Gravity-assist maneuvers in implementation of Martian manned expedition with an electric rocket propulsion
Authors: Sinitsin A.A.
Published in issue: #8(92)/2019
DOI: 10.18698/2308-6033-2019-8-1912
Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control
The paper focuses on the analysis of energy-ballistic efficiency of gravity-assist maneuvers in the implementation of the Martian manned expedition in the period 2049–2050. The purpose of this analysis was to identify the opportunities for improving the energy-ballistic performance indicators of the Martian manned expedition through gravity-assist maneuvers around the Earth and Venus. The methodical approach to calculating the main energy-ballistic indicators of the Martian manned expedition is based on dividing the flight trajectory into sections. To determine the main characteristics of these sections, the statement corresponding to the restricted two-body problem was used. The heliocentric trajectory sections were optimized using the Pontryagin maximum principle. The families of solutions with a gravity-assist maneuver near Venus were obtained, differing in the direction of the flyby of Venus and the height of the flight orbit pericenter. The research shows the existence of extremals close in characteristics, which are with the fly-by orbit pericenter altitude restriction and without it. A comparison was made in terms of the duration of the expedition and the initial mass with solutions without a gravity-assist maneuver.
References
[1] Abdulkhalikov R.M., Adov A.A., Akimov V.N., et al. Pilotiruemaya expeditsiya na Mars [Martian manned expedition]. Koroteev A.S. ed. Moscow, Tsiolkovsky Russian Academy of Cosmonautics Publ., 2006, 320 p.
[2] Bezyaev I.V., Stoyko S.F. Kosmicheskaya tekhnika i tekhnologii — Space Engineering and Technology, 2018, no. 3 (22), pp. 17–31.
[3] Sevastyanov N.N., Sinyavskiy V.V., Yuditskiy V.D. Izvestiya RAN. Energetika — Proceedings of the Russian Academy of Sciences. Power Engineering, 2007, no. 3, pp. 46–56.
[4] Konstantinov M.S., Leb Kh.V., Petukhov V.G., Popov G.A. Trudy MAI (Proceedings of MAI), 2011, no. 42. Available at: http://trudymai.ru/published.php?ID=24274 (accessed May 13, 2019).
[5] Lebedev V.N. Raschet dvizheniya kosmicheskogo apparata s maloy tyagoy. Matematicheskie metody v dinamike kosmicheskikh apparatov. Vypusk no. 5 [Calculation of low trust spacecraft motion. Mathematical methods in the spacecraft dynamics. No. 5.]. Moscow, Computing Center of the Academy of Sciences of the USSR, 1968, 108 p.
[6] Fedotov G.G. Kosmicheskie issledovaniya — Cosmic Research, 2001, vol. 39, no. 6, pp. 613–621.
[7] Pontryagin L.S., Boltyanskiy V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimalnykh protsessov [Mathematical theory of optimal processes]. Moscow, Nauka Publ., 1983, 392 p.
[8] Bryson Jr A.E., Yu-Chi Ho. Applied Optimal Control. Optimization, Estimation and Control. Waltham, Massachusetts, Toronto, London, 1969. [In Russ.: Bryson Jr A.E., Yu-Chi Ho. Prikladnaya teoriya optimalnogo upravleniya. Moscow, Mir Publ., 1972, 544 p.].
[9] Hairer E., Norsett S.P., Wanner G. Solving Ordinary Differential Equations, Nonstiff Problems. Berlin, Heidelberg, Springer-Verlag, 1987, 528 p. [In Russ.: Hairer E., Norsett S.P., Wanner G. Reshenie obyknovennykh differentsialnykh uravneniy. Nezhestkie zadachi. Moscow, Mir Publ., 1990, 512 p.].
[10] Piteva E.V., et al. Efemeridy EPM2008 [Ephemeris EPM2008]. Available at: ftp://quasar.ipa.nw.ru/incoming/EPM/EPM2008 (accessed May 13, 2019).
[11] Colasurdo G., Casalino L., Pastrone D. Optimization of V Earth-Gravity-Assist Trajectories. Journal of Guidance, Control and Dynamics, November–December 1998, vol. 21, no. 6, pp. 991–995.
[12] Casalino L., Colasurdo G., Pastrone D. Optimal Low-Thrust Escape Trajectories Using Gravity Assist. Journal of Guidance, Control and Dynamics, September–October 1999, vol. 22, no. 5, pp. 637–642.
[13] Fedotov G.G. Kosmicheskie issledovaniya — Cosmic Research, 2004, vol. 42, no. 4, pp. 404–413.
[14] Konstantinov M.S., Thein M. Method of interplanetary trajectory optimization for the spacecraft with low thrust and swing-bys. Acta Astronautica, 136 (2017), pp. 297–311.
[15] Konstantinov M.S., Petukhov V.G., Thein M. Optimizatsiya traektorii geliotsentricheskikh pereletov [Optimization of trajectories of heliocentric flights]. Moscow, MAI Publ., 2015, 260 p.
[16] Orlov A.A. Optimizatsiya slozhnykh skhem pereleta KA s elektroraketnymi dvigatelyami pri granichnykh usloviyakh smeshannogo tipa. Diss. … kand. tekh. nauk [Optimization of complex flight patterns of spacecraft with electric propulsion under mixed boundary conditions. Cand. eng. sc. diss.]. Moscow, MAI Publ., 2018, 155 p.
[17] Marec J.P. Optimal Space Trajectories. Elsevier Scientific Publ., 1979.
[18] Sinitsyn А.А. Kosmicheskaya tekhnika i tekhnologii — Space Engineering and Technology, 2016, no. 4 (15), pp. 80–90.