Date YMD = 2019 10 22  Tuesday (Gregorian) Time UT HMS = 00 00 00.000 = +0 day = UTFrac ±Delta T HMS = +00 00 00.000 = +0 day = dTFrac JD12 = 2458779 JD00 = 2458778.5 = (JD12  0.5) JDTT = 2458778.5 = (JD00 + UTFrac + dTFrac) T = 0.1980424366872005 Julian centuries from J2000.0  Nutation In Obliquity of the Ecliptic (IAU 1980 Series) Delta epsilon = 0.000438670995° = 01.579" 
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 pseudocode 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. WillmannBell, Inc. ISBN 0943396611 Ref: Explanatory Supplement to the Astronomical Almanac (1992) p111 to p114 ISBN 0935702687 WikiRef: http://en.wikipedia.org/wiki/Nutation

Pseudocode Algorithm To Compute The Nutation In Obliquity of the Ecliptic
for any given JDTT Argument.
The following PHP function returns the nutation in obliquity in decimal degrees
for given JD argument.
The following C++/CPP function returns the nutation in obliquity in decimal degrees
for given JD argument.
The following VB.NET function returns the nutation in obliquity in decimal degrees.
VB.NET function to compute the nutation in obliquity in decimal degrees for given JDTT argument. © Jay Tanner  PHP Science Labs  2019 