Abstract
In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three–axial rigid Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth’s rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary–lunar mean longitudes. This form of the Earth’s rotation problem is compatible with the general planetary theory involving the separation of the short–period and long–period variables and avoiding the appearance of the non–physical secular terms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdullah K., Albouy A.: On a strange resonance noticed by M. Herman. Regul. Chaotic Dyn. 6, 421–432 (2001)
Bretagnon P.: Termes à longues periodes dans le système solaire. Astron. Astrophys 30, 141 (1974)
Bretagnon P., Rocher P., Simon J.-L.: Theory of the rotation of the rigid earth. Astron. Astrophys 319, 305–317 (1997)
Bretagnon P., Francou G., Rocher P., Simon J.-L.: SMART97: a new solution for the rotation of the rigid Earth. Astron. Astrophys 329, 329–338 (1998)
Brumberg V.A.: Analytical Techniques of Celestial Mechanics. Springer, Heidelberg (1995)
Brumberg V.A.: Relativistic celestial mechanics on the verge of its 100 year anniversary (Brouwer Award lecture). Celest. Mech. Dyn. Astron. 106, 209–234 (2010). doi:10.1007/s10569-009-9237-y
Brumberg V.A., Ivanova T.V.: On the solution of the secular system of the equations of motion of the moon in trigonometric. Form. Bull. ITA 15, 424 (1985) (in Russian)
Brumberg V.A., Ivanova T.V.: New approach to the earth’s rotation problem consistent with the general planetary theory. In: Wytrzyszczak, I.M., Lieske, J.H., Feldman, R.A. (eds.) Dynamics and Astrometry of Natural and Artificial Celestial Bodies (IAU Colloquium No. 165, Poznan), pp. 301–306. Kluwer (1997)
Brumberg V.A., Ivanova T.V.: Precession/nutation solution consistent with the general planetary theory. Celest. Mech. Dyn. Astron. 97, 189–210 (2007)
Cunningham L.E.: On the computation of the spherical harmonic terms needed during the numerical integration of the orbital motion of an artificial satellite. Celest. Mech. 2, 207–216 (1970)
Ivanova, T.V.: PSP: A new poisson series processor. In: Ferraz-Mello, S., Morando, B., Arlot, J.-E. (eds.) Dynamics, Ephemerides and Astrometry of the Solar System (IAU Symposium 172, Paris), p. 283. Kluwer (1995)
Laskar J.: Large scale chaos and marginal stability in the solar system. Celest. Mech. Dyn. Astron. 64, 115 (1996)
Laskar J., Joutel F., Boudin F.: Orbital, precessional, and inclination quantities for the earth from −20 Myr to + 10 Myr. Astron. Astrophys. 270, 522 (1993)
Maciejewski A.J.: Hamiltonian formalism for Euler parameters. Celest. Mech. 37, 47 (1985)
Sharaf S.G., Boudnikova N.A.: On secular perturbations in the elements of the earth’s orbit and their influence on the climates in the geological past. Bull. ITA 11, 231 (1967). (in Russian)
Smart W.M.: Celestial Mechanics. Longmans, London (1953)
Tisserand F.: Traité de Mécanique Céleste, t. 2. Gauthier-Villars, Paris (1891)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brumberg, V.A., Ivanova, T.V. On constructing the general Earth’s rotation theory. Celest Mech Dyn Astr 109, 385–408 (2011). https://doi.org/10.1007/s10569-011-9334-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10569-011-9334-6