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Astron. Astrophys. 319, 305-317 (1997)

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Theory of the rotation of the rigid Earth

P. Bretagnon , P. Rocher and J.L. Simon

Bureau des longitudes URA 707 du CNRS 77, Avenue Denfert-Rochereau, F-75014 Paris, France

Received 14 June 1996 / Accepted 30 July 1996


We present the computation of the precession and nutation expressions built with the analytical theories of the motion of the Moon, the Sun and the planets of the Bureau des longitudes. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth limited to [FORMULA] for j from 2 to 5, [FORMULA], [FORMULA], [FORMULA], [FORMULA] for k from 1 to 3 and [FORMULA], [FORMULA]. We have determined the analytical variations of the angles [FORMULA] and [FORMULA] fixing the equator with respect to the ecliptic J2000. We find, in [FORMULA], a secular term of [FORMULA] µas per year. We use for the constant of the general precession the Williams' (1994) value [FORMULA]. The corresponding value of the dynamical flattening of the Earth [FORMULA] is [FORMULA]. In this work we used a truncated solution for the motion of the Moon. We have compared our analytical solution with a numerical integration. The differences are smaller than 16 µas for [FORMULA] and 8 µas for [FORMULA].

Key words: astrometry – celestial mechanics – reference systems – Earth

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998