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eraPn00

[epsa, rb, rp, rbp, rn, rbpn] = ERFA.pn00(date1, date2, dpsi, deps)

Precession-nutation, IAU 2000 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)
   dpsi,deps    double          nutation (Note 2)

Returned:

   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 (Note 8)

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 caller is responsible for providing the nutation components; they are in longitude and obliquity, in radians and are with respect to the equinox and ecliptic of date. For high-accuracy applications, free core nutation should be included as well as any other relevant corrections to the position of the CIP.

  2. The returned mean obliquity is consistent with the IAU 2000 precession-nutation models.

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

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

  5. 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.

  6. 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).

  7. 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.

  8. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the order given.

Called:

   eraPr00      IAU 2000 precession adjustments
   eraObl80     mean obliquity, IAU 1980
   eraBp00      frame bias and precession matrices, IAU 2000
   eraCr        copy r-matrix
   eraNumat     form nutation matrix
   eraRxr       product of two r-matrices

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