Cosmic Research

, Volume 56, Issue 4, pp 317–330 | Cite as

Design of Interplanetary Transfers with Passive Gravity Assists and Deep Space Maneuvers

  • M. G. ShirobokovEmail author
  • S. P. Trofimov
  • M. Yu. Ovchinnikov


In the paper, the problem of designing interplanetary trajectories with several swing-bys and deep-space maneuvers is solved using the method of virtual trajectories developed by the authors. The algorithms for the calculation of both heliocentric and planetocentric trajectory arcs are presented, including the case of resonant trajectories. The results of applying the method of virtual trajectories to the problem of designing an interplanetary transfer to Jupiter are given and compared with the baseline trajectories for the Juno, Europa Clipper, and Laplace missions.


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  1. 1.
    Di Lizia, P., Radice, G., Izzo, D., and Vasile, M., On the solution of interplanetary trajectory design problems by global optimisation methods, in Proc. Global Optimisation Workshop, Almería, Spain, 2005, pp. 159–164.Google Scholar
  2. 2.
    Okhotsimskii D.E. and Sikharulidze, Yu.G., Osnovy mekhaniki kosmicheskogo poleta (Basics of Space Flight Mechanics), Moscow: Nauka, 1990.Google Scholar
  3. 3.
    Levantovskii, V.I., Mekhanika kosmicheskogo poleta v elementarnom izlozhenii (Elementary Space Flight Mechanics), Moscow: Nauka, 1980.Google Scholar
  4. 4.
    Hughes, G. and McInnes, C.R., Solar sail hybrid trajectory optimisation, Adv. Astronaut. Sci., 2001, vol. 109, pp. 2369–2380.Google Scholar
  5. 5.
    Rogata, P., Di Sotto, E., Graziano, M., and Graziani, F., Guess value for interplanetary transfer design through genetic algorithms, in Proc. 13th AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puerto Rico, 2003, AAS03-140.Google Scholar
  6. 6.
    Dachwald, B., Optimization of solar sail interplanetary trajectories using evolutionary neurocontrol, J. Guid. Control Dyn., 2004, vol. 27, no. 1, pp. 66–72.CrossRefADSGoogle Scholar
  7. 7.
    Wirthman, D.J., Park, S.Y., and Vadali, S.R., Trajectory optimization using parallel shooting method on parallel computer, J. Guid. Control Dyn., 1995, vol. 18, no. 2, pp. 377–379.CrossRefADSGoogle Scholar
  8. 8.
    Hartmann, J.W., Coverstone-Carroll, V.L., and Williams, S.N., Optimal interplanetary spacecraft trajectories via a Pareto genetic algorithm, J. Astronaut. Sci., 1998, vol. 46, no. 3, pp. 267–282.MathSciNetGoogle Scholar
  9. 9.
    Vasile, M., A global approach to optimal space trajectory design, Adv. Astronaut. Sci., 2003, vol. 114, pp. 621–640.Google Scholar
  10. 10.
    Sentinella, M.R., Comparison and integrated use of differential evolution and genetic algorithms for space trajectory optimisation, in Proc. IEEE Congress on Evolutionary Computation, Singapore, 2007.Google Scholar
  11. 11.
    Storn, R.M. and Price, K.V., Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim., 1997, vol. 11, pp. 341–359.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Storn, R.M., Price, K.V., and Lampinen, J.A., Differential Evolution: A Practical Approach to Global Optimization, Springer, Berlin, 2005.zbMATHGoogle Scholar
  13. 13.
    Kennedy, J. and Eberhart, R., Particle swarm optimization, in Proc. IEEE International Conference on Neural Networks, Perth, Australia, 1995.Google Scholar
  14. 14.
    Fedotov, G.G., Optimization of flight trajectories of a spacecraft with electric propulsion using the gravitational maneuver, Cosmic Res., 2004, vol. 42, no. 4, pp. 389–397.CrossRefADSGoogle Scholar
  15. 15.
    Grigoriev, I.S. and Grigoriev, K.G., The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I, Cosmic Res., 2007, vol. 45, no. 4, pp. 339–347.CrossRefADSGoogle Scholar
  16. 16.
    Petukhov, V.G., Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method, Cosmic Res., 2008, vol. 46, no. 3, pp. 219–232.CrossRefADSGoogle Scholar
  17. 17.
    Lancaster, E.R. and Blanchard, R.C., A unified form of Lambert’s theorem, NASA technical note TND-5368, 1969.Google Scholar
  18. 18.
    Gooding, R.H., A procedure for the solution of Lambert’s orbital boundary-value problem, Celestial Mech. Dyn. Astron., 1990, vol. 48, no. 2, pp. 145–165.zbMATHADSGoogle Scholar
  19. 19.
    Kowalkowski, T.D., Johannesen, J.R., and Lam, T., Launch period development for the Juno Mission to Jupiter, Proc. AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, Hawaii, 2008, AIAA2008–7369.Google Scholar
  20. 20.
    Buffington, B., Trajectory design for the Europa Clipper mission concept, Proc. AIAA/AAS Astrodynamics Specialist Conference, San Diego, California, 2014, AIAA2014–4105.Google Scholar
  21. 21.
    Boutonnet, A. and Schoenmaekers, J., JUICE: Consolidated report on mission analysis (CReMA), ESA WP-578, no. 1, Darmstadt, Germany: ESA: 2012.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • M. G. Shirobokov
    • 1
    Email author
  • S. P. Trofimov
    • 1
  • M. Yu. Ovchinnikov
    • 1
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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