Preamble

The axis of the Earth's rotation is inclined to the pole of the ecliptic (normal to the orbital plane) by 23°.45. This gives us the seasons. But the axis does not maintain a constant orientation in space. Gravitational interactions between the equatorial bulge and the Moon and Sun cause a slow precession of the axis about the ecliptic pole. The axis describes a cone with a 47° angle in a period of 25,730 years, fast enough for precise astronomical measurement, but not so fast that navigation by the stars is seriously inconvenienced. This is the most obvious of the complications to simple rotation. In an illuminating survey of the history of the subject, Ekman (1993) notes that the precession was observed by Hipparchus, who, in about 125 BC, reported a measure of its rate in remarkable agreement with modern estimates.

To see how the precession arises, consider a small satellite in a circular orbit that is inclined to the equatorial plane. Since the Earth is not spherical, its gravitational force on the satellite is directed precisely towards the centre of the Earth only when the satellite is above the equator (or, of course, one of the poles if it is in a polar orbit). At intermediate latitudes the latitude variation of gravity imparts a torque tending to pull the satellite orbit towards the equatorial plane. The torque acts in a sense perpendicular to the angular momentum vector, causing a precession of the orbit.