Obliquity of the ecliptic

The angle between the plane of the ecliptic (or the plane of the earth's orbit) and the plane of the earth's equator; the "tilt" of the earth.

The obliquity of the ecliptic is computed from the following formula:

where t is the year for which the obliquity is desired. For 1999, the value was 23°26′21.89″. It is the oblique orientation of the earth's axis relative to its orbit that accounts for the seasons, for, in the period of a year, the angle of incidence of incoming solar radiation varies by nearly 47° at any one place. Particularly at high latitudes, this results in a great seasonal temperature contrast. M. Milankovitch has calculated that the obliquity of the ecliptic varies between 24.5° and 22° in the course of 40 000 years. This variation may be considered as a long-period climatic control and is included in the astronomical theory of ice ages.

The path that a satellite follows in its motion through space relative to the attracting body.

Any function of time f(t) is periodic with period t if f(t) = f(t + τ) for all times t, where τ is the smallest number for which this equality holds.