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 = 2017 03 25 - Saturday (Gregorian) 
 Time  UT HMS =  00 00 00.000 = +0 day = UTFrac
 ±Delta T HMS = +00 00 00.000 = +0 day = dTFrac

 JD12 = 2457838
 JD00 = 2457837.5 = (JD12 - 0.5)

 JD = 2457837.5 = (JD00 + UTFrac + dTFrac)
  T = 0.1722792607802874 Julian centuries from J2000.0

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 Nutation In Obliquity of the Ecliptic (IAU 1980 Series)

 Delta epsilon = -0.002103027098° = -07.571"


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 JD 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
JDGeneral JD number for given date, time and ΔT
TTime factor in Julian centuries reckoned from J2000.0, corresponding to JD
DegToRadThis is a conversion factor used to convert degrees into equivalent radians.  We multiply degrees by this factor to obtain the equivalent radians.
wNutation series accumulator variable
w1Mean elongation of the moon from the sun.
w2Mean solar anomaly.
w3Mean lunar anomaly.
w4Lunar argument of latitude.
w5Longitude of ascending node of lunar orbit on the ecliptic as measured from the mean equinox of date.
dEpsDegNutation in ecliptical longitude expressed in degrees.



Algorithm To Compute The Nutation In Obliquity of the Ecliptic




The following PHP function returns the nutation in obliquity in decimal degrees.

PHP function to compute the nutation in obliquity in decimal degrees for given JD argument.




The following C++/CPP function returns the nutation in obliquity in decimal degrees.

CPP function to compute 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 JD argument.


© Jay Tanner - PHP Science Labs - 2017