NEW FINITE TRIGONOMETRIC SERIES FOR THE EARTH ROTATION PARAMETERS

Folgueira M., Sevilla M.J.

Instituto de Astronomia y Geodesia (CSIC-UCM), Facultad de CC. Matematicas,
Universidad Complutense de Madrid, 28040 Madrid, Spain.

The potential gravitational energy in the hamiltonian theory of the rotation of a rigid Earth around its center of mass is function of two set of variables:

  1. variables which describe the rotational motion of the Earth, such as Andoyer variables,
  2. variables which describe the perturbed motion of the Moon and the Sun.

In the present paper, the developments of Legendre polynomial and Legendre associated functions in terms of Andoyer variables and five new variables for the motion of the Moon and the Sun, are presented. Such developments are used to get the expression of the potential gravitational energy due to the Moon and the Sun.

Once this energy is obtained, it is possible to apply the Hori-Deprit's averaging perturbation method to the dynamical equations of the rotational motion of a rigid Earth. New finite trigonometric series for the Earth Rotation Parameters will be carried out.