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A note on weak stability boundaries. (English) Zbl 1162.70006

Summary: This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points \(L_1\) and \(L_2\), as boundary of the weak stability region, is shown.

MSC:

70F07 Three-body problems
37N05 Dynamical systems in classical and celestial mechanics
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[1] Belbruno, E.A. Lunar capture orbits, a method for constructing Earth–Moon trajectories and the lunar GAS mission. Proceedings of AIAA/DGLR/JSASS Inter. Propl. Conf. AIAA paper No. 87-1054 (1987)
[2] Belbruno, E.A., Miler, J.K. A ballistic lunar capture trajectory for the Japanese spacecraft hiten. Jet Propulsion Laboratory, IOM 312/90.4–1371-EAB (1990)
[3] Belbruno, E.A. The dynamical mechanism of ballistic lunar capture transfers in the four body from the perspective of invariant manifolds and hill’s regions. Institut d’Estudis Catalans, CRM Preprint No. 270, Barcelona (1994)
[4] Belbruno, E.A., Humble R., Coil, J. Ballistic capture lunar transfer determination for the U.S. Air Force Academy Blue Moon Mission. AAS/AIAA Spaceflight Mechanics Meeting, Paper No. AAS 96-171 (1997)
[5] Belbruno, E.A., Carrico, J.P. Calculation of weak stability boundary ballistic lunar transfer trajectories. AIAA/AAS Astrodynamics Specialist Conference, Paper No. AIAA 2000–4142 (2000)
[6] Belbruno E.A. (2002) Analytic estimation of weak stability boundaries and low energy transfers. Contemp Math 292, 17–45 · Zbl 1021.70012
[7] Belbruno E.A. (2004) Capture Dynamics and Chaotic Motions in Celestial Mechanics. Princeton University Press, Princeton, NI (2004) · Zbl 1057.70001
[8] Belló, M., Graziani, F., Teofilato, P., Circi, C., Porfilio, M. Hechler, M. A systematic analysis on weak stability boundary transfers to the moon. 51st International Astronautical Congress, Paper No. IAF–00-A.6.03 (2000)
[9] Biesbroek, R. Study on lunar trajectories from GTO by using weak stability boundary transfers and swing-by’s. European Space Agency, ESTEC working paper No. 2014 (1997)
[10] Circi C., Teofilato P. (2001) On the dynamics of weak stability boundary lunar transfers. Celestial Mech. Dyn. Astron. 79, 41–72 · Zbl 0987.70017 · doi:10.1023/A:1011153610564
[11] Gómez G., Llibre J., Matínez R., Simó C. (2001a) Dynamics and Mission Design Near Libration Point Orbits–Volume I: Fundamentals: The Case of Collinear Libration Points. World Scientific, Singapore · Zbl 0971.70004
[12] Gómez G., Jorba À., Masdemont J., Simó C. (2001b) Dynamics and Mission Design Near Libration Point Orbits–Volume IV: Advanced Methods for Triangular Points. World Scientific, Singapore · Zbl 0969.70002
[13] Hämmerlin C., Hoffmann K.H. (1990) Numerical Mathematics. Springer, Berlin
[14] Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D. Shoot the moon. AAS/AIAA Space Flight Mechanics Meeting, Paper No. AAS 00-166 (2000)
[15] Koon W.S., Lo M.W., Marsden J.E., Ross S.D. (2001) Low energy transfer to the moon. Celestial Mech. Dyn. Astron. 81, 63–73 · Zbl 0995.70009 · doi:10.1023/A:1013359120468
[16] Miller, J.K., Belbruno, E.A. A method for the construction of a lunar transfer trajectory using ballistic capture. AAS/AIAA Spaceflight Mechanics Meeting, Paper No. AAS 91-100 (1991)
[17] Pollard H. (1996) Mathematical Introduction to Celestial Mechanics. Prentice Hall, Englewood Cliffs, NJ · Zbl 0141.23803
[18] Szebehely V. (1967) Theory of Orbits. Academic Press, New york · Zbl 0158.43206
[19] Yagasaki K. (2004a) Sun-perturbed Earth-to-Moon transfers with low energy and moderate flight time. Mech. Dyn. Astron. 90, 197–212 · Zbl 1147.70316 · doi:10.1007/s10569-004-0406-8
[20] Yagasaki K. (2004b) Computation of low energy Earth-to-Moon transfers with moderate flight time. Physica D 197, 313–331 · Zbl 1076.70019 · doi:10.1016/j.physd.2004.07.005
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