Resonance Phenomena at Rotations of Artificial and Natural Celestial Bodies

  • V. V. Beletskii
Conference paper
Part of the COSPAR-IAU-IUTAM book series (IUTAM)


In recent years the study of the rotational motions of celestial bodies has been concentrated upon the resonance (synchronization) of these motions. Synchronous rotations of the natural celestial bodies have been developed in the systems of the Jupiter, Saturn and Mars satellites. Such synchronizations have been also discovered in the rotation of Mercury and Venus. To these should be added the well-known synchronous rotation of the Moon. These facts allow us to consider the tendency to synchronous rotation as an objective Law of Nature. The passive stabilization systems of the artificial satellites make use of this tendency.

The resonance rotations of the celestial bodies are described by specifically constructed theories. These theories acknowledge synchronization of the rotational motion as a regular law of nature. The theory enables us to substantiate the empirical laws of the Moon’s rotation, i.e, Cassini’s laws, and to construct the generalized Cassini’s laws to which Mercury’s rotation is subjected.

The generalized Cassini’s laws describe a double synchronization first, between the axial rotation of a celestial body and its orbital motion and second, between the motion of an axis of rotation of the body and the disturbed orbital procession.

The Moon has double synchronization 1:1 and 1:1, Mercury has also double synchronization 3:2 and 1:1.

This double synchronization described by the generalized Cassini’s law can be successfully used for passive satellite stabilization, for example, for the double orbital stabilization of orbital stations.

Magnetic and gravitational field interaction creates the conditions for specific satellite stabilization; for example, synchronization of type 2:1 can be expected for some natural satellites of the great planets. To intensify magnetic stabilization the gravitational field can be used for the artificial satellites.

Resonance between the rotational and translational movements of a body leads to qualitatively new effects. At the expense of this resonance it is possible to change essentially the satellite orbit (in theory even from circular to parabolic orbit). Due to the smallness of interaction of the rotational and translational movements this fact is of purely theoretical interest; nevertheless it is discussed in the literature. The idea of “gravicraft” is based on this principle.

The present review describes briefly the history of development and investigation of resonance phenomena in the rotations of the natural and artificial celestial bodies. Here we use the facts and results of papers (1–3,39,40) and some other investigations.


Angular Velocity Celestial Body Orbital Motion Resonance Rotation Resonance Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Beletskii, V.V.: The Cassini’s Laws. Inst. Prik. Matem. AN SSSR preprint, n. 79 Moscow (1971).Google Scholar
  2. 2.
    Beletskii, V.V.: Resonance Rotation of Celestial Bodies and Cassini’s Laws. Celes. Mech. 6,n. 3 (1972).Google Scholar
  3. 3.
    Goldreich; Peale, S.: The Dynamics of Planetary Rotations. Annual Review of Astronomy and Astrophysics. 6, Palo Alto, California, 1968.Google Scholar
  4. 4.
    Moltchanov, A.M.: The Resonant Structure of the Solar System. ICARUS-Intern. J. of the Solar System 8, n. 2 (1968).Google Scholar
  5. 5.
    McCord, T.B.; Johnson, T.V.; Elias, J.H.: Saturn and its Satellites. Astrophys. J. 165 (1971) 413.CrossRefGoogle Scholar
  6. 6.
    Express-informatisia. “Astronavtika i raketodinamika.” n. 12, 1972.Google Scholar
  7. 7.
    Pettengill, G.H.; Dyce, R.B.: A radar determination of the rotation of the planet Mercury. Nature n. 206 (1965) 1240.CrossRefGoogle Scholar
  8. 8.
    Dyce, R.B.; Pettengill, G.H.; Shapiro, I.I.: Astron. J. 72 (1967) 351.CrossRefGoogle Scholar
  9. 9.
    Colombo, G.: Rotational Period of the Planet Mercury. Nature n. 208 (1965) 575.CrossRefGoogle Scholar
  10. 10.
    Beletskii, V.V.: Letter to the editor of Fisica v Schkole. n. 6 (1948).Google Scholar
  11. 11.
    Kotelnikov, V.A.: Radar Observations of Venus in the USSR for 1964. DAN SSSR (1st ed.) 163 (1965).Google Scholar
  12. 12.
    Rjiga, O.N.: Results of Radar Observations of Planets. Kosmitcheskie Issledovania 7, n. 1 (1969).Google Scholar
  13. 13.
    Carpenter, R.L.: Study of Venus by CW radar-1964 results. Astron. J. 71 (1966) 142.CrossRefGoogle Scholar
  14. 14.
    Goldstein, R.M.: Moon and Planet. North-Holland, Amsterdam, 1967.Google Scholar
  15. 15.
    Goldreich, P.; Peale, S.: Astron. J. 71 (1966) 425; Nature n. 209 (1966) 1117.Google Scholar
  16. 16.
    Handbook of Celestial Mechanics and Astrodynamics. Edited by G. N. Dubochin. Nauka, Moscow, 1971.Google Scholar
  17. 17.
    Tisserand, F.: Traité de mecanique celeste, tome II, Paris, 1891.Google Scholar
  18. 18.
    Lagrange, J.L.; Oeuvres, Tome V.; Gauthier-Villars, Paris, 1870.Google Scholar
  19. 19.
    Laplace, P.S.: Mecanique celeste, Paris, 1793.Google Scholar
  20. 20.
    Habibulin, Ch.T.: Trudi Kazanskoi gor. astr. observat., n. 34, Kazan, 1966.Google Scholar
  21. 21.
    Kulikov, K.A.; Burevitch, V.B.: Principles of Lunar Astronomy. Nauka, Moscow, 1972.Google Scholar
  22. 22.
    Beletskii, V.V.: The Librations of Satellites. In Iskustvenie sputniki zemli. AN SSSR (3rd ed.) (1959) 13–31.Google Scholar
  23. 23.
    Beletskii, V.V.: The motion of a satellite with respect to its center of mass. In Iskustvenie sputniki zemli. AN SSSR (6th ed.) (1961) 11–32.Google Scholar
  24. 24.
    Beletskii, V.V.: The motion of a satellite with respect to its center of mass. Nauka, Moscow, 1965.Google Scholar
  25. 25.
    Beletskii, V.V.: The motion of a satellite with respect to its center of mass. In Iskustvenie sputniki zemli. AN SSSR (1958) 25–43.Google Scholar
  26. 26.
    Tchernousko, F.L.: The motion of a satellite with respect to its center of mass by the action of gravitational moments. PMM (3rd ed.) 27 (1963) 474–483.Google Scholar
  27. 27.
    Tchernousko, F.L.: Resonance effects in the motion of a satellite with respect to the center of mass. Jornal Vitchisl. Matem. i Matem. Fis., 3, n. 3 (1963) 528–538.Google Scholar
  28. 28.
    Torgevskii, A.P.: The motion of a satellite with respect to the center of mass and resonance effects.Google Scholar
  29. 29.
    Trushin, S.I.: The effect of the motion of the perigee in the problem of the rotation of a satellite. In Kosmitch. issled. 8, n. 4 (1970) 628–629.Google Scholar
  30. 30.
    Colombo, G.: Cassini’s Second and Third Laws. The Astron. J. n. 1344 (1966) 891.Google Scholar
  31. 31.
    Holland, R.L.; Sperling, H.J.: A first-order theory for the rotational motion of a triaxial rigid body orbiting and oblate primary. Astron. J. 74, n. 3 (1969).Google Scholar
  32. 32.
    Peale, S.: Generalized Cassini’s Laws. The Astron. J. n. 1368 (1969) 483.Google Scholar
  33. 33.
    Beletskii, V.V.: The motion of a dynamically symmetric satellite. In Kosm. Issled. 1 (1963) 339–385.Google Scholar
  34. 34.
    Lutz, F.H.; Abbiz, M.Z.: Rotation locks for near-symmetric satellites. Celes. Mech. n. 1 (1969).Google Scholar
  35. 35.
    Shapiro, I.I.: Radar Astronomy, General Relativity and Celestial Mechanics. In “Modern Questions of Celestial Mechanics,” Bressanone, 1967, Coordinator: Prof. G. Colombo. Edizioni Gremonese, Roma, 1968.Google Scholar
  36. 36.
    Lidov, M.L.; Neichtadt, A.I.: The method of the canonic transforms and the Cassini’s laws in the problem of the rotation of celestial bodies. Institut prikladnoi matematiki AN SSSR, preprint n. 9, Moscow, 1973.Google Scholar
  37. 37.
    Johnson, D.B.: Precession Rate Matching a Space Station in Orbit about an Oblate Planet. Journal of Spacecraft and Rockets 10, n. 7 (1973).Google Scholar
  38. 38.
    Hara, M.: Effect of Magnetic and Gravitational Torques on Spinning Satellite Attitude. AIAA J. II, n. 12 (1973).Google Scholar
  39. 39.
    Beletskii, V.V.; Truchin, S.I.: The resonances in the rotation of celestial bodies and the generalized Cassini’s laws. In Mekanika tverdovo tela. 6th ed.: “Naukova dumka,” Kiev, 1974.Google Scholar
  40. 40.
    Beletskii, V.V.; Truchin, S.I.: Stability of the generalized Cassini’s laws. In Mekanika tverdovo tela. 6th ed.: “Naukova dumka,” Kiev, 1974.Google Scholar
  41. 41.
    Beletskii, V.V.; Heitov, A.A.: Magneto-gravitational stabilization of a satellite. AN SSSR, n. 4, “Mekanika tverdovo tela,” (1973).Google Scholar
  42. 42.
    Beletskii, V.V.; Guivertz, M.E.: The motion of an oscillating rod subjected to a gravitational field. In Kosmitcheskie Issledovania 5, n. 6 (1967).Google Scholar
  43. 43.
    Beletskii, V.V.: The motion of celestial bodies. Nauka, Moscow, 1971.Google Scholar
  44. 44.
    Blehman, I.I.: Synchronization of dynamic systems. Nauka, Moscow, 1971.Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1975

Authors and Affiliations

  • V. V. Beletskii
    • 1
  1. 1.MoscowRussia

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