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Stable spatial orbits around collinear libration points

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Abstract

A technique of generation of spatial periodic solutions to the restricted circular three-body problem from periodic orbits of the planar problem has been used for the families of orbits around collinear libration points L 1 and L 2. Developing the families obtained at the 1: 1 resonance, we have obtained stable solutions both in the Earth-Moon system and in the Sun-Earth system. Of course, the term “around the libration point” is rather conventional; the obtained orbits become more similar to the orbits around the smaller attracting body. The further development of the family of orbits “around” the libration point L 2 in the Sun-Earth system made it possible to find the orbits satisfying the new, much more rigorous constraints on cooling the spacecraft of the Millimetron project.

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References

  1. Kreisman, B.B., Investigation of the Millimetron Spacecraft Orbits, Most Promising for Solving the Posed Scientific Problems, in Materialy tekhnicheskikh predlozhenii po KNA observatorii “Millimetron”, (Technical Proposal for Space Research Laboratory Millimetron), Moscow: Astro Space Center of Lebedev Phys. Inst., 2006, Part 2.

    Google Scholar 

  2. Kreisman, B.B., Stable Spatial Orbits around Collinear Libration Points, in Tezisy dokladov XXXI akademicheskikh chtenii po kosmonavtike (Abstracts of Reports of the 31st Academic Readings in Astronautics), Moscow, 2007.

  3. Kreisman, B.B., Families of Periodic Solutions in Three-Dimensional Restricted Three-Body Problem, Kosm. Issled., 2009, vol. 47, no. 1, pp. 64–78. [Cosmic Research, pp. 53–67].

    Google Scholar 

  4. Kreisman, B.B., Application of Periodic Solutions of Three-Dimensional Three-Body Problem to Designing the Orbit of a Space Telescope, Kosm. Issled., 2009, vol. 47, no. 5, pp. 444–452. [Cosmic Research, pp. 409–416].

    Google Scholar 

  5. Szebehely, V., Theory of Orbits. The Restricted Problem of Three Bodies, New York and London: Academic Press, 1967. Translated under the title Teoriya orbit: ogranichennaya zadacha trekh tel, Moscow: Nauka, 1982.

    Google Scholar 

  6. Poincare, H., Novye metody nebesnoi mekhaniki, Izbrannye trydy, T. 1, 2 (New Methods of Celestial Mechanics, Selected Papers, vols. 1 and 2), Moscow: Nauka, 1972.

    Google Scholar 

  7. Goudas, C.L., Three-Dimensional Periodic Orbits and Their Stability, Icarus, 1963, no. 2, pp. 1–18.

  8. Henon, M., Vertical Stability of Periodic Orbits in the Restricted Problem, Astron. Astrophys., 1973, vol. 28, no. 3, pp. 415–426.

    ADS  Google Scholar 

  9. Lidov, M.L., One Family of Three-Dimensional Periodic Orbits near the Moon and Planets, Dokl. Akad. Nauk SSSR, 1977, vol. 233, no. 6, pp. 1068–1071.

    ADS  Google Scholar 

  10. Zagouras, C. and Markellos, V.V., Axisymmetric Periodic Orbits in the Restricted Problem in Three Dimensions, Astron. Astrophys., 1977, vol. 59, no. 1, pp. 79–89.

    MATH  MathSciNet  ADS  Google Scholar 

  11. Markellos, V.V., Bifurcation of Plane with Three-Dimensional Asymmetric Periodic Orbits in the Restricted Three-Body Problem, Mon. Not. Royal Astr. Soc., 1977, no. 180, pp. 103–116.

  12. Markellos, V.V., Asymmetric Periodic Orbits in Three Dimensions, Mon. Not. Royal Astr. Soc., 1978, no. 184, pp. 273–281.

  13. Kazantzis, P.G., The Structure of Periodic Solutions in the Restricted Problem of Three Bodies, Astrophys. Space Sci., 1978, vol. 59, pp. 355–371.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Bruno, A.D., Ogranichennaya zadacha trekh tel. Ploskie periodicheskie resheniya (Restricted Three-Body Problem: Planar Periodic Solutions), Moscow, 1990.

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  1. Astro Space Center, Lebedev Physical Institute of Russian Academy of Sciences, Profsoyuznaya ul. 84/32, Moscow, Russia

    B. B. Kreisman

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  1. B. B. Kreisman
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Original Russian Text © B.B. Kreisman, 2010, published in Kosmicheskie Issledovaniya, 2010, Vol. 48, No. 3, pp. 271–278.

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Kreisman, B.B. Stable spatial orbits around collinear libration points. Cosmic Res 48, 265–272 (2010). https://doi.org/10.1134/S0010952510030081

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