Theory of the Rotation of the Rigid Earth
Abstract
An analytical theory is developed for planes normal to the angularmomentum axis, to the figure axis, and to the rotational axis of the triaxial rigid Earth. One of the purposes of this paper is to determine the effect on nutation and precession of Eckertet al.'s improvement to Brown's tables of the Moon and to check Woolard's theory from a different point of view. The present theory is characterized by the use of Andoyer variables, a moving reference plane, and Hori's averaging perturbation method. A comparison with Woolard's results shows that (1) the maximum difference in nutation for the plane normal to the angularmomentum axis, calculated from the same constants as Woolard adopted, reaches 0″.0017, (2) the discrepancy in Oppolzer terms is large compared with the discrepancy in nutation for the plane normal to the angularmomentum axis, and (3) the present theory does not include some of the secular terms that are incorporated in Woolard's theory and that have an effect on the establishment of a reference system. The nutation coefficients ≥0″.0001 for the three abovementioned planes are calculated by using the numerical values recommended at the working meeting of the International Astronomical Union held in Washington in September 1974. The effects on precession and nutation due to the higher geopotential (n≥3) are also investigated. Any future revision of the lunar theory will not alter the values of the coefficients of the nutational terms derived here.
 Publication:

Celestial Mechanics
 Pub Date:
 April 1977
 DOI:
 10.1007/BF01228425
 Bibcode:
 1977CeMec..15..277K
 Keywords:

 Earth Rotation;
 Equations Of Motion;
 Nutation;
 Perturbation Theory;
 Rigid Structures;
 Spin Dynamics;
 Disturbing Functions;
 EarthMoon System;
 Ecliptic;
 Hamiltonian Functions;
 Long Term Effects;
 Precession;
 Astronomy