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# pn00b

erfa.pn00b(date1, date2)

  Precession-nutation, IAU 2000B model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly.

  Parameters:
    date1 double array
    date2 double array
  Returns:
    dpsi double array
    deps double array
    epsa double array
    rb double array
    rp double array
    rbp double array
    rn double array
    rbpn double array

  Notes

  Wraps ERFA function `eraPn00b`. The ERFA documentation is:

      - - - - - - - - -
       e r a P n 0 0 b
      - - - - - - - - -

      Precession-nutation, IAU 2000B model:  a multi-purpose function,
      supporting classical (equinox-based) use directly and CIO-based
      use indirectly.

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

      Returned:
         dpsi,deps    double          nutation (Note 2)
         epsa         double          mean obliquity (Note 3)
         rb           double[3][3]    frame bias matrix (Note 4)
         rp           double[3][3]    precession matrix (Note 5)
         rbp          double[3][3]    bias-precession matrix (Note 6)
         rn           double[3][3]    nutation matrix (Note 7)
         rbpn         double[3][3]    GCRS-to-true matrix (Notes 8,9)

      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 (luni-solar + planetary, IAU 2000B) in
          longitude and obliquity are in radians and with respect to the
          equinox and ecliptic of date.  For more accurate results, but
          at the cost of increased computation, use the eraPn00a function.
          For the utmost accuracy, use the eraPn00 function, where the
          nutation components are caller-specified.

      3)  The mean obliquity is consistent with the IAU 2000 precession.

      4)  The matrix rb transforms vectors from GCRS to J2000.0 mean
          equator and equinox by applying frame bias.

      5)  The matrix rp transforms vectors from J2000.0 mean equator and
          equinox to mean equator and equinox of date by applying
          precession.

      6)  The matrix rbp transforms vectors from GCRS to mean equator and
          equinox of date by applying frame bias then precession.  It is
          the product rp x rb.

      7)  The matrix rn transforms vectors from mean equator and equinox
          of date to true equator and equinox of date by applying the
          nutation (luni-solar + planetary).

      8)  The matrix rbpn transforms vectors from GCRS to true equator and
          equinox of date.  It is the product rn x rbp, applying frame
          bias, precession and nutation in that order.

      9)  The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
          Pole are elements (3,1-3) of the GCRS-to-true matrix,
          i.e. rbpn[2][0-2].

      10) It is permissible to re-use the same array in the returned
          arguments.  The arrays are filled in the stated order.

      Called:
         eraNut00b    nutation, IAU 2000B
         eraPn00      bias/precession/nutation results, IAU 2000

      Reference:

         Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
         "Expressions for the Celestial Intermediate Pole and Celestial
         Ephemeris Origin consistent with the IAU 2000A precession-
         nutation model", Astron.Astrophys. 400, 1145-1154 (2003).

         n.b. The celestial ephemeris origin (CEO) was renamed "celestial
              intermediate origin" (CIO) by IAU 2006 Resolution 2.

      This revision:  2021 May 11

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