K.: Sun-perturbed Earth-to-Moon transfers with low energy and moderate flight time. Celest. Mech. Dynam. Astron. 90(3–4), 197–212 (2004b)
Yakubovich V.A., Starzhinskii V.M.: Linear Differential Equations with Periodic Coefficients. John Wiley & Sons, New York (1975)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Leiva, A.M., Briozzo, C.B. Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem. Celest Mech Dyn Astr 101, 225–245 (2008). https://doi.org/10.1007/s10569-008-9134-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10569-008-9134-9