PMPX Subroutine

  1. astro_module.f90
  2. astro_module
  3. PMPX

public subroutine PMPX(rc, dc, pr, pd, px, rv, pmt, pob, pco)

Proper motion and parallax.

Status: support routine.

Notes

  1. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.

  2. The proper motion time interval is for when the starlight reaches the solar system barycenter.

  3. To avoid the need for iteration, the Roemer effect (i.e. the small annual modulation of the proper motion coming from the changing light time) is applied approximately, using the direction of the star at the catalog epoch.

References

  • 1984 Astronomical Almanac, pp B39-B41.

  • Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books (2013), Section 7.2.

History

  • IAU SOFA revision: 2017 March 11

Arguments

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

ICRS RA at catalog epoch (radians)
real(kind=wp), intent(in) :: dc

ICRS Dec at catalog epoch (radians)
real(kind=wp), intent(in) :: pr

RA proper motion (radians/year; Note 1)
real(kind=wp), intent(in) :: pd

Dec proper motion (radians/year)
real(kind=wp), intent(in) :: px

parallax (arcsec)
real(kind=wp), intent(in) :: rv

radial velocity (km/s, +ve if receding)
real(kind=wp), intent(in) :: pmt

proper motion time interval (SSB, Julian years)
real(kind=wp), intent(in), dimension(3):: pob

SSB to observer vector (au)
real(kind=wp), intent(out), dimension(3):: pco

coordinate direction (BCRS unit vector)

Calls

proc~~pmpx~~CallsGraph proc~pmpx PMPX proc~pdp PDP proc~pmpx->proc~pdp

Called by

proc~~pmpx~~CalledByGraph proc~pmpx PMPX proc~atciq ATCIQ proc~atciq->proc~pmpx proc~atciqn ATCIQN proc~atciqn->proc~pmpx proc~atci13 ATCI13 proc~atci13->proc~atciq proc~atco13 ATCO13 proc~atco13->proc~atciq

Contents

Source Code

PMPX

Source Code

    subroutine PMPX ( rc, dc, pr, pd, px, rv, pmt, pob, pco )

    implicit none

    real(wp),intent(in) :: rc !! ICRS RA at catalog epoch (radians)
    real(wp),intent(in) :: dc !! ICRS Dec at catalog epoch (radians)
    real(wp),intent(in) :: pr !! RA proper motion (radians/year; Note 1)
    real(wp),intent(in) :: pd !! Dec proper motion (radians/year)
    real(wp),intent(in) :: px !! parallax (arcsec)
    real(wp),intent(in) :: rv !! radial velocity (km/s, +ve if receding)
    real(wp),intent(in) :: pmt !! proper motion time interval (SSB, Julian years)
    real(wp),dimension(3),intent(in) :: pob !! SSB to observer vector (au)
    real(wp),dimension(3),intent(out) :: pco !! coordinate direction (BCRS unit vector)

    !  Days per Julian millennium
    real(wp),parameter :: djm = 365250.0_wp

    !  Astronomical unit (m, IAU 2012)
    real(wp),parameter :: aum = 149597870.7e3_wp

    !  Light time for 1 au, Julian years
    real(wp),parameter :: aulty = aum/cmps/d2s/djy

    !  Km/s to au/year
    real(wp),parameter :: vf = d2s*djm/aum

    integer :: i
    real(wp) :: sr, cr, sd, cd, x, y, z, p(3), pdb, &
                dt, pxr, w, pdz, pm(3)

    !  Catalog spherical coordinates to unit vector (and useful functions).
    sr = sin(rc)
    cr = cos(rc)
    sd = sin(dc)
    cd = cos(dc)
    x = cr*cd
    y = sr*cd
    z = sd
    p(1) = x
    p(2) = y
    p(3) = z

    !  Component of observer vector in star direction.
    call PDP ( p, pob, pdb )

    !  Proper motion time interval (y), including Roemer effect.
    dt = pmt + pdb*aulty

    !  Space motion (radians per year).
    pxr = px*das2r
    w = vf*rv*pxr
    pdz = pd*z
    pm(1) = - pr*y - pdz*cr + w*x
    pm(2) =   pr*x - pdz*sr + w*y
    pm(3) =          pd*cd  + w*z

    !  Coordinate direction of star (unit vector, BCRS).
    do i=1,3
       p(i) = p(i) + dt*pm(i) - pxr*pob(i)
    end do
    call PN ( p, w, pco )

    end subroutine PMPX