Resonance Phenomena at Rotations of Artificial and Natural Celestial Bodies
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.
KeywordsAngular Velocity Celestial Body Orbital Motion Resonance Rotation Resonance Zone
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- 1.Beletskii, V.V.: The Cassini’s Laws. Inst. Prik. Matem. AN SSSR preprint, n. 79 Moscow (1971).Google Scholar
- 2.Beletskii, V.V.: Resonance Rotation of Celestial Bodies and Cassini’s Laws. Celes. Mech. 6,n. 3 (1972).Google Scholar
- 3.Goldreich; Peale, S.: The Dynamics of Planetary Rotations. Annual Review of Astronomy and Astrophysics. 6, Palo Alto, California, 1968.Google Scholar
- 4.Moltchanov, A.M.: The Resonant Structure of the Solar System. ICARUS-Intern. J. of the Solar System 8, n. 2 (1968).Google Scholar
- 6.Express-informatisia. “Astronavtika i raketodinamika.” n. 12, 1972.Google Scholar
- 10.Beletskii, V.V.: Letter to the editor of Fisica v Schkole. n. 6 (1948).Google Scholar
- 11.Kotelnikov, V.A.: Radar Observations of Venus in the USSR for 1964. DAN SSSR (1st ed.) 163 (1965).Google Scholar
- 12.Rjiga, O.N.: Results of Radar Observations of Planets. Kosmitcheskie Issledovania 7, n. 1 (1969).Google Scholar
- 14.Goldstein, R.M.: Moon and Planet. North-Holland, Amsterdam, 1967.Google Scholar
- 15.Goldreich, P.; Peale, S.: Astron. J. 71 (1966) 425; Nature n. 209 (1966) 1117.Google Scholar
- 16.Handbook of Celestial Mechanics and Astrodynamics. Edited by G. N. Dubochin. Nauka, Moscow, 1971.Google Scholar
- 17.Tisserand, F.: Traité de mecanique celeste, tome II, Paris, 1891.Google Scholar
- 18.Lagrange, J.L.; Oeuvres, Tome V.; Gauthier-Villars, Paris, 1870.Google Scholar
- 19.Laplace, P.S.: Mecanique celeste, Paris, 1793.Google Scholar
- 20.Habibulin, Ch.T.: Trudi Kazanskoi gor. astr. observat., n. 34, Kazan, 1966.Google Scholar
- 21.Kulikov, K.A.; Burevitch, V.B.: Principles of Lunar Astronomy. Nauka, Moscow, 1972.Google Scholar
- 22.Beletskii, V.V.: The Librations of Satellites. In Iskustvenie sputniki zemli. AN SSSR (3rd ed.) (1959) 13–31.Google Scholar
- 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.Beletskii, V.V.: The motion of a satellite with respect to its center of mass. Nauka, Moscow, 1965.Google Scholar
- 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.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.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.Torgevskii, A.P.: The motion of a satellite with respect to the center of mass and resonance effects.Google Scholar
- 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.Colombo, G.: Cassini’s Second and Third Laws. The Astron. J. n. 1344 (1966) 891.Google Scholar
- 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.Peale, S.: Generalized Cassini’s Laws. The Astron. J. n. 1368 (1969) 483.Google Scholar
- 33.Beletskii, V.V.: The motion of a dynamically symmetric satellite. In Kosm. Issled. 1 (1963) 339–385.Google Scholar
- 34.Lutz, F.H.; Abbiz, M.Z.: Rotation locks for near-symmetric satellites. Celes. Mech. n. 1 (1969).Google Scholar
- 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.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.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.Hara, M.: Effect of Magnetic and Gravitational Torques on Spinning Satellite Attitude. AIAA J. II, n. 12 (1973).Google Scholar
- 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.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.Beletskii, V.V.; Heitov, A.A.: Magneto-gravitational stabilization of a satellite. AN SSSR, n. 4, “Mekanika tverdovo tela,” (1973).Google Scholar
- 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.Beletskii, V.V.: The motion of celestial bodies. Nauka, Moscow, 1971.Google Scholar
- 44.Blehman, I.I.: Synchronization of dynamic systems. Nauka, Moscow, 1971.Google Scholar