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Sun-perturbed earth-to-moon transfers with low energy and moderate flight time

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Abstract

We construct a spacecraft transfer with low cost and moderate flight time from the Earth to the Moon. The motion of the spacecraft is modeled by the planar circular restricted three-body problem including a perturbation due to the solar gravitation. Our approach is to reduce computation of optimal transfers to a non-linear boundary value problem. Using a computer software called AUTO, we solve it and continue its solutions numerically to obtain the optimal transfers. Our result also shows that the use of the solar gravitation can further lower the transfer cost drastically.

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References

  • K. T. Alligood T. D. Sauer J. A. Yorke (1996) Chaos: An Introduction to Dynamical Systems Springer-Verlag New York Occurrence Handle0867.58043

    MATH  Google Scholar 

  • Belbruno, E. A.: 1987, ‘Lunar capture orbit, a method of constructing Earth–Moon trajectories and the lunar GAS mission’, Proceedings of AIAA/DGLR/JSASS International Electric Propulsion Conference, 11–13 May 1987, Colorado Springs, Paper No. AIAA 87-1054.

  • E. A. Belbruno (1994) ‘The dynamical mechanism of ballistic lunar capture transfers from the perspective of invariant manifolds and Hill’s regions’ Centre de Recerca Matematica (CRM), Institute d’Estudis Catalans Barcelona

    Google Scholar 

  • Belbruno, E. A.: 2002, ‘Analytic estimation of weak stability boundaries and low energy transfers’, In: A. Chenciner, R. Cushman, C. Robinson and Z. J. Xia (eds.),Celestial Mechanics, Contemporary Mathematics, Vol. 292, pp. 17–45, American Mathematical Society, Providence.

  • Belbruno, E. A. and Carrico, J. P.: 2000, ‘Calculation of weak stability boundary ballistic lunar transfer trajectories’, Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, 14–17 August 2000, Denver, Paper No. AIAA 2000-4142.

  • Belbruno, E. A., Humble, R. and Coil, J.: 1997, ‘Ballistic capture lunar transfer determination for the U.S. Air Force Academy blue Moon mission’, In: K. C. Howell, D. A. Cicci, J. E. Cochran, Jr. and T. S. Kelso (eds.), AAS/AIAA Spaceflight Mechanics Meeting, 10–12 February 1997, Huntsville, AL, AAS Vol. 95, Part II, pp. 869–880.

  • E. A. Belbruno J. K. Miller (1993) ArticleTitle‘Sun-perturbed Earth-to-Moon transfers with ballistic capture’ J. Guid. Cont. Dyn 16 770–775 Occurrence Handle10.2514/3.21079 Occurrence Handle1993JGCD...16..770B

    Article  ADS  Google Scholar 

  • Bello Mora, M., Graziani, F., Teofilatto, P., Circi, C., Porofilo, M. and Hechler, M.: 2000, ‘A systematic analysis on weak stability boundary–transfers to the Moon’, Proceedings of the 51st International Astronautical Congress, 2-6 October 2000, Rio de Janeiro, Brazil, Paper No. IAF-00-A.6.03.

  • E. M. Bollt J. D. Meiss (1995) ArticleTitle‘Targeting chaotic orbits to the Moon through recurrence’, Phys Lett. A 204 373–378 Occurrence Handle10.1016/0375-9601(95)00502-T Occurrence Handle1995PhLA..204..373B

    Article  ADS  Google Scholar 

  • C. D. Brown (1998) Spacecraft Mission Design 2nd edn American Institute of Aeronautics and Astronautics, Reston, VA

    Google Scholar 

  • E. J. Doedel A. R. Champneys T. F. Fairgrieve Y. A. Kuznetsov B. Sandstede X. Wang (1997) ‘AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont)’ Concordia University Montreal

    Google Scholar 

  • E. J. Doedel R. C. Paffenroth H. B. Keller D. J. Dichmann J. Galán-Vioque A. Vanderbauwhede (2003) ArticleTitle‘Computation of periodic solutions of conservative systems with application to the 3-body problem’, Int. J. Bifurcation Chaos 13 1353–1381 Occurrence Handle10.1142/S0218127403007291 Occurrence Handle1129.70316

    Article  MATH  Google Scholar 

  • J. R. Dormand P. J. Prince (1989) ArticleTitle‘Practical Runge-Kutta processes’ SIAM J. Sci. Stat. Comput 10 977–989 Occurrence Handle10.1137/0910057 Occurrence Handle0704.65053 Occurrence Handle1009550

    Article  MATH  MathSciNet  Google Scholar 

  • E. Hairer S. P. Nørsett G. Wanner (1993) Solving Ordinary Differential Equations I EditionNumber2 Springer-Verlag Berlin Occurrence Handle0789.65048

    MATH  Google Scholar 

  • W. S. Koon M. W. Lo J. E. Marsden S. D. Ross (2000a) ArticleTitle‘Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics’ Chaos 10 427–469 Occurrence Handle10.1063/1.166509 Occurrence Handle0987.70010 Occurrence Handle2000Chaos..10..427K Occurrence Handle1765636

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Koon, W. S., Lo, M. W., Marsden, J. E. and Ross, S. D.: 2000b, ‘Shoot the moon’, In: C. A. Kluever, B. Neta, C. D. Hall and J. M. Hanson (eds.), AAS/AIAA Spaceflight Mechanics Meeting, 23–26 January 2000, Clearwater, FL, AAS Vol. 105, Part II, pp. 1017–1030.

  • W. S. Koon M. W. Lo J. E. Marsden S. D. Ross (2001) ArticleTitle‘Low energy transfer to the Moon’ Celest. Mech. Dynam. Astron 81 63–73 Occurrence Handle10.1023/A:1013359120468 Occurrence Handle0995.70009 Occurrence Handle2001CeMDA..81...63K Occurrence Handle1878097

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • H. E. Nusse J. A. Yorke (1997) Dynamics: Numerical Explorations EditionNumber2 Springer-Verlag New York

    Google Scholar 

  • C. G. Schroer E. Ott (1997) ArticleTitle‘Targeting in Hamiltonian systems that have mixed regular/chaotic phase space’ Chaos 7 512–519 Occurrence Handle10.1063/1.166277 Occurrence Handle12779678 Occurrence Handle0933.37035 Occurrence Handle1997Chaos...7..512S Occurrence Handle1604662

    Article  PubMed  MATH  ADS  MathSciNet  Google Scholar 

  • V. G. Szebehely (1967) Theory of Orbits, The Restricted Problem of Three Bodies Academic Press New York and London

    Google Scholar 

  • V. G. Szebehely H. Mark (1998) Adventures in Celestial Mechanics EditionNumber2 John Wiley and Sons New York Occurrence Handle0954.70001

    MATH  Google Scholar 

  • S. Wiggins (1990) Introduction to Applied Nonlinear Dynamical Systems and Chaos Springer-Verlag New York Occurrence Handle0701.58001

    MATH  Google Scholar 

  • Yagasaki, K.: 2004, ‘Computation of low energy Earth-to-Moon transfers with moderate flight time; Physica (in press).

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Correspondence to Kazuyuki Yagasaki.

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Yagasaki, K. Sun-perturbed earth-to-moon transfers with low energy and moderate flight time. Celestial Mech Dyn Astr 90, 197–212 (2004). https://doi.org/10.1007/s10569-004-0406-8

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