Abstract
The stable distant retrograde orbits (DROs) around the Moon are considered as potential parking orbits for cislunar stations that are important facilities in cislunar space. Transfer orbits from DROs to lunar orbits will be fundamental and routine for operations of the cislunar stations. This paper studies transfer orbits from DROs to low lunar orbits with inclinations between 0° and 90°. Ten DROs are selected for the construction of transfers. The planar transfer orbits from each DRO to the LLO with zero inclination are firstly obtained and compared in the planar circular restricted three-body problem (PCR3BP) to reveal basic characteristics of the transfer solutions. The planar transfers are classified into several types based on characteristics. Each type is discussed in details, especially their transfer cost and time. Based on the planar transfers, nonplanar transfer orbits are constructed in the circular restricted three-body problem (CR3BP). Some nonplanar transfers are selected and compared to show effects of the LLO inclination. Then, the planar transfer orbits are refined in the planar bicircular restricted four-body problem (PBR4BP) with the gravity of the Sun. The comparison between results in the PCR3BP and PBR4BP shows that the gravity of the Sun can increase transfer options and reduce the transfer cost. Further analysis is carried out based on the realistic results in the PBR4BP, including the ballistic capture, departure and insertion locations, transfer cost and time, etc. The results are useful for selecting parking DROs and designing transport systems to the Moon.
Similar content being viewed by others
References
Belbruno, E., Miller, J.: A ballistic lunar capture trajectory for the Japanese spacecraft hiten. Jet Propulsion Laboratory, IOM 312/90.4–1371-EAB (1990)
Belbruno, E., Miller, J.: Sun-perturbed Earth-to-Moon transfers with ballistic capture. J. Guid. Control Dyn. 16, 770–775 (1993)
Belbruno, E.: Lunar capture orbits, a method of constructing Earth–Moon trajectories and the lunar GAS mission. In: AIAA Paper 971054, Proceedings of the AIAA/DGLR/JSASS International Electric Propulsion Conference (1987)
Boudad, K., Howell, K., Davis, D.: Near rectilinear halo orbits in cislunar space within the context of the bicircular four-body problem. In: 2nd IAA/AAS SciTech Forum, Moscow, Russia (2019)
Broucke, R.A.: Periodic orbits in the restricted three body problem with earth-moon masses (1968)
Bucci, L., Colagrossi, A., Lavagna, M.: Rendezvous in lunar near rectilinear halo orbits. Adv. Astronaut. Sci. Technol. 1(1), 39–43 (2018)
Capdevila L., Guzzetti D., Howell K.: Various transfer options from Earth into distant retrograde orbits in the vicinity of the Moon. In: AAS/AIAA Space Flight Mechanics Meeting, p. 118 (2014)
Capdevila, L., Howell, K.: A transfer network linking Earth, Moon, and the triangular libration point regions in the Earth-Moon system. Adv. Space Res. 62(7), 1826–1852 (2018)
Conte, D.Di, Carlo, M., Ho, K., David, B., Massimiliano, V.: Earth-Mars transfers through Moon distant retrograde orbits. Acta Astron. 143, 372–379 (2018)
Crusan J., Bleacher J., Caram J., et al.: NASA’s Gateway: An Update on Progress and Plans for Extending Human Presence to Cislunar Space//2019 IEEE Aerospace Conference. IEEE, pp. 1–19 (2019)
Davis, D.C., Bhatt, S.A., Howell, K.C., et al.: Orbit maintenance and navigation of human space-craft at cislunar near rectilinear halo orbits. 27th AAS/AIAA Space Flight Mechanics Meeting, San-Antonio, TX, USA, February 5–9, 2017, Paper AAS 17-269, 20 p. (2017)
Demeyer, J., Gurfil, P.: Transfer to distant retrograde orbits using manifold theory. J. Guid. Control Dyn. 30(5), 1261–1267 (2007)
Enright, P.J., Conway, B.A.: Discrete approximations to optimal trajectories using direct transcription and nonlinear programming. J. Guid. Control Dyn. 15, 994–1002 (1992)
Folta D.C., Bosanac N., Cox A., Howell, K.: The lunar IceCube mission design: construction of feasible transfer trajectories with a constrained departure. In: AAS/AIAA Space Flight Mechanics Meeting, Napa, California (2016)
Guzzetti, D., Zimovan, E.M., Howell, K., et al.: Stationkeeping analysis for spacecraft in lunar near rectilinear halo orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting, pp. 1–20 (2017)
Hénon, M.: Numerical exploration of the restricted problem, V. Astron. Astrophys. 1, 223–238 (1969)
Howell, K., Breakwell, J.: Almost rectilinear halo orbits. Celest. Mech. 32(1), 29–52 (1984)
Howell, K.: Three-dimensional, periodic, ‘halo’ orbits. Celest. Mech. 32(1), 53–71 (1984)
ISECG: The Global Exploration Roadmap (2018). https://www.globalspace-exploration.org/wordpress/wpcontent/isecg/GER_2018_small_mobile.pdf. Retrieved 12 Jun 2018
Koon, W.S., Lo, M.W., Marsden, J.E., et al.: Dynamical Systems, the Three-Body Problem and Space Mission Design. California Institute of Technology, Pasadena (2006)
Koon, W.S., Lo, M.W., Marsden, J.E., et al.: Low energy transfer to the Moon. Celest. Mech. Dyn. Astron. 81(1–2), 63–73 (2001)
Markellos, V.V.: Numerical investigation of the planar restricted three-bodyproblem. Celest. Mech. 10(1), 87–134 (1974)
Ming, X., Shijie, X.: Exploration of distant retrograde orbits around Moon. Acta Astron. 65(5-6), 853–860 (2009)
Ocampo, C., Rosborough, G.: Transfer trajectories for distant retrograde orbiters of the Earth. Adv. Astron. Sci. 82, 1177–1200 (1993)
Oshima, K., Topputo, F., Yanao, T.: Low-energy transfers to the Moon with long transfer time. Celest. Mech. Dyn. Astron. 131(1), 4 (2019)
Oshima, K.: The use of vertical instability of L1 and L2 planar Lyapunov orbits for transfers from near rectilinear halo orbits to planar distant retrograde orbits in the Earth-Moon system. Celest. Mech. Dyn. Astron. 131(3), 14 (2019)
Scott, C., Spencer, D.: Calculating transfer families to periodic distant retrograde orbits using differential correction. J. Guid. Control Dyn. 33(5), 1592–1605 (2010a)
Scott, C., Spencer, D.: Transfers to sticky distant retrograde orbits. J. Guid. Control Dyn. 33(6), 1940–1946 (2010b)
Short, C., Howell, K., Haapala, A., Dichmann, D.: Mode analysis for long-term behavior in a resonant Earth-Moon trajectory. J. Astronaut. Sci. 64, 156–187 (2017)
Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. From Newton to Chaos. Plenum Press, New York (1995)
Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press Inc, New York (1967)
Topputo, F., Zhang, C.: Survey of direct transcription for low-thrust space trajectory optimization with applications. In: Abstract and Applied Analysis. Hindawi (2014)
Topputo, F.: On optimal two-impulse Earth-Moon transfers in a four-body model. Celest. Mech. Dyn. Astron. 117, 279–313 (2013)
Trofimov, S., Shirobokov, M., Tselousova, A., et al.: Transfers from near-rectilinear halo orbits to low-perilune orbits and the Moon’s surface. Acta Astron. 167, 260–271 (2020)
Whitley, R., Martinez, R.: Options for staging orbits in cislunar space. In: 2016 IEEE Aerospace Conference. IEEE, pp. 1–9 (2016)
Winter, O.C.: The stability evolution of a family of simply periodic lunar orbits. Planet. Space Sci. 48(1), 23–28 (2000)
Yagasaki, K.: Sun-perturbed Earth-to-Moon transfers with low energy and moderate flight time. Celest. Mech. Dyn. Astron. 90, 197–212 (2004)
Zimovan, E.M., Howell, K.C., Davis, D.C.: Near rectilinear halo orbits and their application in cis-lunar space. In: 3rd IAA Conference on Dynamics and Control of Space Systems, Moscow, Russia. 20 (2017)
Acknowledgements
YW thanks the support of the National Natural Science Foundation of China (11872007) and the Fundamental Research Funds for the Central Universities. HZ thanks the support of the Key Research Program of the Chinese Academy of Sciences (ZDRW-KT-2019-1-0102).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they do not have any commercial or associative interest that represents a conflict of interest in connection with the paper submitted.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article is part of the topical collection on Toward the Moon and Beyond.
Guest Editors: Terry Alfriend, Pini Gurfil and Ryan P. Russell.
Rights and permissions
About this article
Cite this article
Zhang, R., Wang, Y., Zhang, H. et al. Transfers from distant retrograde orbits to low lunar orbits. Celest Mech Dyn Astr 132, 41 (2020). https://doi.org/10.1007/s10569-020-09982-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10569-020-09982-4