The obliquity of the ecliptic is the angle of inclination of the Earth's axis of rotation.
The mean obliquity of the ecliptic is
calculated by a formula of Laskar (1986), given in
Jean Meeus: "Astronomical Algorithms", p. 135.
According to Meeus the accuracy of the formula is
0.01'' between AD 1000 and 3000, and a few seconds
of arc after 10,000 years.
The nutation in obliquity is computed by
the most important terms of the "1980 IAU Theory of
Nutation" (accuracy 0.01'').
The value of 2000, Jan 1 at 12 UT (Julian Day 2451545.0) is:
At present, the mean obliquity currently decreases by 0.0130° (46.8'') per century.
Near the year 12030 a minimum will be reached (22° 36' 41 '').
About the year -7530 there was a maximum inclination (24° 14' 07 '').
The true obliquity is taking into account the nutation of the Earth's axis:
eps = eps0 + Δeps
The nutation is a peridic oscillation of the rotational axis of the Earth around it's mean position. Nutation is due mainly to the action of the Moon. The most important term has a period of 18.6 years.
Δeps is computed by a formula in Jean Meeus: "Astronomical Algorithms" (accuracy of 0.1'').
The results of my applet for a large period of time (-20,000 to +20,000):
Compare the results:
Precession and the Obliquity of the Ecliptik (Haluk Akcam, Jan. 01, 2004)