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## Archive of Issues

Russia Saint Petersburg
Year
2013
Issue
2
Pages
116-126
 Section Mechanics Title Orbits of distant satellites of stars Author(-s) Proskurin S.A.a, Ossipkov L.P.a Affiliations Saint Petersburg State Universitya Abstract Planar motion of point mass in the field of a point mass (a star) and the Galaxy was studied numerically. The tidal (quadratic) approximation for the galactic potential was accepted. The equations of motion were integrated for the time interval equal to $60/\sqrt{A(A-b)}$ ($A$, $B$ are Oort's coefficients). A particle was considered as escaping if its distance from the star exceeded two distances of the libration points. It was found that osculating eccentricities of remaining particles could be decreasing systematically or almost constant. Table 1 shows dependence of orbit types on initial conditions. Keywords stellar dynamics, celestial mechanics, orbits of satellites of stars, comet orbits UDC 523.64-52, 524.3/.4-32 MSC 85A05 DOI 10.20537/vm130212 Received 29 January 2013 Language Russian Citation Proskurin S.A., Ossipkov L.P. Orbits of distant satellites of stars, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 2, pp. 116-126. References Antonov V.A., Latyshev I.N. Possible existence of distant companions of stars, Sov. Astron., 1972, vol. 15, no. 4, pp. 676–681. Latyshev I.N. Geometry of orbits for distant companions of stars, Bull. Inst. Teoret. Astron., 1975, vol. 14, no. 1, pp. 16–24. Subbotin M.F. Vvedenie v teoreticheskuyu astronomiyu (Introduction into theoretical astronomy), Moscow: Nauka, 1968, 800 p. Ossipkov L.P. Ordinary differential equations in problems of stellar dynamics, Matematicheskie metody issledovaniya kosmicheskikh sistem (Mathematical methods of studying space systems), Saint Petersburg: Phys. Faculty of Saint Petersburg Univ., 2003, pp. 73–131. Heggie D.C. Escape in Hill’s problem, The restless Universe, Bristol: Inst. of Physics Publ., 2001, pp. 109–128. Moiseev N.D. On some general methods of qualitative studying forms of motion in problems of celestial mechanics. 2. On conditions of existing trajectories not crossing boundaries of a given domain, Tr. Gos. Astron. Inst. Im. P.K. Sternberga, 1939, vol. 9, no. 2, pp. 5–45. Breiter S., Dybczynsky P.A., Elipe A. The action of the Galactic disc on the Oort cloud comets, Astron. Astrophys., 1996, vol. 315, no. 3, pp. 68–624. Byl J. Galactic perturbation on nearly periodic cometary orbits, Moon and Planets, 1983, vol. 29, no. 1, pp. 121–137. Heisler J., Tremaine S. The influence of the Galactic tidal field on the Oort comet cloud, Icarus, 1986, vol. 63, no. 1, pp. 13–26. Fouchard M. New fast models of the Galactic tide, Monthly Notices Roy. Astron. Soc., 2004, vol. 349, no. 1, pp. 347–356. Mikkola S., Nurmi P. Computing secular motion under slowly rotating quadratic perturbation, Monthly Notices Roy. Astron. Soc., 2004, vol. 371, no. 1, pp. 421–423. Breiter S., Fouchard M., Ratajczak R., Borczyk W. Two fast integrators for the Galactic tide effects in the Oort cloud, Monthly Notices Roy. Astron. Soc., 2007, vol. 377, no. 3, pp. 1151–1161. Matese J.J., Whitman P. A model of the Galactic tidal interaction with the Oort comet cloud, Cel. Mech. Dyn. Astron., 1992, vol. 54, no. 1, pp. 13–35. Matese J.J., Whitmire D. Tidal impact of distant galactic matter on the Oort comet cloud, Astrophys. J. (Letters), 1996, vol. 472, no. 1, pp. L41–L43. Breiter S., Ratajczak R. Vectorial elements for the Galactic disc tide effects in cometary motion, Monthly Notices Roy. Astron. Soc., 2005, vol. 364, no. 3, pp. 1222–1228. Torbett M.V. Injection of Oort cloud comets to the inner Solar system by galactic tidal fields, Monthly Notices Roy. Astron. Soc., 1986, vol. 223, no. 2, pp. 885–895. Brasser R. Some properties of a two-body system under the influence of the Galactic tidal field, Monthly Notices Roy. Astron. Soc., 2001, vol. 324, no. 3, pp. 1109–1116. Gardner E., Nurmi P., Flynn C., Mikkola S. The effect of the Solar motion on the flux of long-period comets, Monthly Notices Roy. Astron. Soc., 2011, vol. 411, no. 2, pp. 947–954. Oort J.H. The structure of the cloud of comets surrounding the Solar system, and a hypothesis concerning its origin, Bull. Astron. Inst. Netherlands, 1950, vol. 11, no. 408, pp. 1–20. Vsekhsvyatskii S.K. Notes on works by J. Oort dealing with problems of origin and evolution of comets, Astron. Zh., 1954, vol. 31, no. 5, pp. 537–543. Kopnin M.Yu., Kopnin Yu.M., Nevzorov E.V. On evolutions of orbits in a planetary system under influence of a nearby star, Astron. Zh., 1996, vol. 73, no. 3, pp. 477–481. Nezhinskii E.M. On stability of the Oort cloud, Bull. Inst. Teoret. Astron., 1971, vol. 13, no. 1, pp. 31–35. Antonov V.A., Todriya Z.P. Systematic and random deformations of long-period comet orbits, Sov. Astron. Lett., 1984, vol. 10, no. 3, p. 166. Antonov V.A., Todriya Z.P. Motion of long-period comets in the perturbation field of the Galaxy. Irregular forces, Sov. Astron., 1987, vol. 31, no. 5, pp. 572–577. Tsitsin F.A., Chepurova V.M., Rastorguev A.S., Genkin I.L. On the relict reservoir of cometary bodies and the region of outer planets of the Solar system, Voprosy nebesnoy mekhaniki i zvezdhoy dinamiki (Problems of celestial mechanics and stellar dynamics), Alma-Ata: Nauka, 1990, pp. 197–200. Tsitsin F.A., Chepurova V.M., Genkin I.L. The relict reservoir of cometary bodies and a unitary state of comets of the Solar system, Astron. Astrophys. Transact., 1999, vol. 17, no. 5, pp. 351–354. Tsitsin F.A. Ocherki sovremennoi kosmogonii Solnechnoi sistemy. Istoki. Problemy. Gorizonty (Essays of the modern cosmogony of the Solar System. Sources. Problems. Horizons), Dubna: Phoenix+, 2009, 356 p. Sokolov L.L. On the comet capture conditions, Stellar Dynamics: from classic to modern, Saint Petersburg: Sobolev Astronomical Institute, 2001, pp. 253–259. Ossipkov L.P. Libration points for the Bok problem, Vestn. St-Peterbg. Univ., Ser. 10, Prikl. Mat. Inf. Prots. Upr., 2007, no. 3, pp. 62–70. Ossipkov L.P. Obshchie printsipy matematicheskogo modelirovaniya zvezdnykh sistem (General principles of mathematical modelling stellar systems), Saint Petersburg: Solo, 2010, 102 p. Ogorodnikov K.F. Dynamics of stellar systems, Pergamon Press: London, 1965, 359 p. Binney J., Merrifield M. Galactic astronomy, Princeton: Princeton Univ. Press, 1998, XVI+798 p. Bok B.J. The stability of moving clusters, Circ. Harvard College Observ., 1934, no. 384, pp. 1–41. Lindblad B. Die Milchstrasse, Handbuch der Astrophysik, Band V / Zweiter Halfte, Berlin: Verlag von Julius Springer, 1933, pp. 937–1076. Buliga S.D., Ossipkov L.P. Eccentricities of planar stellar orbits, Vestn. Udmurt. Univ. Ser. Astron., 2011, no. 1, pp. 1–18. Ross D.J., Mennim A., Heggie D.C. Escape from a tidally limited star cluster, Monthly Notices Roy. Astron. Soc., 1997, vol. 284, no. 4, pp. 811–814. Full text