PN06 Subroutine

  1. astro_module.f90
  2. astro_module
  3. PN06

public subroutine PN06(date1, date2, dpsi, deps, epsa, rb, rp, rbp, rn, rbpn)

Precession-nutation, IAU 2006 model: a multi-purpose routine, supporting classical (equinox-based) use directly and CIO-based use indirectly.

Status: support routine.

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

 2450123.7D0        0D0        (JD method)
  2451545D0      -1421.3D0     (J2000 method)
 2400000.5D0     50123.2D0     (MJD method)
 2450123.5D0       0.2D0       (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 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.

  3. The returned mean obliquity is consistent with the IAU 2006 precession.

  4. The matrix RB transforms vectors from GCRS to mean J2000.0 by applying frame bias.

  5. The matrix RP transforms vectors from mean J2000.0 to mean of date by applying precession.

  6. The matrix RBP transforms vectors from GCRS to mean of date by applying frame bias then precession. It is the product RP x RB.

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

  8. The matrix RBPN transforms vectors from GCRS to true of date (CIP/equinox). It is the product RN x RBP, applying frame bias, precession and nutation in that order.

  9. The X,Y,Z coordinates of the Celestial Intermediate Pole are elements (3,1-3) of the matrix RBPN.

References

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

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

History

  • IAU SOFA revision: 2013 November 14

Arguments

TypeIntentOptionalAttributesName
real(kind=wp), intent(in) :: date1

TT as a 2-part Julian Date (Note 1)
real(kind=wp), intent(in) :: date2

TT as a 2-part Julian Date (Note 1)
real(kind=wp), intent(in) :: dpsi

nutation (Note 2)
real(kind=wp), intent(in) :: deps

nutation (Note 2)
real(kind=wp), intent(out) :: epsa

mean obliquity (Note 3)
real(kind=wp), intent(out), dimension(3,3):: rb

frame bias matrix (Note 4)
real(kind=wp), intent(out), dimension(3,3):: rp

precession matrix (Note 5)
real(kind=wp), intent(out), dimension(3,3):: rbp

bias-precession matrix (Note 6)
real(kind=wp), intent(out), dimension(3,3):: rn

nutation matrix (Note 7)
real(kind=wp), intent(out), dimension(3,3):: rbpn

GCRS-to-true matrix (Note 8)

Calls

proc~~pn06~~CallsGraph proc~pn06 PN06 proc~pfw06 PFW06 proc~pn06->proc~pfw06 proc~rxr RXR proc~pn06->proc~rxr proc~tr TR proc~pn06->proc~tr proc~fw2m FW2M proc~pn06->proc~fw2m proc~obl06 OBL06 proc~pfw06->proc~obl06 proc~ir IR proc~fw2m->proc~ir proc~rz RZ proc~fw2m->proc~rz proc~rx RX proc~fw2m->proc~rx

Called by

proc~~pn06~~CalledByGraph proc~pn06 PN06 proc~pn06a PN06A proc~pn06a->proc~pn06

Contents

Source Code

PN06

Source Code

    subroutine PN06 ( date1, date2, dpsi, deps, &
                      epsa, rb, rp, rbp, rn, rbpn )

    implicit none

    real(wp),intent(in) :: date1 !! TT as a 2-part Julian Date (Note 1)
    real(wp),intent(in) :: date2 !! TT as a 2-part Julian Date (Note 1)
    real(wp),intent(in) :: dpsi !! nutation (Note 2)
    real(wp),intent(in) :: deps !! nutation (Note 2)
    real(wp),intent(out) :: epsa !! mean obliquity (Note 3)
    real(wp),dimension(3,3),intent(out) :: rb !! frame bias matrix (Note 4)
    real(wp),dimension(3,3),intent(out) :: rp !! precession matrix (Note 5)
    real(wp),dimension(3,3),intent(out) :: rbp !! bias-precession matrix (Note 6)
    real(wp),dimension(3,3),intent(out) :: rn !! nutation matrix (Note 7)
    real(wp),dimension(3,3),intent(out) :: rbpn !! GCRS-to-true matrix (Note 8)

    !  JD for MJD 0
    real(wp),parameter :: djm0 = 2400000.5_wp

    !  Reference epoch (J2000.0), MJD
    real(wp),parameter :: djm00 = 51544.5_wp

    real(wp) :: gamb, phib, psib, eps, rt(3,3)

    !  Bias-precession Fukushima-Williams angles of J2000.0 = frame bias.
    call PFW06 ( djm0, djm00, gamb, phib, psib, eps )

    !  B matrix.
    call FW2M ( gamb, phib, psib, eps, rb )

    !  Bias-precession Fukushima-Williams angles of date.
    call PFW06 ( date1, date2, gamb, phib, psib, eps )

    !  Bias-precession matrix.
    call FW2M ( gamb, phib, psib, eps, rbp )

    !  Solve for precession matrix.
    call TR ( rb, rt )
    call RXR ( rbp, rt, rp )

    !  Equinox-based bias-precession-nutation matrix.
    call FW2M ( gamb, phib, psib+dpsi, eps+deps, rbpn )

    !  Solve for nutation matrix.
    call TR ( rbp, rt )
    call RXR ( rbpn, rt, rn )

    !  Obliquity, mean of date.
    epsa = eps

    end subroutine PN06