Abstract
This work studies a special type of cislunar periodic orbits in the circular restricted three-body problem called resonance transition periodic orbits, which switch between different resonances and revolve about the secondary with multiple loops during one period. In the practical computation, families of multiple periodic orbits are identified first, and then the invariant manifolds emanating from the unstable multiple periodic orbits are taken to generate resonant homoclinic connections, which are used to determine the initial guesses for computing the desired periodic orbits by means of multiple-shooting scheme. The obtained periodic orbits have potential applications for the missions requiring long-term continuous observation of the secondary and tour missions in a multi-body environment.
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References
Anderson, R.L., Campagnola, S., Lantoine, G.: Celest. Mech. Dyn. Astron. 150(2), 1 (2016)
Belbruno, E., Marsden, B.G.: Astron. J. 113(4), 1433 (1997)
Belbruno, E., Topputo, F., Gidea, M.: Adv. Space Res. 42(8), 1330 (2008)
Betts, J.T.: J. Guid. Control Dyn. 21(2), 193 (1998)
Broucke, R.A.: Technical report 32-1168 (1968)
Broucke, R.: AIAA J. 7(6), 1003 (1969)
Canalias, E., Gómez, G., Marcote, M., et al.: Assessment of mission design including utilization of libration points and weak stability boundaries. ESA Advanced Concept Team (2004)
Capdevila, L., Guzzetti, D., Howell, K.: In: AIAA Space Flight Mechanics Meeting (2004)
Carrico, J., Dichmann, D., Policastri, L., et al.: AIAA Astrodynamics Specialist Conference, Girdwood, Alaska (2011)
Demeyer, J., Gurfil, P.: J. Guid. Control Dyn. 30(5), 1261 (2007)
Deprit, A., Henrard, J.: Astron. J. 72, 158 (1967)
Doedel, E.J., Romanov, V.A., Paffenroth, R.C., et al.: Chaos 17(08), 2625 (2007)
Gómez, G., Masdemont, J., Simó, C.: J. Astronaut. Sci. 46(2), 135 (1998)
Hénon, M.: Astron. Astrophys. 1, 223 (1969)
Hénon, M.: Celest. Mech. 10(3), 375 (1974)
Hou, X.Y., Liu, L.: Astron. J. 137(6), 4577 (2009)
Howell, K.C.: Celest. Mech. 32(1), 53 (1984)
Jorba, À., Masdemont, J.: Physica D 132, 189 (1999)
Kechichian, J.A., Campbell, E.T., Werner, M.F., et al.: Acta Astronaut. 56(5), 495 (2005)
Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Chaos 10(2), 427 (2000)
Koon, W.S., Lo, M.W., Marsden, J.E., et al.: Celest. Mech. Dyn. Astron. 81(1–2), 27 (2001)
Koon, W.S., Lo, M.W., Marsden, J.E., et al.: Dynamical Systems, The Three-Body Problem and Space Mission Design. Springer, New York (2007)
Lara, M.: Celest. Mech. Dyn. Astron. 86(2), 143 (2003)
Lara, M.: Celest. Mech. Dyn. Astron. 129, 285 (2017)
Lara, M., Pelźez, J.: Astron. Astrophys. 389(2), 692 (2002)
Lara, M., Russell, R., Villac, B.: J. Guid. Control Dyn. 30(2), 409 (2007)
Lei, H.L., Xu, B.: Mon. Not. R. Astron. Soc. 434(2), 1376 (2013)
Lei, H.L., Xu, B.: Astrophys. Space Sci. 362(4), 75 (2017a)
Lei, H.L., Xu, B.: Commun. Nonlinear Sci. Numer. Simul. 54, 466 (2017b)
Leiva, A.M., Briozzo, C.B.: Acta Astronaut. 58(8), 379 (2006)
Lo, M.W., Parker, J.S.: AAS/AIAA Astrodynamics Specialist Conference. Number AAS, 2005–380 (2005)
Markellos, V.V.: Celest. Mech. 10(1), 87 (1974)
Markellos, V.V.: Celest. Mech. 12(2), 215 (1975)
Papadakis, K.E.: Earth Moon Planets 103(1–2), 25 (2008)
Parker, J.S., Davis, K.E., Born, G.H.: Acta Astronaut. 67(5), 623 (2010)
Poincaré, H.: New Methods of Celestial Mechanics. Springer, Media (1992)
Pontani, M., Conway, B.A.: J. Guid. Control Dyn. 33(5), 1429 (2010)
Ricker, G.R., Winn, J.N., Vanderspek, R., et al.: J. Astron. Telesc. Instrum. Syst. 1(1), 014003 (2015)
Scott, C.J., Spencer, D.B.: J. Guid. Control Dyn. 33(5), 1592 (2010)
Standish, E.M.: JPL Interoffice Memorandum IOM 312. D-98-048 (1998)
Stramacchia, M., Colombo, C., Bernelli-Zazzera, F.: Adv. Space Res. 58(6), 967 (2016)
Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic press, New York (1967)
Valsecchi, G.B., Perozzi, E., Rossi, A.: Proceedings of the International Astronomical Union, vol. 10, p. 488 (2012)
Vaquero, M., Howell, K.C.: J. Guid. Control Dyn. 37(4), 1143 (2014)
Acknowledgements
This work was carried out with financial support of the National Natural Science Foundation (No. 11603011, 41774038), the Natural Science Foundation of Jiangsu province (No. BK20160612), the visiting scholar program of China Scholarship Council (No. 201706195002), the National Basic Research Program 973 of China (2015CB857100), the Satellite Communication and Navigation Collaborative Innovation Center (No. SatCN-201409) and National Defense Scientific Research Fund (No. 2016110C019). Lei H.L. wishes to thank Dr. Jinglang Feng for her kind help on improving the use of language, and the authors are much obliged to the reviewer, for his/her insightful comments that greatly improved the quality of this paper. We thank Dr. Martin Lara.
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Lei, H., Xu, B. Resonance transition periodic orbits in the circular restricted three-body problem. Astrophys Space Sci 363, 70 (2018). https://doi.org/10.1007/s10509-018-3290-5
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DOI: https://doi.org/10.1007/s10509-018-3290-5