NUTATIONS OF THE EARTH

Abstract

The figure of the Earth is very nearly that of an oblate spheroid. Its moments of inertia about principal axes in the equatorial plane differ from each other only by about two parts in 105, and may be taken to have a common value A, for the purposes of nutation theory. The moment of inertia C about the third principal axis, in the direction of the poles, is larger by about one part in 300. The dynamical ellipticity, defined as e == (C A)/ A, has the dominant role in determining the Earth's nutations. The flattening of the Earth's surface, i.e. its geometrical ellipticity, is defined as the fractional difference between the equatorial axis and the polar axis, and is also about 1/300. This equatorial bulge and the associated difference between C and A are almost wholly accounted for by centrifugal forces associated with a rotation of the Earth about its polar axis at a mean rate of one cycle per sidereal day (1 cpsd), equivalent to an angular velocity 00 which is 7.29212 x 10-5 rad sec-1 at present. We will find it convenient to express all angular velocities in units of 00• In the following, an angular velocity JD.o, or the equivalent frequency f cpsd, will often be