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# nut00a

erfa.nut00a(date1, date2)

  Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation with free core nutation omitted).

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

  Notes

  Wraps ERFA function `eraNut00a`. The ERFA documentation is:

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

      Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation
      with free core nutation omitted).

      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.

         Both the luni-solar and planetary nutations are included.  The
         latter are due to direct planetary nutations and the
         perturbations of the lunar and terrestrial orbits.

      3) The function computes the MHB2000 nutation series with the
         associated corrections for planetary nutations.  It is an
         implementation of the nutation part of the IAU 2000A precession-
         nutation model, formally adopted by the IAU General Assembly in
         2000, namely MHB2000 (Mathews et al. 2002), but with the free
         core nutation (FCN - see Note 4) omitted.

      4) The full MHB2000 model also contains contributions to the
         nutations in longitude and obliquity due to the free-excitation
         of the free-core-nutation during the period 1979-2000.  These FCN
         terms, which are time-dependent and unpredictable, are NOT
         included in the present function and, if required, must be
         independently computed.  With the FCN corrections included, the
         present function delivers a pole which is at current epochs
         accurate to a few hundred microarcseconds.  The omission of FCN
         introduces further errors of about that size.

      5) The present function provides classical nutation.  The MHB2000
         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 MHB2000 algorithm also provides "total" nutations, comprising
         the arithmetic sum of the frame bias, precession adjustments,
         luni-solar nutation and planetary nutation.  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 sub-mas accuracy at current dates.
         However, there are three shortcomings in the MHB2000 model that
         must be taken into account if more accurate or definitive results
         are required (see Wallace 2002):

           (i) The MHB2000 total nutations are simply arithmetic sums,
               yet in reality the various components are successive Euler
               rotations.  This slight lack of rigor leads to cross terms
               that exceed 1 mas after a century.  The rigorous procedure
               is to form the GCRS-to-true rotation matrix by applying the
               bias, precession and nutation in that order.

          (ii) Although the precession adjustments are stated to be with
               respect to Lieske et al. (1977), the MHB2000 model does
               not specify which set of Euler angles are to be used and
               how the adjustments are to be applied.  The most literal
               and straightforward procedure is to adopt the 4-rotation
               epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR
               to psi_A and DEPSPR to both omega_A and eps_A.

         (iii) The MHB2000 model predates the determination by Chapront
               et al. (2002) of a 14.6 mas displacement between the
               J2000.0 mean equinox and the origin of the ICRS frame.  It
               should, however, be noted that neglecting this displacement
               when calculating star coordinates does not lead to a
               14.6 mas change in right ascension, only a small second-
               order distortion in the pattern of the precession-nutation
               effect.

         For these reasons, the ERFA functions do not generate the "total
         nutations" directly, though they can of course easily be
         generated by calling eraBi00, eraPr00 and the present function
         and adding the results.

      7) The MHB2000 model contains 41 instances where the same frequency
         appears multiple times, of which 38 are duplicates and three are
         triplicates.  To keep the present code close to the original MHB
         algorithm, this small inefficiency has not been corrected.

      Called:
         eraFal03     mean anomaly of the Moon
         eraFaf03     mean argument of the latitude of the Moon
         eraFaom03    mean longitude of the Moon's ascending node
         eraFame03    mean longitude of Mercury
         eraFave03    mean longitude of Venus
         eraFae03     mean longitude of Earth
         eraFama03    mean longitude of Mars
         eraFaju03    mean longitude of Jupiter
         eraFasa03    mean longitude of Saturn
         eraFaur03    mean longitude of Uranus
         eraFapa03    general accumulated precession in longitude

      References:

         Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
         Astron.Astrophys. 387, 700

         Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
         Astron.Astrophys. 58, 1-16

         Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
         107, B4.  The MHB_2000 code itself was obtained on 9th September
         2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.

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

         Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
         Astron.Astrophys.Supp.Ser. 135, 111

         Wallace, P.T., "Software for Implementing the IAU 2000
         Resolutions", in IERS Workshop 5.1 (2002)

      This revision:  2021 July 20

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