Abstract
The paper considers the ballistic design of spacecraft (SC) transfer to the neighborhood of the L 2 point and subsequent entry of the SC into the halo orbit. Trajectory calculations of one-impulse Earth-halo orbit transfers with and without using a lunar gravitational maneuver are presented. For the calculation of one-impulse trajectories of Earth-halo-orbit transfers, an algorithm for constructing initial approximations is applied. These approximations are constructed by calculating and analyzing the isolines as a function of two variables. This function is represented by the pericenter height of the outgoing orbit over the Earth’s surface. The arguments of the function are special parameters that characterize the halo orbit. The mentioned algorithm allows one to obtain halo orbits with specified geometrical characteristics both in the ecliptic plane, and in the plane orthogonal to it. The estimates of the characteristic velocity expenses for maintaining SC in the selected halo orbit are obtained. The described technique was used to search for working orbits of the Spectr-RG and Millimetron spacecraft. Examples of orbits obtained are presented.
Similar content being viewed by others
References
Markeev, A.P., Tochki libratsii v nebesnoi mekhanike i kosmodinamike (Libration Points in Celestial Mechanics and Cosmodynamics), Moscow: Nauka, 1978.
Marshal, C., The Three-Body Problem, Amsterdam: Elsevier, 1990. Translated under the title Zadacha trekh tel, Moscow-Izhevsk: Inst. Komp. Issled., 2004.
Farquhar, R.W., The Control and Use of Libration-Point Satellites, Ph.D. Dissertation, Stanford, CA: Dept. of Aeronautics and Astronautics, Stanford University, 1968.
Canalias, E., Gomez, G., Marcote, M., and Masdemont, J.J., Assessment of Mission Design Including Utilization of Libration Points and Weak Stability Boundaries, Department de Matematica Aplicada, Universitat Politecnica de Catalunya and Department de Matematica Aplicada, Universitat de Barcellona. http://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-MAD-ARI-03-4103a-InterplanetaryHighways-Barcellona.pdf
Lidov, M.L., Lyakhova, V.A., and Teslenko, N.M., Trajectories of the flight the Earth-Moon-halo-irbit in the neighborhood of the L 2 point of the Earth-Sun system, Cosmic Research, 1992, vol. 30, no. 4, p. 353.
Il’in, I.S., Zaslavsky, G.S., Lavrenov, S.M., et al., Ballistic design of trajectories of transfer from an orbit of Earth’s satellite to a halo-orbit in the neighborhood of L 2 point of the Sun-Earth system, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2013, no. 6. http://keldysh.ru/papers/2013/prep2013_6.pdf
Lidov, M.L., Lyakhova, V.A., and Teslenko, N.M., One-impulse transfer to a conventionally periodic orbit in the neighborhood of L 2 point of the Earth-Sun system and associated problems, Cosmic Research, 1987, vol. 25, no. 2, p. 129.
Eismont, N., Dunham, D., Jen, S.-C., and Farquhar, R., Lunar swingby as a tool for halo-orbit optimization in Relict-2 project, Proc. ESA Symposium on Spacecraft Flight Dynamics, Darmstadt, Germany, September 30–October 4, 1991 (ESA SP-326, December 1991), pp. 435–439.
Lidov, M.L., Lyakhova, V.A., and Teslenko, N.M., Characteristics of control in inserting a spacecraft to neighborhood of L 2 point of the Sun-Earth system with the use of gravity of the Moon (Relict-2 project), Cosmic Research, 1993, vol. 31, no. 5, p. 457.
Il’in, I.S., Sazonov, V.V., and Tuchin, A.G., Construction of restricted orbits in the neighborhood of libration point L 2 of the Sun-Earth system, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2012, no. 65. http://keldysh.ru/papers/2012/prep2012_65.pdf
Il’in, I.S., Sazonov, V.V., and Tuchin, A.G., Trajectory of transfer from a low near-Earth orbit to a manifold of restricted orbits in the neighborhood of libration point L 2 of the Sun-Earth system, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2012, no. 66. http://keldysh.ru/papers/2012/prep2012_66.pdf
Duboshin, G.N., Nebesnaya mekhanika. Analiticheskie i kachestvennye metody (Celestial Mechanics: Analytical and Qualitative Methods), Moscow: Nauka, 1978.
Szebehely, V., Theory of Orbits. The Restricted Problem of Three Bodies, New York-London: Academic Press, 1967. Translated under the title Teoriya orbit: ogranichennaya zadacha trekh tel, Moscow: Nauka, 1982.
Kreisman, B.B., Stable spatial orbits around collinear libration points, Cosmic Research, 2010, vol. 48, no. 3, pp. 265–272.
Gill, P.E., Murray, W., and Wright, M.H., Practical Optimization, London: Academic Press, 1981. Translated under the title Prakticheskaya optimizatsiya, Moscow: Mir, 1985.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.S. Il’in, G.S. Zaslavsky, S.M. Lavrenov, V.V. Sazonov, V.A. Stepanyantz, A.G. Tuchin, D.A. Tuchin, V.S. Yaroshevsky, 2014, published in Kosmicheskie Issledovaniya, 2014, Vol. 52, No. 6, pp. 476–488.
Rights and permissions
About this article
Cite this article
Il’in, I.S., Zaslavsky, G.S., Lavrenov, S.M. et al. Ballistic design of transfer trajectories from artificial-satellite earth orbit to halo orbit in the neighborhood of the L 2 point of the Sun-Earth system. Cosmic Res 52, 437–449 (2014). https://doi.org/10.1134/S0010952514060021
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0010952514060021