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# nut00b

erfa.nut00b(date1, date2)

  Nutation, IAU 2000B model.

  Parameters:
    date1 double array
    date2 double array
  Returns:
    dpsi double array
    deps double array

  Notes

  Wraps ERFA function `eraNut00b`. The ERFA documentation is:

      - - - - - - - - - -
       e r a N u t 0 0 b
      - - - - - - - - - -

      Nutation, IAU 2000B model.

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

      Returned:
         dpsi,deps     double    nutation, luni-solar + planetary (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.

      2) The nutation components in longitude and obliquity are in radians
         and with respect to the equinox and ecliptic of date.  The
         obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
         value of 84381.448 arcsec.  (The errors that result from using
         this function with the IAU 2006 value of 84381.406 arcsec can be
         neglected.)

         The nutation model consists only of luni-solar terms, but
         includes also a fixed offset which compensates for certain long-
         period planetary terms (Note 7).

      3) This function is an implementation of the IAU 2000B abridged
         nutation model formally adopted by the IAU General Assembly in
         2000.  The function computes the MHB_2000_SHORT luni-solar
         nutation series (Luzum 2001), but without the associated
         corrections for the precession rate adjustments and the offset
         between the GCRS and J2000.0 mean poles.

      4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400
         terms.  The IAU 2000B model (McCarthy & Luzum 2003) contains only
         77 terms, plus additional simplifications, yet still delivers
         results of 1 mas accuracy at present epochs.  This combination of
         accuracy and size makes the IAU 2000B abridged nutation model
         suitable for most practical applications.

         The function delivers a pole accurate to 1 mas from 1900 to 2100
         (usually better than 1 mas, very occasionally just outside
         1 mas).  The full IAU 2000A model, which is implemented in the
         function eraNut00a (q.v.), delivers considerably greater accuracy
         at current dates;  however, to realize this improved accuracy,
         corrections for the essentially unpredictable free-core-nutation
         (FCN) must also be included.

      5) The present function provides classical nutation.  The
         MHB_2000_SHORT algorithm, from which it is adapted, deals also
         with (i) the offsets between the GCRS and mean poles and (ii) the
         adjustments in longitude and obliquity due to the changed
         precession rates.  These additional functions, namely frame bias
         and precession adjustments, are supported by the ERFA functions
         eraBi00  and eraPr00.

      6) The MHB_2000_SHORT algorithm also provides "total" nutations,
         comprising the arithmetic sum of the frame bias, precession
         adjustments, and nutation (luni-solar + planetary).  These total
         nutations can be used in combination with an existing IAU 1976
         precession implementation, such as eraPmat76,  to deliver GCRS-
         to-true predictions of mas accuracy at current epochs.  However,
         for symmetry with the eraNut00a  function (q.v. for the reasons),
         the ERFA functions do not generate the "total nutations"
         directly.  Should they be required, they could of course easily
         be generated by calling eraBi00, eraPr00 and the present function
         and adding the results.

      7) The IAU 2000B model includes "planetary bias" terms that are
         fixed in size but compensate for long-period nutations.  The
         amplitudes quoted in McCarthy & Luzum (2003), namely
         Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
         the "total nutations" method described in Note 6.  The Luzum
         (2001) values used in this ERFA implementation, namely -0.135 mas
         and +0.388 mas, are optimized for the "rigorous" method, where
         frame bias, precession and nutation are applied separately and in
         that order.  During the interval 1995-2050, the ERFA
         implementation delivers a maximum error of 1.001 mas (not
         including FCN).

      References:

         Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
         for the precession quantities based upon the IAU /1976/ system of
         astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)

         Luzum, B., private communication, 2001 (Fortran code
         MHB_2000_SHORT)

         McCarthy, D.D. & Luzum, B.J., "An abridged model of the
         precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
         85, 37-49 (2003)

         Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
         Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)

      This revision:  2021 May 11

      Copyright (C) 2013-2023, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.