PFW06 Subroutine

  1. astro_module.f90
  2. astro_module
  3. PFW06

public subroutine PFW06(date1, date2, gamb, phib, psib, epsa)

Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).

Status: canonical model.

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. Naming the following points:

       e = J2000.0 ecliptic pole,
   p = GCRS pole,
   E = mean ecliptic pole of date,

    and P = mean pole of date,

    the four Fukushima-Williams angles are as follows:

    GAMB = gamma_bar = epE
PHIB = phi_bar = pE
PSIB = psi_bar = pEP
EPSA = epsilon_A = EP

  3. The matrix representing the combined effects of frame bias and precession is:

    PxB = R_1(-EPSA).R_3(-PSIB).R_1(PHIB).R_3(GAMB)

  4. The matrix representing the combined effects of frame bias, precession and nutation is simply:

    NxPxB = R_1(-EPSA-dE).R_3(-PSIB-dP).R_1(PHIB).R_3(GAMB)

    where dP and dE are the nutation components with respect to the ecliptic of date.

Reference

  • Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351

History

  • IAU SOFA revision: 2009 December 15

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(out) :: gamb

F-W angle gamma_bar (radians)
real(kind=wp), intent(out) :: phib

F-W angle phi_bar (radians)
real(kind=wp), intent(out) :: psib

F-W angle psi_bar (radians)
real(kind=wp), intent(out) :: epsa

F-W angle epsilon_A (radians)

Calls

proc~~pfw06~~CallsGraph proc~pfw06 PFW06 proc~obl06 OBL06 proc~pfw06->proc~obl06

Called by

proc~~pfw06~~CalledByGraph proc~pfw06 PFW06 proc~pnm06a PNM06A proc~pnm06a->proc~pfw06 proc~bp06 BP06 proc~bp06->proc~pfw06 proc~pmat06 PMAT06 proc~bp06->proc~pmat06 proc~pmat06->proc~pfw06 proc~pn06 PN06 proc~pn06->proc~pfw06 proc~gst06a GST06A proc~gst06a->proc~pnm06a proc~s06a S06A proc~s06a->proc~pnm06a proc~xys06a XYS06A proc~xys06a->proc~pnm06a proc~c2i06a C2I06A proc~c2i06a->proc~pnm06a proc~apco13 APCO13 proc~apco13->proc~pnm06a proc~pn06a PN06A proc~pn06a->proc~pn06 proc~apci13 APCI13 proc~apci13->proc~pnm06a proc~eo06a EO06A proc~eo06a->proc~pnm06a proc~pb06 PB06 proc~pb06->proc~pmat06 proc~ecm06 ECM06 proc~ecm06->proc~pmat06 proc~atco13 ATCO13 proc~atco13->proc~apco13 proc~atci13 ATCI13 proc~atci13->proc~apci13 proc~atic13 ATIC13 proc~atic13->proc~apci13 proc~eceq06 ECEQ06 proc~eceq06->proc~ecm06 proc~ee06a EE06A proc~ee06a->proc~gst06a proc~c2t06a C2T06A proc~c2t06a->proc~c2i06a proc~atoc13 ATOC13 proc~atoc13->proc~apco13 proc~eqec06 EQEC06 proc~eqec06->proc~ecm06

Contents

Source Code

PFW06

Source Code

    subroutine PFW06 ( date1, date2, gamb, phib, psib, epsa )

    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(out) :: gamb !! F-W angle gamma_bar (radians)
    real(wp),intent(out) :: phib !! F-W angle phi_bar (radians)
    real(wp),intent(out) :: psib !! F-W angle psi_bar (radians)
    real(wp),intent(out) :: epsa !! F-W angle epsilon_A (radians)

    real(wp) :: t

    !  Interval between fundamental date J2000.0 and given date (JC).
    t = ( ( date1-dj00 ) + date2 ) / djc

    !  P03 bias+precession angles.
    gamb =        (    -0.052928_wp    + &
                  (    10.556378_wp    + &
                  (     0.4932044_wp   + &
                  (    -0.00031238_wp  + &
                  (    -0.000002788_wp + &
                  (     0.0000000260_wp ) &
                                 * t ) * t ) * t ) * t ) * t ) * das2r
    phib =        ( 84381.412819_wp    + &
                  (   -46.811016_wp    + &
                  (     0.0511268_wp   + &
                  (     0.00053289_wp  + &
                  (    -0.000000440_wp + &
                  (    -0.0000000176_wp ) &
                                 * t ) * t ) * t ) * t ) * t ) * das2r
    psib =        (    -0.041775_wp    + &
                  (  5038.481484_wp    + &
                  (     1.5584175_wp   + &
                  (    -0.00018522_wp  + &
                  (    -0.000026452_wp + &
                  (    -0.0000000148_wp ) &
                                 * t ) * t ) * t ) * t ) * t ) * das2r
    epsa = OBL06 ( date1, date2 )

    end subroutine PFW06