Flight Control in a Halo Orbit in Vicinity of the L2 Point in the Earth--Moon System using a Solar Sail

Abstract

n the context of the forthcoming Moon exploration and development initiatives, relay satellites for facilitating communication between the Earth and the Moon, particularly in regard to the far side and Polar Regions of the Moon, where permanent bases are planned, attract significant attention. This study focuses on the solar sails application in controlling motion of such relay satellites aimed at achieving efficient, precise, and long-term orbit keeping. A high-accuracy dynamic model of the spacecraft motion is created based on the ephemeris forecast of the celestial body motion, accompanied by the solar sail dynamic model with the controllable reflectivity. Using these models, the paper determines a reference halo orbit for the solar sail spacecraft in vicinity of the L2 point in the Earth--Moon system (EML2) through application of the multiple-shooting method. Subsequently, a solar sail control algorithm for tracking the reference orbit and applying the sliding mode method is developed, along with determination of the solar sail optimal parameters. A comparative analysis with the China's Queqiao relay satellite that utilizes chemical propulsion for the orbit keeping indicates that introduction of a solar sail could lead to the 66 % reduction in the fuel mass for orbit keeping, and achieving the comparable orbit keeping capabilities

The work was financially supported by the China Scholarship Council

Please cite this article as:

Yu W., Starinova O.L. Flight control in a halo orbit in vicinity of the L2 point in the Earth--Moon system using a solar sail. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2025, no. 2 (153), pp. 70--83. EDN: OWONJP

Литература

[1] Heidmann J. A proposal for a radio frequency interference-free dedicated lunar far side crater for high sensitivity radioastronomy: programmatic issues. Acta Astronaut., 2000, vol. 46, no. 8, pp. 555--558. DOI: https://doi.org/10.1016/S0094-5765(00)00002-3

[2] Li S., Lucey P.G., Milliken R.E., et al. Direct evidence of surface exposed water ice in the lunar polar regions. PNAS, 2018, vol. 115, no. 36, pp. 8907--8912. DOI: https://doi.org/10.1073/pnas.1802345115

[3] Binder A.B. Lunar prospector: overview. Science, 1998, vol. 281, no. 5382, pp. 1475--1476. DOI: https://doi.org/10.1126/science.281.5382.1475

[4] Robinson M.S., Brylow S.M., Tschimmel M., et al. Lunar reconnaissance orbiter camera (LROC) instrument overview. Space Sc. Rev., 2010, vol. 150, no. 1, pp. 81--124. DOI: https://doi.org/10.1007/s11214-010-9634-2

[5] Colaprete A., Elphic R.C., Heldmann J., et al. An overview of the lunar crater observation and sensing satellite (LCROSS). Space Sc. Rev., 2012, vol. 167, no. 1, pp. 3--22. DOI: https://doi.org/10.1007/s11214-012-9880-6

[6] Kato M., Sasaki S., Takizawa Y., et al. The Kaguya mission overview. Space Sc. Rev., 2010, vol. 154, no. 1, pp. 3--19. DOI: https://doi.org/10.1007/s11214-010-9678-3

[7] Dachev T.P., Tomov B.T., Matviichuk Y.N., et al. An overview of RADOM results for Earth and Moon radiation environment on Chandrayaan-1 satellite. Adv. Space Res., 2011, vol. 48, no. 5, pp. 779--791. DOI: https://doi.org/10.1016/j.asr.2011.05.009

[8] Sweetser T.H., Broschart S.B., Angelopoulos V., et al. ARTEMIS mission design. In: The ARTEMIS Mission. Cham, Springer Nature, 2014, pp. 61--91. DOI: https://doi.org/10.1007/978-1-4614-9554-3_4

[9] Xu L., Li H., Pei Z., et al. A brief introduction to the international lunar research station program and the interstellar express mission. Chin. J. Space Sc., 2022, vol. 42, no. 4, pp. 511--513. DOI: https://doi.org/10.11728/cjss2022.04.yg28

[10] Zhdanov V.L. [Russian-Chinese international cooperation in the field of space exploration]. Fundamentalnye i prikladnye nauchnye issledovaniya: aktualnye voprosy, dostizheniya i innovatsii. Sb. st. LXII Mezhdunar. nauch.-prakt. konf. [Fundamental and applied scientific research: topical issues, achievements and innovations. Proc. LXII Int. Sc.-Pract. Conf.]. Penza, Nauka i Prosveshchenie Publ., 2022, pp. 313--315 (in Russ.). EDN: ORPSJZ

[11] Lihua Z., Liang X., Ji S., et al. One year on-orbit operation of queqiao lunar relay communications satellite. Aerospace China, 2019, vol. 20, no. 3, pp. 5--13. DOI: https://doi.org/10.3969/j.issn.1671-0940.2019.03.001

[12] Folta D., Woodard M., Cosgrove D. Stationkeeping of the first Earth--Moon libration orbiters: the ARTEMIS mission. AAS/AIAA Astrodynamics Specialist Conf., 2011, vol. 142, pp. 1697--1715.

[13] Lei L., Jianfeng C., Songji H., et al. Maintenance of relay orbit about the Earth--Moon collinear libration points. Journal of Deep Space Exploration, 2015, vol. 2, no. 4, pp. 318--324. DOI: https://dx.doi.org/10.15982/j.issn.2095-7777.2015.04.004

[14] Gao S., Zhou W.Y., Zhang L., et al. Trajectory design and flight results for Change 4-relay satellite. Sc. Sin. Technol., 2019, vol. 49, no. 2, pp. 156--165. DOI: https://doi.org/10.1360/N092018-00393

[15] Jianfeng D., Xie L., Cuilan L., et al. Orbit determination and analysis of Chang’E-4 relay satellite on mission orbit. Journal of Deep Space Exploration, 2019, vol. 6, no. 3, pp. 247--253. DOI: https://dx.doi.org/10.15982/j.issn.2095-7777.2019.03.008

[16] Tsuda Y., Mori O., Funase R., et al. Achievement of IKAROS --- Japanese deep space solar sail demonstration mission. Acta Astronaut., 2013, vol. 82, no. 2, pp. 183--188. DOI: https://doi.org/10.1016/j.actaastro.2012.03.032

[17] Zhao J., Tian Q., Hu H.Y. Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate-based method. Acta Mech. Sin., 2013, vol. 29, no. 1, pp. 132--142. DOI: https://doi.org/10.1007/s10409-013-0002-9

[18] Yu W., Starinova O.L. Study on displaced orbits below the Moon’s south pole near l2 point based on solar sail. Mekhatronika, Avtomatizatsiya, Upravlenie, 2023, vol. 24, no. 12, pp. 652--659. DOI: https://doi.org/10.17587/mau.24.652-659

[19] Yu W., Wu K. [Characteristics and method of maintaining the motion of a solar sail in a halo orbit near point L2 in the Earth--Moon system]. Aviatsiya i kosmonavtika. Tez. 20 Mezhdunar. konf. [Aviation and Cosmonautics. Abs. 20th Int. Conf.]. Moscow, Pero Publ., 2021, pp. 372--374 (in Russ.). EDN: TTSTFY

[20] Khabibullin R.M., Starinova O.L. An analysis of guided motion of a research spacecraft with a solar sail. Izvestiya vysshikh uchebnykh zavedeniy, Mashinostroyeniye [BMSTU Journal of Mechanical Engineering], 2019, no. 12, pp. 94--103 (in Russ.).DOI: http://dx.doi.org/10.18698/0536-1044-2019-12-94-103

[21] Bray T.A., Gouclas C.L. Doubly symmetric orbits about the collinear Lagrangian points. Astron. J., 1967, no. 72, pp. 202--213. DOI: https://doi.org/10.1086/110218

[22] Breakwell J.V., Brown J.V. The ‘halo’ family of 3-dimensional periodic orbits in the Earth--Moon restricted 3-body problem. Celest. Mech., 1979, vol. 20, no. 4, pp. 389--404. DOI: https://doi.org/10.1007/BF01230405

[23] Howell K.C. Families of orbits in the vicinity of the collinear libration points. J. Astronaut. Sc., 2001, vol. 49, pp. 107--125. DOI: https://doi.org/10.1007/BF03546339

[24] Chunzhui D., Fain M.K., Starinova O.L. Analysis and design of halo orbits in cislunar space. IOP Conf. Ser.: Mater. Sc. Eng., 2020, vol. 984, pp. 12--33. DOI: https://doi.org/10.1088/1757-899X/984/1/012033