Analytic estimates and topological properties of the weak stability boundary. (English) Zbl 1266.70023
Summary: The weak stability boundary (WSB) is the transition region of the phase space where the change from gravitational escape to ballistic capture occurs. Studies on this complicated region of chaotic motion aim to investigate its unique, fuel saving properties to enlarge the frontiers of low energy transfers. This “fuzzy stability” region is characterized by highly sensitive motion, and any analysis of it has been carried out almost exclusively using numerical methods. On the contrary this paper presents, for the planar circular restricted 3-body problem, (1) an analytic definition of the WSB which is coherent with the known algorithmic definitions; (2) a precise description of the topology of the WSB; (3) analytic estimates on the “stable region” (nearby the smaller primary) whose boundary is, by definition, the WSB.
References:
| [1] | Arnol’d, V.I., Kozlov, V.V., Neishtadt, A.: I. Mathematical aspects of classical and celestial mechanics. Dynamical systems. III.’ Encyclopaedia of Mathematical Sciences. Springer, Berlin ISBN: 978-3-540-28246-4; 3-540-28246-7 (2006) |
| [2] | Belbruno, E.: Lunar capture orbits. A method of constructing earth-moon trajectories and the lunar gas mission. In: Proceedings of AIAA/DGLR/JSASS, pp. 87–1054 (1987) |
| [3] | Belbruno, E.: Examples of the Nonlinear Dynamics of Ballistic Capture and Escape in the Earth-Moon System. AIAA paper, vol. 90, p. 2896 (1990) |
| [4] | Belbruno E.: Fast resonance shifting as a mechanism of dynamical instability illustrated by comets and the CHE yrajectories. Ann. N Y Acad. Sci. 822, 195–226 (1997) · doi:10.1111/j.1749-6632.1997.tb48343.x |
| [5] | Belbruno E.: Capture Dynamics and Chaotic Motions in Celestial Mechanics: With Applications to the Construction of Low Energy Transfers. Princeton University Press, Princeton (2004) · Zbl 1057.70001 |
| [6] | Belbruno E., Miller J.: Sun-perturbed Earth-to-Moon transfers with a ballistic capture. J. Guidance Control Dyn. 16(4), 770–775 (1993) · doi:10.2514/3.21079 |
| [7] | Bello-Mora, M., Graziani, F., Teofilatto, P., Circi, C., Porfilio, M., Hechler, M.: A systematic analysis on weak stability boundary transfers to the Moon. Paper IAF-00-A.6.03. In: Proceedings of the International Astronautical Conference (2000) |
| [8] | Carrico J.P., Belbruno E.: Calculation of weak stability boundary ballistic lunar transfer trajectories. American Institute of Aeronautics and Astronautics, USA (2006) |
| [9] | Celletti, A., Chierchia, L.: KAM stability and celestial mechanics. Members in American Mathematical Society 187(878) (2007) · Zbl 1129.70012 |
| [10] | García F., Gómez G.: A note on weak stability boundaries. Celest. Mech. Dyn. Astron. 97, 87–100 (2007) · Zbl 1162.70006 · doi:10.1007/s10569-006-9053-6 |
| [11] | Goldstein, Poole, Safko: Classical Mechanics. Addison Wesley, London, 3 edn, ISBN-13: 978-020165702 (2001) |
| [12] | Gómez G., Jorba A., Masdemont J.J., Simó C.: Study of the transfer from the earth to a halo orbit around the equilibrium point L 1. Celest. Mech. Dyn. Astron. 56(4), 541–562 (1993) · Zbl 0780.70007 · doi:10.1007/BF00696185 |
| [13] | Gómez G., Koon W.S., Lo M.W., Marsden J.E., Masdemont J., Ross S.D.: Connecting orbits and invariant manifolds in the spatial restricted three-body problem. Nonlinearity 17(5), 1571–1606 (2004) · Zbl 1115.70007 · doi:10.1088/0951-7715/17/5/002 |
| [14] | Koon W.S., Lo M.W., Marsden J.E., Ross S.D.: Low energy transfer to the Moon. Celest. Mech. Dyn. Astron. 81, 63–73 (2001) · Zbl 0995.70009 · doi:10.1023/A:1013359120468 |
| [15] | Mingotti G., Topputo F., Bernelli-Zazzera F.: Low-energy, low-thrust transfers to the Moon. Celest. Mech. Dyn. Astron. 105, 61–74 (2009) · Zbl 1223.70091 · doi:10.1007/s10569-009-9220-7 |
| [16] | Romagnoli D., Circi C.: Earth-Moon weak stability boundaries in the restricted three and four body problem. Celest. Mech. Dyn. Astron. 103, 79–103 (2009) · Zbl 1167.70006 · doi:10.1007/s10569-008-9169-y |
| [17] | Stiefel E.L., Scheifele G.: Linear and regular celestial mechanics. Perturbed two-body motion, numerical methods, canonical theory. Springer, New York (1971) · Zbl 0226.70005 |
| [18] | Topputo, F.: Low-thrust non-Keplerian erbits: Analysis, design, and control. PhD Thesis, Politecnico di Milano (2007) |
| [19] | Topputo F., Belbruno E.: Computation of weak stability boundaries: Sun-Jupiter system. Celest. Mech. Dyn. Astron. 105, 3–17 (2009) · Zbl 1223.70053 · doi:10.1007/s10569-009-9222-5 |
| [20] | Topputo, F., Belbruno, E., Gidea, M.: Resonant motion, ballistic escape, and their applications in astrodynamics, Science Direct (2008) |
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