Abstract
The problem of the joint influence of the oblateness of a central planet and attraction by its most massive (or main) satellites and the Sun on the orbital evolution of a satellite with a negligible mass is considered. For an arbitrary angle between the equatorial plane of the planet and the plane of its heliocentric orbit, the evolution equations have been derived in the planeto-equatorial elements of the satellite orbit. Integrable cases of the evolution problem are described. The influence of Uranus’s main satellites on the orbital evolution of its real and hypothetical satellites has been revealed through numerical calculations and analytical estimations.
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Allan, R.R. and Cook, G.E., The long-period motion of a plane of a distant circular orbit, Proc. Roy. Astron. Soc. A, 1964, vol. 280, no. 1380, pp. 97–109.
Emelyanov, N.V. and Nikonchuk, D.V., Ephemerides of the main uranian satellites, Mon. Not. Roy. Astron. Soc., 2013, vol. 436, pp. 3668–3679.
Kinoshita, H. and Nakai, H., Analytical solution of the Kozai resonance and its application, Celest. Mech. and Dyn. Astron., 1999, vol. 75, pp. 125–147.
Kinoshita, H. and Nakai, H., General solution of the Kozai mechanism, Celest. Mech. Dyn. Astron., 2007, vol. 98, pp. 67–74.
Kozai, Y., Secular perturbations of asteroids with high inclination and eccentricity, Astron. J., 1962, vol. 67, pp. 591–598.
Lidov, M.L., Orbits evolution of planets artificial satellites caused by external bodies’ gravity, Iskusstv. Sputniki Zemli, 1961, no. 8, pp. 5–45.
Lidov, M.L., On the approximated analysis of the orbit evolution of artificial satellites. In M. Roy Ed. Dynamics of Satellites. Symp. Paris, May 28–30, 1962. Springer-Verlag, Berlin-Gotingen, Heidelberg, 1963.
Lidov, M.L. and Yarskaya, M.V., Integrable cases in the problem of the evolution of a satellite orbit under the joint effect of an outside body and of the noncentrality of the planetary field, Cosmic Research, 1974, vol. 12, no. 2, pp. 139–152.
Nikonchuk, D.V., Nonlinear theory of secular perturbations of satellites of an oblate planet, Astron. Lett., 2012, vol. 38, no. 12, pp. 904–920.
Nikonchuk, D.V., The theory of the major Uranus satellites motion according to observations, Cand. Sci. Phys.-Math.) Dissertation, Moscow: MSU, 2013. http://www.sai.msu.ru/dissovet/Nikonchuk_PhD.pdf
Prokhorenko, V.I., A Geometric Study of Solutions to Restricted Circular Double-Averaged Three-Body Problem, Cosmic Research, 2001, vol. 39, no 6, pp. 583–593.
Sekiguchi, N., On the libration of the orbital plane of a stationary artificial satellite with a circular orbit, Publ. Astron. Soc. Jpn., 1961, vol. 13, no. 2, pp. 207–211.
Vashkov’yak, M.A. and Lidov, M.L., Systems of Synchronous Artificial Satellites in Stable Circular Orbits, Cosmic Research, 1983, vol. 21, no 1, pp. 9–15.
Vashkov’yak, M.A., Celestial-mechanical peculiarities of Uranus’s satellite system, Astron. Lett., 2001, vol. 27, no. 7, pp. 464–469.
Vashkov’yak, M.A. and Teslenko, N.M., Peculiarities of Uranus’s satellite system, Astron. Lett., 2002, vol. 28, no. 9, pp. 641–650.
Vashkov’yak, M.A., Evolution of the orbits of distant satellites of Uranus, Astron. Lett., 1999, vol. 25, no. 7, pp. 476–481.
Vashkov’yak, M.A., Vashkov’yak, S.N., and Emel’yanov, N.V., On the expansion of the secular part of the perturbing function of mutual attraction in the satellite system of planets, Solar Syst. Res., 2013a, vol. 47, no. 1, pp. 31–37.
Vashkov’yak, M.A., Vashkov’yak, S.N., and Emel’yanov, N.V., General presentation of secular part of the perturbing function of mutual attraction in the satellite system of a planet, Solar Syst. Res., 2013b, vol. 47, no. 5, pp. 414–417.
Vashkov’yak, M.A., Vashkov’yak, S.N., and Emel’yanov, N.V., The Expansion of Secular Part of Perturbing Function for the Orbits with Comparable Semi-Major Axis, Solar Syst. Res., 2015, vol. 49. no 3, pp.191–204.
Vashkovjak, M.A., On the stability of the circular ‘asteroid’ orbits in an N-planetary system, Celest. Mech., 1976, vol. 13, no. 3, pp. 313–324.
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Original Russian Text © M.A. Vashkov’yak, S.N. Vashkov’yak, N.V. Emel’yanov, 2015, published in Astronomicheskii Vestnik, 2015, Vol. 49, No. 4, pp. 283–299.
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Vashkov’yak, M.A., Vashkov’yak, S.N. & Emel’yanov, N.V. On the evolution of satellite orbits under the action of the planet’s oblateness and attraction by its massive satellites and the sun. Sol Syst Res 49, 247–262 (2015). https://doi.org/10.1134/S0038094615040085
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DOI: https://doi.org/10.1134/S0038094615040085