Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit

Crewed space missions in recent years have aroused great interest from space agencies since maintaining a human presence in space opens the possibilities of exploring beyond what is known until now. However, guaranteeing this continuous permanence in space stations represents a significant challenge...

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Autores:: Ramírez Zuluaga, Gerardo de Jesús

Tipo de recurso:: Trabajo de grado de pregrado

Fecha de publicación:: 2025

Institución:: Universidad de Antioquia

Repositorio:: Repositorio UdeA

Idioma:: eng

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dc.title.eng.fl_str_mv	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit
title	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit
spellingShingle	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit Manned space flight Vuelos espaciales tripulados Orbital transfer (Space flight) Transferencia orbital (Vuelo espacial) Mathematical optimization Optimización matemática Logistics Logística Astronautics Astronáutica Lunar Gateway (Estación espacial) Resupply plan http://id.loc.gov/authorities/subjects/sh85080584 http://id.loc.gov/authorities/subjects/sh85095313 http://id.loc.gov/authorities/subjects/sh85082127 http://id.loc.gov/authorities/subjects/sh85078128 http://id.loc.gov/authorities/subjects/sh85008947 ODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovación
title_short	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit
title_full	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit
title_fullStr	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit
title_full_unstemmed	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit
title_sort	Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit
dc.creator.fl_str_mv	Ramírez Zuluaga, Gerardo de Jesús
dc.contributor.advisor.none.fl_str_mv	Puerta Ibarra, Juan Francisco
dc.contributor.author.none.fl_str_mv	Ramírez Zuluaga, Gerardo de Jesús
dc.subject.lcsh.none.fl_str_mv	Manned space flight Vuelos espaciales tripulados Orbital transfer (Space flight) Transferencia orbital (Vuelo espacial) Mathematical optimization Optimización matemática Logistics Logística Astronautics Astronáutica
topic	Manned space flight Vuelos espaciales tripulados Orbital transfer (Space flight) Transferencia orbital (Vuelo espacial) Mathematical optimization Optimización matemática Logistics Logística Astronautics Astronáutica Lunar Gateway (Estación espacial) Resupply plan http://id.loc.gov/authorities/subjects/sh85080584 http://id.loc.gov/authorities/subjects/sh85095313 http://id.loc.gov/authorities/subjects/sh85082127 http://id.loc.gov/authorities/subjects/sh85078128 http://id.loc.gov/authorities/subjects/sh85008947 ODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovación
dc.subject.proposal.spa.fl_str_mv	Lunar Gateway (Estación espacial)
dc.subject.proposal.eng.fl_str_mv	Resupply plan
dc.subject.lcshuri.none.fl_str_mv	http://id.loc.gov/authorities/subjects/sh85080584 http://id.loc.gov/authorities/subjects/sh85095313 http://id.loc.gov/authorities/subjects/sh85082127 http://id.loc.gov/authorities/subjects/sh85078128 http://id.loc.gov/authorities/subjects/sh85008947
dc.subject.ods.none.fl_str_mv	ODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovación
description	Crewed space missions in recent years have aroused great interest from space agencies since maintaining a human presence in space opens the possibilities of exploring beyond what is known until now. However, guaranteeing this continuous permanence in space stations represents a significant challenge, especially in the development of this work, which proposes the resupply of a station beyond Earth's orbit. In this work, a resupply strategy is developed for the lunar Gateway station to achieve optimal and efficient planning. The study is divided into two main stages. The first consists of the logistical analysis of the crew's needs to maintain the proper development of their activities in space environment conditions, taking as reference three sources of information in order to generate a daily consumption estimate per crew member for each of the essential resources identified. The second focuses on the optimization of the total Delta V required during the transfer maneuvers, seeking to minimize the fuel mass and, in turn, achieving this reduction to lower the costs associated with each mission; this optimization was achieved using NASA's General Mission Analysis Tool (GMAT), allowing reliable results to be obtained. Subsequently, the integration of both stages makes it possible to generate an optimal and sustainable resupply plan. The results support the proposal of a sustainable and scalable resupply plan capable of adapting to the crew's consumption needs.
publishDate	2025
dc.date.accessioned.none.fl_str_mv	2025-11-13T12:23:36Z
dc.date.issued.none.fl_str_mv	2025
dc.type.none.fl_str_mv	Trabajo de grado - Pregrado
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dc.type.content.none.fl_str_mv	Text
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dc.type.version.none.fl_str_mv	info:eu-repo/semantics/draft
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dc.identifier.citation.none.fl_str_mv	Ramírez Zuluaga, G. J. “Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit”, Bachelor’s degree project, Aerospace Engineering, Universidad de Antioquia, Carmen de Viboral, Antioquia, Colombia, 2025.
dc.identifier.uri.none.fl_str_mv	https://hdl.handle.net/10495/48216
identifier_str_mv	Ramírez Zuluaga, G. J. “Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit”, Bachelor’s degree project, Aerospace Engineering, Universidad de Antioquia, Carmen de Viboral, Antioquia, Colombia, 2025.
url	https://hdl.handle.net/10495/48216
dc.language.iso.none.fl_str_mv	eng
language	eng
dc.relation.references.none.fl_str_mv	[1] B. Hill, “45thSpace Congress “The Next Great Steps”: Space Policy Directive-1,” 2018. [2] M. Smith, D. Craig, N. Herrmann, E. Mahoney, J. Krezel, N. McIntyre, and K. Goodliff, “The artemis program: An overview of nasa’s activities to return humans to the moon,” in 2020 IEEE aerospace conference. IEEE, 2020, pp. 1–10. [3] B. Reeves, “Gateway Payload Users Guide,” 2024. [4] D. E. Lee, “White paper: Gateway destination orbit model: A continuous 15 year nrho reference trajectory,” Tech. Rep., 2019. [5] T. Sasaki, M. Hidaka, Y. Tomita, Y. Hachiya, Y. Kondo, R. Nakamura, and T. Yamamoto, “Proximity Operation and Automated Docking on HTV-X: Guidance, Navigation, and Control Strategy,” in 2022 IEEE Aerospace Conference (AERO). IEEE, 2022, pp. 1–10. [6] Z. Pirtle, K. McBrayer, and A. Beauchemin, “Artemis, ethics and society: Synthesis from a workshop,” in Artemis, Ethics and Society: Synthesis from a Workshop, 2023. [7] R. N. Schmitt, M. F. Becker, D. DeLaurentis, and K. Oguri, “Design of space systems and operational mission architectures using sandbox games,” Acta Astronautica, 2025. [8] E. Lehnhardt, T. Travis, and D. Connell, “The Gateway Program as Part of NASA’s Plans for Human Exploration Beyond Low Earth Orbit,” in 2024 IEEE Aerospace Conference. IEEE, 2024, pp. 1–6. [9] S. Fuller, E. Lehnhardt, J. Olansen, J. S. Mason, D. Connell, T. Travis, and C. Fleming, “Gateway Program Development Progress,” in 75th International Astronautical Congress (IAC), no. IAC-24, B3, 1, 10, x85927. International Astronautical Federation (IAF), 2024. [10] A. Halford, S. Savage, B. Walsh, S. Christe, A. Pulkkinen, P. O’Brien, and A. Young, “Artemis, Gateway, the return to the Moon and forward to Mars for Heliophysics,” in Bulletin of the American Astronomical Society. American Astronomical Society, 2022. [11] S. Fuller, E. Lehnhardt, C. Zaid, and K. Halloran, “Gateway program status and overview,” Journal of Space Safety Engineering, vol. 9, no. 4, pp. 625–628, 2022. [12] E. Lehnhardt, S. Fuller, J. Quasny, D. Connell, C. Zaid, and K. Halloran, “The Gateway as a Building Block for Space Exploration and Development,” in 73rd International Astronautical Congress, no. IAC-22, D3, 1, 1, x69482, 2022. [13] T. Sahinkaya, “International Space Station Resupply Trip Minimization,” 2018. [14] K. Shiraki and N. Tsuji, “Japan’s ISS Program Status,” in 57th International Astronautical Congress, 2005, pp. B4–1. [15] J. S. Parker and G. H. Born, “Direct lunar halo orbit transfers,” The Journal of the astronautical sciences, vol. 56, no. 4, pp. 441–476, 2008. [16] Y. Matsumoto, R. Nakamura, T. Ikenaga, and S. Ueda, “Recovery Orbit Search Scheme for Major Maneuver Failure in NRHO Transfer Orbit Using Lunar Flyby,” in 2023 IEEE Aerospace Conference. IEEE, 2023, pp. 1–9. [17] J. Kikuchi, R. Nakamura, and S. Ueda, “Comparison of transfer trajectory to NRHO and operation plan for logistics resupply mission to gateway,” Acta Astronautica, vol. 223, pp. 577–584, 2024. [18] M. W. Harris, “Locally Optimal Trajectories from Low Lunar Orbit to Near Rectilinear Halo Orbits,” in 2022 IEEE Aerospace Conference (AERO). IEEE, 2022, pp. 1–6. [19] R. Nakamura, J. Kikuchi, T. Sasaki, Y. Matsumoto, M. Hidaka, N. Murakami, S. Ueda, and N. Satoh, “Rendezvous trajectory design of logistics resupply missions to the lunar gateway in near-rectilinear halo orbit,” Journal of Space Safety Engineering, vol. 10, no. 2, pp. 144–154, 2023. [20] J. Kikuchi, R. Nakamura, and S. Ueda, “Extended perilune rendezvous method for low Delta-V transition to NRHO for cargo transportation mission to gateway,” Acta Astronautica, vol. 224, pp. 89–98, 2024. [21] J. C. KING, “A natural first approximation to low-thrust trajectories between satellite orbits of the earth and moon,” AIAA Journal, vol. 3, no. 8, pp. 1432–1439, 1965. [22] S. P. Hughes, D. J. Conway, and J. Parker, “Using the general mission analysis tool (GMAT),” in AAS Guidance and Control Conference, no. GSFC-E-DAA-TN39043, 2017. [23] S. Hughes et al., “General Mission Analysis Tool (GMAT), Product Description,” Goddard Space Flight Center, 2007. [24] NASA Goddard Space Flight Center, GMAT Yukon: General Mission Analysis Tool, NASA, 2020. [Online]. Available: https://documentation.help/gmat/Yukon.html [25] ——, Fmincon Optimizer - GMAT Documentation, NASA, 2020. [Online]. Available: https://documentation.help/gmat/FminconOptimizer.html [26] ——, VF13ad Optimizer - GMAT Documentation, NASA, 2020. [Online]. Available: https://documentation.help/gmat/VF13ad.html [27] J. P. Scott, D. A. Green, G. Weerts, and S. N. Cheuvront, “Body size and its implications upon resource utilization during human space exploration missions,” Scientific Reports, vol. 10, no. 1, p. 13836, 2020. [28] W. Willett, P. J. Skerrett, and E. L. Giovannucci, Eat, drink, and be healthy: the Harvard Medical School guide to healthy eating. Simon and Schuster, 2017. [29] D. A. Schulsinger, “Hydration: Why We Drink, When to Drink, What to Drink, and How Much to Drink, That Is the Question!” in Kidney Stone Disease: Say NO to Stones! Springer, 2014, pp. 175–180. [30] E. Ortiz-Prado, J. F. Dunn, J. Vasconez, D. Castillo, and G. Viscor, “Partial pressure of oxygen in the human body: a general review,” American journal of blood research, vol. 9, no. 1, p. 1, 2019. [31] M. R. Aczel, “What is the nitrogen cycle and why is it key to life?” Frontiers for Young Minds, vol. 7, 2019. [32] A. Riaz, A. Siddique, and N. H. Malik, “Identification of the Factors Responsible for the Usage of Clothes,” Pakistan Journal of Life and Social Sciences, vol. 2, no. 1, pp. 49–50, 2004. [33] UNICEF, “Higiene,” 2025, accedido: 2025-05-05. [Online]. Available: https://www.unicef.org/wash/hygiene [34] L. GAIA, “A CLOSED LOOP HABITAT FOR THE MOON.” [35] P. Wieland, “Designing for human presence in space: an introduction to environmental control and life support systems (ECLSS),” Tech. Rep., 2005. [36] M. K. Ewert and C. Stromgren, “Astronaut mass balance for long duration missions,” in international Conference on Environmental Systems (ICES 2019), no. ICES-2019-126, 2019. [37] M. K. Ewert, E. Orndoff, M. R. Sivik, K. L. Niehaus, W. C. Shearouse, J. M. Zinna, S. G. Patterson, D. L. Muirhead, and W. A. Jackson, “Clothes cleaning research for space exploration,” in International Conference on Environmental Systems 2022, 2022. [38] K. Takada, D. Hornyak, J. Garr, S. Van Keuren, C. Faulkner, and A. ElSherbini, “Status of the advanced oxygen generation assembly,” in International Conference on Environmental Systems, no. ICES-2024-101, 2024. [39] RocketLaunch.Live, “ISS Cargo Launch Schedule,” https://www.rocketlaunch.live/?includePast=1&tag=iss-cargo, accessed: 2025-05-05. [40] B. Barbee, “Mission Planning for the Mitigation of Hazardous Near Earth Objects,” Master of Science in Engineering, The University of Texas, Austin, Texas, 2005. [41] Taitus Software, “Orbital Elements,” n.d. [Online]. Available: https://taitussoftware.com/kb/orbital-elements/ [42] J. L. Russell, “Kepler’s laws of planetary motion: 1609–1666,” The British journal for the history of science, vol. 2, no. 1, pp. 1–24, 1964. [43] D. A. Vallado, Fundamentals of astrodynamics and applications. Springer Science & Business Media, 2001, vol. 12. [44] H. D. Curtis, Orbital mechanics for engineering students. Butterworth-Heinemann, 2019. [45] D.-H. Cho and H. Bnag, “Low-thrust guidance scheme for the spacecraft using B-plane targeting and Lyapunov feedback control,” in 2012 12th International Conference on Control, Automation and Systems. IEEE, 2012, pp. 1969–1973. [46] E. M. Zimovan, K. C. Howell, and D. C. Davis, “Near rectilinear halo orbits and their application in cis-lunar space,” in 3rd IAA Conference on Dynamics and Control of Space Systems, Moscow, Russia, vol. 20, 2017, p. 40. [47] M. Whitmore, J. Boyer, and K. Holubec, “NASA-STD-3001, space flight human-system standard and the human integration design handbook,” in Industrial and systems engineering research conference, no. JSC-CN-25695, 2012. [48] M. Roston, B. Dooley, and H. Ueno, “New Japanese Rocket Is Destroyed During First Test Flight to Space.” The New York Times (Digital Edition), pp. NA–NA, 2023.
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spelling	Puerta Ibarra, Juan FranciscoRamírez Zuluaga, Gerardo de Jesús2025-11-13T12:23:36Z2025Ramírez Zuluaga, G. J. “Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit”, Bachelor’s degree project, Aerospace Engineering, Universidad de Antioquia, Carmen de Viboral, Antioquia, Colombia, 2025.https://hdl.handle.net/10495/48216Crewed space missions in recent years have aroused great interest from space agencies since maintaining a human presence in space opens the possibilities of exploring beyond what is known until now. However, guaranteeing this continuous permanence in space stations represents a significant challenge, especially in the development of this work, which proposes the resupply of a station beyond Earth's orbit. In this work, a resupply strategy is developed for the lunar Gateway station to achieve optimal and efficient planning. The study is divided into two main stages. The first consists of the logistical analysis of the crew's needs to maintain the proper development of their activities in space environment conditions, taking as reference three sources of information in order to generate a daily consumption estimate per crew member for each of the essential resources identified. The second focuses on the optimization of the total Delta V required during the transfer maneuvers, seeking to minimize the fuel mass and, in turn, achieving this reduction to lower the costs associated with each mission; this optimization was achieved using NASA's General Mission Analysis Tool (GMAT), allowing reliable results to be obtained. Subsequently, the integration of both stages makes it possible to generate an optimal and sustainable resupply plan. The results support the proposal of a sustainable and scalable resupply plan capable of adapting to the crew's consumption needs.Las misiones espaciales tripuladas en los últimos años han despertado un gran interés por parte de las agencias espaciales ya que mantener una presencia humana en el espacio abre las posibilidades de explorar más allá de lo que se conoce hasta ahora. Sin embargo, garantizar esta permanencia continua en las estaciones espaciales representa un desafió significativo, sobre todo en el desarrollo de este trabajo que plantea el reabastecimiento de una estación más allá de la orbita terrestre. En este trabajo se desarrolla una estrategia de reabastecimiento para la estación lunar Gateway para lograr una planificación óptima y eficiente. El estudio se divide en dos etapas principales. La primera consta en análisis logístico de las necesidades de los tripulantes para mantener el desarrollo adecuado de sus actividades en condiciones de ambiente espacial, tomando como referencia tres fuentes de información buscando generar un estimado diario de consumo por tripulante para cada uno de los recursos esenciales identificados. La segunda se concentra en la optimización del Delta V total requerido durante las maniobras de transferencia, buscando minimizar la masa del combustible y a su vez, logrando esta reducción disminuir los costos asociados a cada misión, esta optimización se consiguió haciendo uso de la herramienta General Mission Analysis Tool (GMAT) de NASA, permitiendo obtener resultados confiables. Posteriormente la integración de ambas etapas permite generar un plan de reabastecimiento optimo y sostenible. Los resultados respaldan la propuesta de un plan de reabastecimiento sostenible y escalable capaz de adaptarse a las necesidades de consumo de los tripulantes.PregradoIngeniero Aeroespacial102 páginasapplication/pdfengUniversidad de AntioquiaIngeniería AeroespacialEl Carmen de Viboral, ColombiaFacultad de IngenieríaCampus El Carmen de Viboralhttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://purl.org/coar/access_right/c_abf2Manned space flightVuelos espaciales tripuladosOrbital transfer (Space flight)Transferencia orbital (Vuelo espacial)Mathematical optimizationOptimización matemáticaLogisticsLogísticaAstronauticsAstronáuticaLunar Gateway (Estación espacial)Resupply planhttp://id.loc.gov/authorities/subjects/sh85080584http://id.loc.gov/authorities/subjects/sh85095313http://id.loc.gov/authorities/subjects/sh85082127http://id.loc.gov/authorities/subjects/sh85078128http://id.loc.gov/authorities/subjects/sh85008947ODS 9: Industria, innovación e infraestructura. Construir infraestructuras resilientes, promover la industrialización inclusiva y sostenible y fomentar la innovaciónDevelopment of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo OrbitTrabajo de grado - Pregradohttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/redcol/resource_type/TPTexthttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/draft[1] B. Hill, “45thSpace Congress “The Next Great Steps”: Space Policy Directive-1,” 2018.[2] M. Smith, D. Craig, N. Herrmann, E. Mahoney, J. Krezel, N. McIntyre, and K. Goodliff, “The artemis program: An overview of nasa’s activities to return humans to the moon,” in 2020 IEEE aerospace conference. IEEE, 2020, pp. 1–10.[3] B. Reeves, “Gateway Payload Users Guide,” 2024.[4] D. E. Lee, “White paper: Gateway destination orbit model: A continuous 15 year nrho reference trajectory,” Tech. Rep., 2019.[5] T. Sasaki, M. Hidaka, Y. Tomita, Y. Hachiya, Y. Kondo, R. Nakamura, and T. Yamamoto, “Proximity Operation and Automated Docking on HTV-X: Guidance, Navigation, and Control Strategy,” in 2022 IEEE Aerospace Conference (AERO). IEEE, 2022, pp. 1–10.[6] Z. Pirtle, K. McBrayer, and A. Beauchemin, “Artemis, ethics and society: Synthesis from a workshop,” in Artemis, Ethics and Society: Synthesis from a Workshop, 2023.[7] R. N. Schmitt, M. F. Becker, D. DeLaurentis, and K. Oguri, “Design of space systems and operational mission architectures using sandbox games,” Acta Astronautica, 2025.[8] E. Lehnhardt, T. Travis, and D. Connell, “The Gateway Program as Part of NASA’s Plans for Human Exploration Beyond Low Earth Orbit,” in 2024 IEEE Aerospace Conference. IEEE, 2024, pp. 1–6.[9] S. Fuller, E. Lehnhardt, J. Olansen, J. S. Mason, D. Connell, T. Travis, and C. Fleming, “Gateway Program Development Progress,” in 75th International Astronautical Congress (IAC), no. IAC-24, B3, 1, 10, x85927. International Astronautical Federation (IAF), 2024.[10] A. Halford, S. Savage, B. Walsh, S. Christe, A. Pulkkinen, P. O’Brien, and A. Young, “Artemis, Gateway, the return to the Moon and forward to Mars for Heliophysics,” in Bulletin of the American Astronomical Society. American Astronomical Society, 2022.[11] S. Fuller, E. Lehnhardt, C. Zaid, and K. Halloran, “Gateway program status and overview,” Journal of Space Safety Engineering, vol. 9, no. 4, pp. 625–628, 2022.[12] E. Lehnhardt, S. Fuller, J. Quasny, D. Connell, C. Zaid, and K. Halloran, “The Gateway as a Building Block for Space Exploration and Development,” in 73rd International Astronautical Congress, no. IAC-22, D3, 1, 1, x69482, 2022.[13] T. Sahinkaya, “International Space Station Resupply Trip Minimization,” 2018.[14] K. Shiraki and N. Tsuji, “Japan’s ISS Program Status,” in 57th International Astronautical Congress, 2005, pp. B4–1.[15] J. S. Parker and G. H. Born, “Direct lunar halo orbit transfers,” The Journal of the astronautical sciences, vol. 56, no. 4, pp. 441–476, 2008.[16] Y. Matsumoto, R. Nakamura, T. Ikenaga, and S. Ueda, “Recovery Orbit Search Scheme for Major Maneuver Failure in NRHO Transfer Orbit Using Lunar Flyby,” in 2023 IEEE Aerospace Conference. IEEE, 2023, pp. 1–9.[17] J. Kikuchi, R. Nakamura, and S. Ueda, “Comparison of transfer trajectory to NRHO and operation plan for logistics resupply mission to gateway,” Acta Astronautica, vol. 223, pp. 577–584, 2024.[18] M. W. Harris, “Locally Optimal Trajectories from Low Lunar Orbit to Near Rectilinear Halo Orbits,” in 2022 IEEE Aerospace Conference (AERO). IEEE, 2022, pp. 1–6.[19] R. Nakamura, J. Kikuchi, T. Sasaki, Y. Matsumoto, M. Hidaka, N. Murakami, S. Ueda, and N. Satoh, “Rendezvous trajectory design of logistics resupply missions to the lunar gateway in near-rectilinear halo orbit,” Journal of Space Safety Engineering, vol. 10, no. 2, pp. 144–154, 2023.[20] J. Kikuchi, R. Nakamura, and S. Ueda, “Extended perilune rendezvous method for low Delta-V transition to NRHO for cargo transportation mission to gateway,” Acta Astronautica, vol. 224, pp. 89–98, 2024.[21] J. C. KING, “A natural first approximation to low-thrust trajectories between satellite orbits of the earth and moon,” AIAA Journal, vol. 3, no. 8, pp. 1432–1439, 1965.[22] S. P. Hughes, D. J. Conway, and J. Parker, “Using the general mission analysis tool (GMAT),” in AAS Guidance and Control Conference, no. GSFC-E-DAA-TN39043, 2017.[23] S. Hughes et al., “General Mission Analysis Tool (GMAT), Product Description,” Goddard Space Flight Center, 2007.[24] NASA Goddard Space Flight Center, GMAT Yukon: General Mission Analysis Tool, NASA, 2020. [Online]. Available: https://documentation.help/gmat/Yukon.html[25] ——, Fmincon Optimizer - GMAT Documentation, NASA, 2020. [Online]. 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

Development of an Optimal Resupply Strategy for the Lunar Gateway in Near-Rectilinear Halo Orbit

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