Optimization of electric propulsion spacecraft transfer to the libration point L2 of the Earth-Moon system

Dynamics, ballistics, flying vehicles movement control


Starinova O. L.*, Fain M. K.**

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: solleo@mail.ru
**e-mail: fain.maxim@gmail.com


The optimal interplanetary trajectories and the trajectories of flights to the Moon pass near the libration point L1 of the Earth-Moon system. Therefore, there is a growing interest in building a space station on the halo orbit near this point. Establishing such a station would require development of a transport system capable of providing the necessary traffic. Implementation of the electric propulsion will greatly improve the mass efficiency of such transport operations and reduce the cost of creation and maintenance of the station.

The exact solution of the problem was established with the use of the Pontryagin’s maximum principle and the numerical integration. In this work we use the Fedorenko successful linearization method that accepts the limitation on composed functions that have Freshe derivatives. The method is based on making the variation optimal control problem the iteration problem of linear programming.

Contrary to the optimal control choice, here the Sun’s perturbation was accounted. According to the above-stated control program the steering angle λ2 could be neglected. The analysis of the optimal solution shows, that the optimal control program for λ1 has three different segments of operation.

The optimal control programs for the Earth-L1 and L1-L2 transfers and corresponding trajectories were obtained. The results are in good agreement with the results obtained by the Pontryagin’s maximum principle.

The applied method demonstrates its effectiveness for the complex optimization of the SC transportation. Findings may be used to calculate the required design-ballistic parameters of the future lunar missions. The optimal interplanetary trajectories and the trajectories of flights to the Moon pass near the libration point L1 of the Earth-Moon system. The usage of the electric propulsion will greatly improve the mass efficiency of such transport operations and reduce the cost of creation and maintenance of the perspective Moon station.


spacecraft, low thrust transfer, trajectory optimization, libration point, space tug


  1. Jones R.M. Comparison of potential electric propulsion systems for orbit transfer, Journal of Spacecraft and Rockets, 1984, vol. 21, no. 1, pp. 88-95.

  2. Rayman M.D., Williams S.N. Design of the first interplanetary solar electric propulsion mission, Journal of Spacecraft and Rockets, 2002, vol. 39, no. 4, pp. 589-595.

  3. Hermel J., Meese R.A., Rogers W.P., Kushida R.O., Beattie J.R. Modular, ion-propelled, orbit-transfer vehicle, Journal of Spacecraft and Rockets, 1988, vol. 25, no. 5, pp. 368-374.

  4. Andrews D.G., Wetzel E.D. Solar Electric Space Tug to Support Moon and Mars Exploration Missions, AIAA Space 2005 Conference & Exhibit, AIAA-05-6739, AIAA, Long Beach, California, 2005.

  5. Koppel C., Moteurs S., Marchandise F., Estublier D., Jolivet L. The SMART-1 Electric Propulsion Subsystem In-Flight Experience, 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA 2004-3435, AIAA, Fort Lauderdale, Florida, 2004.

  6. Galabova K., Bounova G., de Weck O., Hastings, D. Architecting a family of space tugs based on orbital transfer mission scenarios, AIAA Space 2003 Conference & Exhibit, AIAA 2003-6368, AIAA, Long Beach, CA, 2003.

  7. Loeb H.W., Feili D., Popov G.A., Obukhov V.A., Balashov V.V., Mogulkin A.I., Murashkov V.M., Nesterenko A.N., Khartov S.A. Design of High-Power High-Specific Impulse RF-IonThruster, 32nd International Electric Propulsion Conference, Wiesbaden, Germany, September 11 — 15, 2011. http://erps.spacegrant.org/uploads/images/images/iepc_articledownload_1988-2007/2011index/IEPC-2011-....

  8. Burke L.M., Martini M.C. Oleson S.R. A High Power Solar Electric Propulsion — Chemical Mission for Human Exploration of Mars," 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA 2014-3719, AIAA, Cleveland, OH, 2014

  9. Yang G. Earth-moon Trajectory Optimization Using Solar Electric Propulsion, Chinese Journal of Aeronautics, 2007, vol. 20, no. 5, pp. 452-463.

  10. Geffroy S. Epenoy R. Optimal low-thrust transfers with constraints---generalization of averaging techniques, ActaAstronautica, Volume 41, Number 3, August 1997, pp. 133-149.

  11. Betts J.T., Erb S.O. Optimal low thrust trajectories to the moon. SIAM Journal on Applied Dynamical Systems, 2003, vol. 2, no. 2, pp. 144-170.

  12. Ozimek M.T., Howell K.C. Low-thrust transfers in the Earth-Moon system, including applications to libration point orbits, Journal of Guidance, Control, and Dynamics, 2010, vol. 33, no. 2, pp. 533-549.

  13. Starinova O.L., Kurochkin D.V., Materova I.L. Optimal control choice of non-Keplerian orbits with low-thrust propulsion, (2012, November). In 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012 (Vol. 1493, No. 1, pp. 964-971). AIP Publishing.

  14. McKay R., Macdonald M., Biggs J., McInnes C. Survey of highly non-Keplerian orbits with low-thrust propulsion, Journal of Guidance, Control, and Dynamics, 2011, vol. 34, no. 3, pp. 645-666.

  15. Salmin V.V., Starinova O.L. Kosmicheskie issledovaniya, 2001, vol. 39 no. 1, pp. 51-59.

  16. Kazmerchuk P.V., Malyshev V.V., Usachev V.E. Izvestiya RAN. Teoriya i sistemy upravleniya., 2007, no. 1, pp. 156-167.

  17. Petukhov V.G. Kosmicheskie issledovaniya, 2004, vol. 42, no. 3, pp. 260­279.

  18. Fain M.K., Starinova O.L. Ballistic optimization of the L1-L2 and L2-L1 low thrust transfers in the Earth-Moon system, (2015, June). In 7th International Conference on Recent Advances in Space Technologies: RAST 2015 (pp. 95-98).

  19. Fain M.K., Starinova O.L. The Stepwise Control Laws in the Problem of the Motion Optimization of the Electric Powered Transfers in the Earth-Moon System, Including L1-L2 and L2-L1 Missions, (2015, September). In 2015 International Conference on Environmental Engineering and Remote Sensing: EERS 2015 (pp. 126-129).


mai.ru — informational site MAI

Copyright © 2000-2024 by MAI