Theory of the Rotation of the Rigid Earth

Abstract

An analytical theory is developed for the three axes of the triaxial rigid earth (the angular-momentum axis, the figure axis, and the rotational axis). A theory on rigid earth rotation will be important to one on a nonrigid earth, since the latter gives only the ratios between the amplitudes of rigid nutation and those of nonrigid nutation. The present theory is characterized by the use of Andoyer variables, Hori’s averaging method, and a moving reference plane. A comparison with Woolard’s theory shows that 1) the maximum difference in nutation of the angular-momentum axis, calculated from the same constants as Woolard adopted, reaches 0.0017; 2) the maximum discrepancy in Oppolzer terms is 0V0012: and 3) the present theory has no secular term either in the first power of time in the obliquity referred to the fixed ecliptic or in the angle between the figure axis and the rotational axis; both these secular terms appeared in Woolard’s theory and have an effect on the establishment of a reference system. Nutation amplitudes as large as O.OOOl are calculated for all three axes. Use is made of Brown’s theory of the moon as improved by Eckert and of numerical values recommended at the working meeting of the International Astronomical Union held in Washington in September 1974. Any future revision of the lunar theory will not alter the values of the amplitudes of the nutational terms derived here.