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Tidal effects in the earth–moon system and the earth's rotation

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Abstract

Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived. Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial logarithmic decrement ν of the Chandler wobble are evaluated: \({\dot \theta }\) mas, \(\dot \omega /\omega = - 5.08{\text{ mas }} = {\text{ }} - 24.6{\text{ }} \times {\text{ }}10^{ - 9} ,{\text{ }}v = - 12.3{\text{ mas}}\).

In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given.

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References

  • Aleshkina, E. Yu., Krasinsky, G. A. and Vasilyev, M. V.: 1996, Analysis of LLR data by the Program System ERA, In: Proceedings IAU Coll. 166 Dynamics and Astrometry of Natural and Artificial Celestial Bodies, Poznan, Poland, July 1–5, pp. 225-232.

  • Dehant, V. and Defraigne, P.: 1997, New transfer functions of a nonrigid Earth, J. Geophys. Res. 102(B12), 27659-27687.

    Article  ADS  Google Scholar 

  • Dickey, J. O., Bender, P. L., Faller, J. E., Newhall, X. X., Ricklefs, R. L., Ries, J. G., Shellus, P. J., Veillet, C., Whipple, A. L., Wiant, J. R., Williams, J. G. and Yoder, C. F.: 1994, Lunar laser ranging: A continuing legacy of the Apollo program, Science 265 (22 July), 482-490.

  • Getino, J. and Ferrandiz, J. M. A.: 1991, Hamiltonian theory for an elastic earth: Elastic energy of deformation, Celest. Mech. Dynam. Astron. 51(1), 17-34.

    Article  MathSciNet  ADS  Google Scholar 

  • Getino, J. and Ferrandiz, J. M.: 1991, A Hamiltonian theory for an elastic Earth: First order analytical integration, Celest. Mech. Dynam. Astron. 51(1), 35-66.

    Article  MathSciNet  ADS  Google Scholar 

  • Goldreich, P.: 1966, History of the lunar orbit, Rev. Geophys. 4, 411-435.

    ADS  Google Scholar 

  • Kinoshita, H.: 1977, Theory of rotation of the rigid earth, Celest. Mech. 15, 227-326.

    MathSciNet  ADS  Google Scholar 

  • Kinoshita, H. and Souchay, J.: 1990, The theory of the nutation for the rigid earth model at the second order, Celest. Mech. Dynam. Astron. 48(3), 187-265.

    MATH  ADS  Google Scholar 

  • MacDonald, G. J. F.: 1964, Tidal friction, Rev. Geophys. 2, 467-541.

    Google Scholar 

  • Molodensky, S. M.: 1984, Tides, nutation and internal structure of the earth (In Russian), Inst. Phys. of Earth, Moscow.

    Google Scholar 

  • Morrison, L. V.: 1973, The secular accelerations of the moon's orbital motion and the earth's rotation, Moon 5, 253-264.

    Article  ADS  Google Scholar 

  • Munk, W. H. and MacDonald, G. J. F.: 1960, The Rotation of the Earth, Cambridge University Press, London.

    Google Scholar 

  • Newhall, X. X., Standish, E. M. and Williams, J. G.: 1983, DE102: a numerically integrated ephemeris of the Moon and planets spanning forty-four centuries, Astron. Astrophys. 125, 150-187.

    MATH  ADS  Google Scholar 

  • Newhall, X. X. and Williams, J. G.: 1996, Estimation of the Lunar Physical Librations, In: Proceedings IAU Coll. 166 Dynamics and Astrometry of Natural and Artificial Celestial Bodies, Poznan, Poland, July 1–5, 22-30.

  • Schutz, R. E., Cheng, M. K., Eanes, R. J., Shum, C. K. and Tapley, B. D.: 1993, Geodynamic results from starlette orbit analysis, Contributions of space geodesy to geodynamics: Earth dynamics, Geodynamics Series 24, 175-190.

    Google Scholar 

  • Seidelmann, P. K.: 1980, IAU Theory of Nutation: the final report of the IAU working group on mutatin, Celest. Mech. 27(1), 79-106.

    MathSciNet  ADS  Google Scholar 

  • Seidelmann, K. (ed.): Explanatary Supplement to the Astronomic Almanac, Univ. Science Books, California, 1992.

    Google Scholar 

  • Wahr, J.M.: 1980, The forced nutations of an elliptical, rotating, elastic and oceanless earth, Geophys J. R. Astr. Soc. 64, 705-727.

    ADS  Google Scholar 

  • Williams, J. G.: 1994, Contributions to the earth's obliquity rate, precession, and nutation, Astron. J. 108(2), 711-724.

    Article  ADS  Google Scholar 

  • Yoder, C. F., Williams, G. and Parke, M. E.: 1981, Tidal variation of earth rotation, Geophys. J. R. Astr. Soc. 86, 881-891.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Astronomy, St. Petersburg, Russia

    G. A. krasinsky

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  1. G. A. krasinsky
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krasinsky, G.A. Tidal effects in the earth–moon system and the earth's rotation. Celestial Mechanics and Dynamical Astronomy 75, 39–66 (1999). https://doi.org/10.1023/A:1008381000993

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