Skip to main content
Log in

New Trends in Numerical Simulation of the Motion of Small Bodies of the Solar System

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

A brief survey of the results obtained by the authors in the development and investigation of the algorithms of numerical simulation of the motion of solar system small bodies is given. New approaches to the construction of the algorithms of high-accuracy numerical simulation of the dynamics of small bodies and the methods of the determination of the domain of their possible motions are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aarseth, S.J. and Zare, K.A.: 1974. ‘Regularization of three-body problem’, Celest. Mech. 10, 185–206, Kluwer Academic Publishers.

    Google Scholar 

  • Avdyushev, V.A.: 1999. ‘A new intermediate orbit in the problem on the motion of an inner satellite of an oblate planet’, Research in Ballistics and Contiguous Problems of Dynamics, Tomsk State University, Tomsk, 3, pp. 126–127 (in Russian).

    Google Scholar 

  • Ayvazyan, S.A., Enyukov, I.S. and Meshalkin, L.D.: 1983, Applied Statistics, Moscow, Finansy i Statistika (in Russian).

    Google Scholar 

  • Batrakov, Yu.V. and Makarova, E.N.: 1979. ‘A generalized Encke method for investigating perturbed motion’, Bull. ITA USSR 14, 397–401, Leningrad, Nauka, (in Russian).

    Google Scholar 

  • Batrakov, Yu.V. and Mirmakhmudov, E.R.: 1991. ‘On effectiveness of using intermediate orbits for computing the perturbed motion’, First Spain-USSR Workshop on Positional Astronomy and Celestial Mechanics Univ. de Valencia Observ. Astronomico, Kluwer Academic Publishers, pp. 71–73.

  • Bordovitsyna, T.V.: 1984, Modern Numerical Methods in Problems of CelestialMechanics, Moscow, Nauka (in Russian).

    Google Scholar 

  • Bordovitsyna, T.V. and Sharkovsky, N.A.: 1994. ‘An efficient algorithm for numerical simulation of the motion of martian satellite, phobos’, Russian Phy. J. 10 (37), 920–924, Consultants Bureau, New York, London.

    Google Scholar 

  • Bordovitsyna, T.V., Bykova, L.E. and Avdyushev, V.A.: 1998a, ‘Problems in applications of regularizing and stabilizing KS-transformations to tasks of dynamics of planets’ natural satellites and asteroids', Astr. Geodezy 16, 33–57, Tomsk State University, Tomsk (in Russian).

    Google Scholar 

  • Bordovitsyna, T.V., Avdyushev, V.A. and Titarenko, V.P.: 1998b. ‘Numerical integration in the general three-body problem’, Research in Ballistics and Contiguous Problems of Dynamics, Tomsk State University, Tomsk, 2, pp. 164–168 (in Russian).

    Google Scholar 

  • Chernitsov, A.M., Baturin, A.P. and Tamarov, V.A.: 1998. ‘Analysis of some methods of determining probabilistic evolutions of the motion of solar system small bodies’, Solar System Research, 32(2), 459–467, Russian Academy of Sciences, Moscow (in Russian).

    Google Scholar 

  • Encke, J.F.: 1852. Über eine neue Methode der Berechung der PlanetenstÖrungen', Astron. Nachr. 33, 377–398.

    Google Scholar 

  • Everhart, E.: 1974. ‘Implicit single sequence method for integrating orbit’, Celest. Mech. 10, 35–55, Kluwer Academic Publishers.

    Google Scholar 

  • Hairer, E., Norsett, S.P. and Wanner, G.: 1987. Solving Ordinary Differential Equations. Nonstiff Problems, Springer-Verlag.

  • Herrick, S.H.: 1972. Astrodynamics Vol. II, Van Nostrand Reinhold Company, London, New York, Cincinnati, Toronto, Melbourne.

    Google Scholar 

  • Milani, A., La Spina, A., Sansaturio, M.E. and Chesley, S.R.: 2000. ‘The asteroid identification problem III. proposing identifications’, Icarus 144, 39–53.

    Google Scholar 

  • Muinonen, K.: 1996. ‘Orbital covariance eigenproblem for asteroids and comets’, Mon. Not. Royal Astr. Soc. 280, 1235–1238.

    Google Scholar 

  • Shaikh, N.A.: 1966. ‘A new perturbation method for computing Earth-Moon trajectories’, Astronaut. Acta. 12, 207–211.

    Google Scholar 

  • Sharkovsky, N.A.: 1990. ‘Modified encke methods’, Software of Theory of Artificial SatelliteMotion, Leningrad, ITA AS USSR, pp. 71–72 (in Russian).

  • Shefer, V.A.: 1990. ‘Application of KS-transformation in problem of investigation of motion of unusual minor planets and comets’, Celest. Mech. & Dyn. Astr. 49, 197–207.

    Google Scholar 

  • Shefer, V.A.: 1998. ‘Generalized encke methods for investigating perturbed motion’, Astronomy and Geodezy, 16, 149–171, Tomsk State University, Tomsk (in Russian).

    Google Scholar 

  • Sorokin, N.A.: 1991, ‘Differential equations of the motion of ASE in the problem of two fixed centers and their integration’, Scientific Info., 69, 114–123, Astronomy Institute of Academy of Sciences of USSR, Moscow (in Russian).

    Google Scholar 

  • Stiefel, E.L. and Scheifele, G.: 1971. Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin, Heidelberg, New York.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bordovitsyna, T., Avdyushev, V. & Chernitsov, A. New Trends in Numerical Simulation of the Motion of Small Bodies of the Solar System. Celestial Mechanics and Dynamical Astronomy 80, 227–247 (2001). https://doi.org/10.1023/A:1012241624469

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012241624469

Navigation