Nutation In Obliquity Of The Ecliptic - IAU 1980 Series Date:   ±Y  M  D Time UT:   H M S ΔT:   ± H M S Calendar Mode:   Julian            Gregorian
 ``` Date YMD = 2019 12 12 - Thursday (Gregorian) Time UT HMS = 00 00 00.000 = +0 day = UTFrac ±Delta T HMS = +00 00 00.000 = +0 day = dTFrac JD12 = 2458830 JD00 = 2458829.5 = (JD12 - 0.5) JDTT = 2458829.5 = (JD00 + UTFrac + dTFrac) T = 0.1994387405886379 Julian centuries from J2000.0 ------------------------------------------------------- Nutation In Obliquity of the Ecliptic (IAU 1980 Series) Delta epsilon = -0.000564732777° = -02.033"```

To Compute The Nutation In Obliquity For Any Given JD Argument

The following algorithm computes the nutation in obliquity of the ecliptic, in degrees, for a given JDTT argument.   It is based on the 1980 IAU Theory of Nutation and Reduction.

This value is the correction to apply to the MEAN value of the obliquity to obtain the TRUE obliquity, with a theoretical precision of ±0.001 arc sec.

As in most computer programming languages, the trigonometric functions (sin, cos, tan, et al.) in the pseudo-code here, assume radian arguments unless otherwise indicated.

In this case, the final result is converted into degrees for convenience.

True Obliquity = Mean Obliquity + Δε

Ref:
Astronomical Algorithms - 2nd Edition (1998)
Jean Meeus
Pub. Willmann-Bell, Inc.
ISBN 0-943396-61-1

Ref:
Explanatory Supplement to the Astronomical Almanac (1992)
p111 to p114
ISBN 0-935702-68-7

WikiRef:
http://en.wikipedia.org/wiki/Nutation

 Elements JDTT Astronomical JD number for given date/time (TT) T Time factor in Julian centuries, corresponding to JDTT, reckoned from J2000.0 DegToRad This is a conversion factor used to convert degrees into equivalent radians.  We multiply degrees by this factor to obtain the equivalent radians. w Nutation series accumulator variable w1 Mean elongation of the moon from the sun. w2 Mean solar anomaly. w3 Mean lunar anomaly. w4 Lunar argument of latitude. w5 Longitude of ascending node of lunar orbit on the ecliptic as measured from the mean equinox of date. dEpsDeg Nutation in ecliptical longitude expressed in degrees.