Advertisement

Celestial Mechanics and Dynamical Astronomy

, Volume 90, Issue 3–4, pp 197–212 | Cite as

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

  • Kazuyuki Yagasaki
Article

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.

Keywords

Earth-to-Moon transfer perturbed three-body problem non-linear boundary value problem numerical continuation stable and unstable manifolds chaos space mission design 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alligood, K. T., Sauer, T. D., Yorke, J. A. 1996Chaos: An Introduction to Dynamical SystemsSpringer-VerlagNew YorkMATHGoogle Scholar
  2. 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. Google Scholar
  3. Belbruno, E. A. 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 CatalansBarcelonaCRM Research Report No. 270Google Scholar
  4. 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.Google Scholar
  5. 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. Google Scholar
  6. 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. Google Scholar
  7. Belbruno, E. A., Miller, J. K. 1993‘Sun-perturbed Earth-to-Moon transfers with ballistic capture’J. Guid. Cont. Dyn16770775CrossRefADSGoogle Scholar
  8. 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. Google Scholar
  9. Bollt, E. M., Meiss, J. D. 1995‘Targeting chaotic orbits to the Moon through recurrence’, PhysLett. A204373378CrossRefADSGoogle Scholar
  10. Brown, C. D. 1998Spacecraft Mission Design2nd ednAmerican Institute of Aeronautics and Astronautics, Reston, VAGoogle Scholar
  11. Doedel, E. J., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Sandstede, B., Wang, X. 1997‘AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont)’Concordia UniversityMontrealGoogle Scholar
  12. Doedel, E. J., Paffenroth, R. C., Keller, H. B., Dichmann, D. J., Galán-Vioque, J., Vanderbauwhede, A. 2003‘Computation of periodic solutions of conservative systems with application to the 3-body problem’, Int. J. Bifurcation Chaos1313531381CrossRefMATHGoogle Scholar
  13. Dormand, J. R., Prince, P. J. 1989‘Practical Runge-Kutta processes’SIAM J. Sci. Stat. Comput10977989CrossRefMATHMathSciNetGoogle Scholar
  14. Hairer, E., Nørsett, S. P., Wanner, G. 1993Solving Ordinary Differential Equations I2Springer-VerlagBerlinMATHGoogle Scholar
  15. Koon, W. S., Lo, M. W., Marsden, J. E., Ross, S. D. 2000a‘Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics’Chaos10427469CrossRefMATHADSMathSciNetGoogle Scholar
  16. 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. Google Scholar
  17. Koon, W. S., Lo, M. W., Marsden, J. E., Ross, S. D. 2001‘Low energy transfer to the Moon’Celest. Mech. Dynam. Astron816373CrossRefMATHADSMathSciNetGoogle Scholar
  18. Nusse, H. E., Yorke, J. A. 1997Dynamics: Numerical Explorations2Springer-VerlagNew YorkGoogle Scholar
  19. Schroer, C. G., Ott, E. 1997‘Targeting in Hamiltonian systems that have mixed regular/chaotic phase space’Chaos7512519CrossRefPubMedMATHADSMathSciNetGoogle Scholar
  20. Szebehely, V. G. 1967Theory of Orbits, The Restricted Problem of Three BodiesAcademic PressNew York and LondonGoogle Scholar
  21. Szebehely, V. G., Mark, H. 1998Adventures in Celestial Mechanics2John Wiley and SonsNew YorkMATHGoogle Scholar
  22. Wiggins, S. 1990Introduction to Applied Nonlinear Dynamical Systems and ChaosSpringer-VerlagNew YorkMATHGoogle Scholar
  23. Yagasaki, K.: 2004, ‘Computation of low energy Earth-to-Moon transfers with moderate flight time; Physica (in press).Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of Mechanical and Systems EngineeringGifu UniversityGifuJapan

Personalised recommendations