The obliquity of the ecliptic is essentially the angle of inclination of the Earth's equator with respect to the plane of its orbit, which to us, produces the apparent relative tilt of the Earth's polar axis which causes the annual seasons.
This angle is approximately ±23.45 degrees and is the apparent maximum/minimum angle of the sun above or below the equator during the year as viewed from Earth. This value varies very slowly as the orbit of the Earth evolves over time.
This is one of the values we need to know when computing the apparent position of a planet as viewed from the Earth as it defines the instantaneous inclination of the Earth's orbit.
The algorithm used here is based on data published by J. Laskar in
Astronomy and Astrophysics, Vol 157, p68 (1986),
New Formulas for the Precession, Valid Over 10000 years,
Provided by the NASA Astrophysics Data System
J. Laskar's Formula For The Mean Obliquity
In this case, the time variable (t) of Table 8 is reckoned in terms
of 10000 Julian years from J2000.0 corresponding to the JD and
may be found from
The value 84381.448 seconds of arc equates to 23° 26' 21.448"
which is the mean obliquity for the ecliptic of J2000.0
Based on the Table 8 data above (bottom NGT column), the
mean obliquity (in arc seconds) of the ecliptic at time (t) is:
This value of the obliquity is the mean value. For the true, apparent obliquity of the date, a small correction for nutation in obliquity must be applied.
The following functions return the mean obliquity in decimal degrees for any given JD argument, based on J. Laskar's long-term mean obliquity equation.
PHP function to compute the mean obliquity in decimal degrees for any given JD argument
CPP function to compute the mean obliquity in decimal degrees for any given JD argument
VB.NET function to compute the mean obliquity in decimal degrees for any given JD argument
© Jay Tanner - PHP Science Labs - 2018