Abstract :
A numerical theory of the rigid Earthʹs rotation taking into account the most essential relativistic perturbations (geodetic perturbations) is developed using improved initial conditions of the numerical integration. The differential equations of the rigid Earthʹs rotation are solved using the Rodrigues-Hamilton parameters, which describe the directions of the principal axes of inertia of the Earth with respect to the fixed ecliptic plane and equinox J2000.0. The rigid Earth rotation is a result of the gravitational interaction of the Earthʹs body with the point mass disturbing bodies (the Sun, Moon, and major planets). The geocentric motions of the disturbing bodies are provided by the ephemeris DE403/LE403 (Standish et al.,1995). The numerical integration of the rotational motion equations of the rigid Earth is carried out over a 200 year time interval from January 1, 2000. The results of the numerical solution of the problem are compared with the semi-analytical theory of the rigid Earthʹs rotation SMART97 (Bretagnon et al., 1998). The possible reason of the discrepancies up to ±300μas between the numerical integration results and the kinematical solution SMART97 (Pashkevich, 2000) are studied. In the result of the present investigation the discrepancies over the whole time interval of comparison are diminished to ±7μas.
