The obliquity of the ecliptic is the angle of inclination of the Earth's axis of rotation.
of the ecliptic is calculated by a formula of Laskar
(1986), given in Jean Meeus: "Astronomical Algorithms", p. 135.
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.
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)