Studying optimal spatial trajectories in a low thrust flight within the Earth–Moon system
Published: 02.07.2024
Authors: Kuvshinova E.Yu.
Published in issue: #7(151)/2024
DOI: 10.18698/2308-6033-2024-7-2374
Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control
The paper considers spatial flight of the electric propulsion system powered spacecraft between the low lunar and near-Earth orbits with a minimum time. The paper objective is to assess the influence of characteristic velocity required for a flight between the lunar and near-Earth orbits, such as the trajectory ballistic parameters, flight angular range (true longitude) and the orbital plane position in vicinity of the Earth and the Moon, on the expenses. Thrust vector direction of the electric rocket propulsion system is determined using the Pontryagin maximum principle. Flight trajectories in the Earth—Moon system were optimized in terms of determining the thrust vector direction of the electric rocket propulsion system within the framework of a single formulation (end-to-end trajectory calculation) taking into account the Earth and the Moon gravity (without using the sphere of action method). Their position was determined according to the EPM 2008 ephemeris model.
EDN KOILKC
References
[1] Zakharov Yu.A. Proektirovanie mezhorbitalnykh kosmicheskikh apparatov [Design of inter-orbital spacecraft]. Moscow, Mashinostroenie, 1984, 176 p.
[2] Grishin S.D., Zakharov Yu.A., Odelevsky V.K. Proektirovanie apparatov s dvigatelyami maloy tyagi [Design of spacecraft equipped with low-trust engines]. Moscow, Mashinostroenie, 1990, 224 p.
[3] Pierson B.L., Kluever C.A. Three-stage approach to optimal low-thrust Earth—Moon trajectories. Journal of Guidance, Control and Dynamics, 1994, vol. 17, no. 6, pp. 1275–1282.
[4] Kluever C.A., Pierson B.L. Optimal low-thrust three-dimensional Earth—Moon trajectories. Journal of Guidance, Control and Dynamics, 1995, vol. 18, no. 4, pp. 830–837.
[5] Kluever C.A., Pierson B.L. Optimal Earth—Moon trajectories using nuclear electric propulsion. Journal of Guidance, Control and Dynamics, 1997, vol. 20, no. 2, pp. 239–245.
[6] Casaregola C., Geurts K., Pergola P., Biagioni L., Andrenucci M. Mission analysis and architecture definition for a small electric propulsion transfer module to the Moon. In: Proceedings of the 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. AIAA 2007-5232, Cincinnati, USA, July 8–11, 2007.
[7] Ivashkin V.V., Petukhov V.G. Traektorii pereleta s maloy tyagoy mezhdu orbitami sputnikov Zemli i Luny pri ispolzovanii orbity zakhvata Lunoy [Trajectories for flight between Earth and Moon satellite orbits using intermediate orbit with capture by Moon]. IPM im. M.V. Keldysha RAN. Preprint no. 81 [Keldysh Institute of Applied Mathematics, Russian Academy of Sciences. Preprint no. 81]. Moscow, 2008, 32 p.
[8] Petukhov V.G. Robastnoe kvazioptimalnoe upravlenie s obratnoy svyazyu dlya pereleta s maloy tyagoy mezhdu nekomplanarnymi ellipticheskoy i krugovoy orbitami [Robust suboptimal feedback control for low-thrust transfer between noncoplanar elliptical and circular orbits]. Vestnik MAI — Aerospace MAI Journal, 2010, vol. 17, no. 3, pp. 50–58.
[9] Grebow D.J., Ozimek M.T., Howell K.C. Advanced modeling of optimal low-thrust Lunar pole-sitter trajectories. In: Proceedings of the 60th International Astronautical Congress. IAC-09-C1.5.4, Daejeon, Korea, October 12–16, 2009.
[10] Perez-Palau D., Epenoy R. Indirect optimization of low-thrust Earth–Moon transfers in the Sun–Earth–Moon System. In: Proceedings of the 68th International Astronautical Congress. IAC-17-C1.6.2, Adelaide, Australia, September 25–29, 2017.
[11] Ivanyukhin A.V., Petukhov V.G., Yoon S.W. Traektorii pereleta k Lune s minimalnoy tyagoy [Minimum-thrust flight trajectories to the Moon]. Kosmicheskie issledovaniya — Cosmic Research, 2022, vol. 60, no. 6, pp. 481–490. https://10.1134/S0010952522050033X
[12] Kuvshinova E.Yu. Metodika opredeleniya optimalnoy traektorii pereleta s maloy tyagoy mezhdu okolozemnoy i okololunnoy orbitami [The methodology for determination of optimal flight path with low thrust between the low-Earth and low-Lunar orbits]. Trudy MAI, 2013, iss. 68. Available at: https://www.trudymai.ru/published.php?ID=41742
[13] Powers W.F., Tapley B.D. Canonical transformation applications to optimal trajectory analysis. American Institute of Aeronautics and Astronautics Journal, 1969, vol. 7, no. 3, pp. 394–399. https://doi.org/10.2514/3.5119
[14] Pityeva E.V. et al. Efemeridy EPM2008 [Ephemeris EPM2008]. Institut prikladnoy astronomii RAN [Institute of Applied Astronomy, Russian Academy of Sciences]. https://ftp.iaaras.ru/pub/epm/EPM2008/
[15] Pontryagin L.S., Boltyansky V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimalnykh protsessov [Mathematical theory of the optimal processes]. 4th edition. Moscow, Nauka Publ., 1983, 392 p.
[16] Petukhov V.G. Minimum-thrust problem and its application to trajectory optimization with thrust switchings. In: Proceedings of the 64th International Astronautical Congress. IAC-13-C1.6.2, Beijing, China, September 23–27, 2013.
[17] Fehlberg E. Classical fifth-, sixth-, seventh-, and eighth-order Runge—Kutta formulas with stepsize control. NASA TR R-287, 1968.
[18] Hairer E., Norsett S.P., Wanner G. Solving Ordinary Differential Equations I. Nonstiff Problems. Berlin, Springer-Verlag, 1987 [In Russ.: Khayrer E., Nersett S., Vanner G. Reshenie obyknovennykh differentsialnykh uravneniy. Nezhestkie zadachi. Moscow, Mir Publ., 512 p.].
[19] Butcher J.C. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons, Ltd., The Atrium, 2003.
[20] Shamanskiy E.V. Metody chislennogo resheniya kraevykh zadach na ETsVM. Chast 2. Nelineynye zadachi i zadachi na sobstvennye znacheniya dlya differentsialnykh uravneniy [Methods for numerical solution of boundary value problems on a computer. Part 2. Nonlinear boundary value problems end eigenvalue problems for differential equations]. Kyiv, Naukova Dumka Publ., 1966, 244 p.
[21] Aoki M. Introduction to Optimization Techniques. Fundamentals and Applications of Nonlinear Programming. Macmillan, 1971 [In Russ.: Aoki M. Vvedenie v metody optimizatsii. Osnovy i prilozheniya nelineynogo programmirovaniya. Moscow, Nauka Publ., 1977, 344 p.].
[22] Akhmetshin R.Z. Ploskaya zadacha optimalnogo pereleta kosmicheskogo apparata s maloy tyagoy s vysokoellipticheskoy orbity na geostatsionar [Plane trajectories of optimal transfer of spacecraft with low thrust from elliptical orbit to geostationary one]. Kosmicheskie issledovaniya — Cosmic Research, 2004, vol. 42, no. 3, pp. 238–249.
[23] Kuvshinova E.Yu. Primenenie mnogorazovykh buksirov s yadernoy elektroraketnoy dvigatelnoy ustanovkoy v lunnoy programme [Application of reusable tugs with nuclear electric propulsion system in the lunar program]. Kosmonavtika i raketostroenie — Cosmonautics and Rocket Engineering, 2017, no. 6 (99), pp. 75–80.