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eraEect00

rv = ERFA.eect00(date1, date2)

Equation of the equinoxes complementary terms, consistent with IAU 2000 resolutions.

Given:

   date1,date2  double   TT as a 2-part Julian Date (Note 1)

Returned (function value):

                double   complementary terms (Note 2)

Notes:

  1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
          date1          date2

       2450123.7           0.0       (JD method)
       2451545.0       -1421.3       (J2000 method)
       2400000.5       50123.2       (MJD method)
       2450123.5           0.2       (date & time method)

The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

  1. The "complementary terms" are part of the equation of the equinoxes (EE), classically the difference between apparent and mean Sidereal Time:
      GAST = GMST + EE

with:

      EE = dpsi * cos(eps)

where dpsi is the nutation in longitude and eps is the obliquity of date. However, if the rotation of the Earth were constant in an inertial frame the classical formulation would lead to apparent irregularities in the UT1 timescale traceable to side- effects of precession-nutation. In order to eliminate these effects from UT1, "complementary terms" were introduced in 1994 (IAU, 1994) and took effect from 1997 (Capitaine and Gontier, 1993):

      GAST = GMST + CT + EE

By convention, the complementary terms are included as part of the equation of the equinoxes rather than as part of the mean Sidereal Time. This slightly compromises the "geometrical" interpretation of mean sidereal time but is otherwise inconsequential.

The present function computes CT in the above expression, compatible with IAU 2000 resolutions (Capitaine et al., 2002, and IERS Conventions 2003).

Called:

   eraFal03     mean anomaly of the Moon
   eraFalp03    mean anomaly of the Sun
   eraFaf03     mean argument of the latitude of the Moon
   eraFad03     mean elongation of the Moon from the Sun
   eraFaom03    mean longitude of the Moon's ascending node
   eraFave03    mean longitude of Venus
   eraFae03     mean longitude of Earth
   eraFapa03    general accumulated precession in longitude

References:

Capitaine, N. & Gontier, A.-M., Astron.Astrophys., 275, 645-650 (1993)

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astron.Astrophys., 406, 1135-1149 (2003)

IAU Resolution C7, Recommendation 3 (1994)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2021 May 11

Copyright (C) 2013-2021, NumFOCUS Foundation. Derived, with permission, from the SOFA library.