Abstract
In this paper, a technique for the analysis and the design of low-energy interplanetary transfers, exploiting the invariant manifolds of the restricted three-body problem, is presented. This approach decomposes the full four-body problem describing the dynamics of an interplanetary transfer between two planets, in two three-body problems each one having the Sun and one of the planets as primaries; then the transit orbits associated to the invariant manifolds of the Lyapunov orbits are generated for each Sun-planet system and linked by means of a Lambert’s arc defined in an intermediate heliocentric two-body system.
The search for optimal transit orbits is performed by means of a dynamical Poincaré section of the manifolds. A merit function, defined on the Poincaré section, is used to optimally generate a transfer trajectory given the two sections of the manifolds. Due to the high multimodality of the resulting optimization problem, an evolutionary algorithm is used to find a first guess solution which is then refined, in a further step, using a gradient method. In this way all the parameters influencing the transfer are optimized by blending together dynamical system theory and optimization techniques.
The proposed patched conic-manifold method exploits the gravitational attractions of the two planets in order to change the two-body energy level of the spacecraft and to perform a ballistic capture and a ballistic repulsion. The effectiveness of this approach is demonstrated by a set of solutions found for transfers from Earth to Venus and to Mars.
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JEHN, R., CAMPAGNOLA, S., GARCIA, Y., and KEMBLE, S. “Low-Thrust Approach and Gravitational Capture at Mercury,” 18th Symposium on Space Flight Dynamics, Munich, Germany, October 11–15, 2004.
BELBRUNO, E. A. and MILLER, J. K. “Sun-Perturbated Earth-to-Moon Transfers with Ballistic Capture,” Journal of Guidance, Control and Dynamics, Vol. 16, No. 3, July-August 1993, pp. 770–775.
LLIBRE, J., MARTÌNEZ, R., and SIMÒ, C. “Transversality of the Invariant Manifolds associated to the Periodic Orbits near L2 in the Restricted Three-Body Problem,” Journal of Differential Equations, No. 58, 1985, pp. 104–156.
HOWELL, K. C., BARDEN, B. T., and LO, M. W. “Application of Dynamical System Theory to Trajectory Design for a Libration Point Mission,” The Journal of the Astronautical Sciences, Vol. 45, No. 2, April-June 1997, pp. 161–178.
KOON, W. S., LO, M. W., MARSDEN, J. E., and ROSS, S. D. “Heteroclinic Connections Between Periodic Orbits and Resonance Transition in Celestial Mechanics,” Chaos, Vol. 10, No. 2, June 2000, pp. 427–469.
KOON, W. S., LO, M. W., MARSDEN, J. E., and ROSS, S. D. “Low Energy Transfers to the Moon,” Celestial Mechanics and Dynamical Astronomy, Vol. 81, No. 1, September 2001, pp. 63–73.
KOON, W. S., LO, M. W., MARSDEN, J. E., and ROSS, S. D. “Constructing a Low Energy Transfer Between Jovian Moons,” Contemporary Mathematics, Vol. 292, February 2002, pp. 129–145.
SZEBEHELY, V. Theory of Orbits: the Restricted Problem of Three Bodies, Academic Press Inc., New York, 1967.
GÒMEZ, G. and MONDELO, J. M. “The Dynamics Around the Collinear Equilibrium Points of the RTBP,” Physica D, Vol. 157, October 2001, pp. 283–321.
JORBA, A. and MASDEMONT, J. “Dynamics in the Center Manifold of the Collinear Points of the Restricted Three Body Problem,” Physica D, Vol. 132, July 1999, pp. 189–213.
YAMATO, H. and SPENCER, D. “Transit-Orbit Search for Planar Restricted Three-Body Problem with Perturbations,” Journal of Guidance, Control and Dynamics, Vol. 27, December 2004, pp. 1035–1045.
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Topputo, F., Vasile, M. & Bernelli-Zazzera, F. Low Energy Interplanetary Transfers Exploiting Invariant Manifolds of the Restricted Three-Body Problem. J of Astronaut Sci 53, 353–372 (2005). https://doi.org/10.1007/BF03546358
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DOI: https://doi.org/10.1007/BF03546358