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eraPn06

[epsa, rb, rp, rbp, rn, rbpn] = ERFA.pn06(date1, date2, dpsi, deps)

Precession-nutation, IAU 2006 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 (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.

  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 2006 precession.

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

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

Called:

   eraPfw06     bias-precession F-W angles, IAU 2006
   eraFw2m      F-W angles to r-matrix
   eraCr        copy r-matrix
   eraTr        transpose r-matrix
   eraRxr       product of two r-matrices

References:

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2021 May 11

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