TPXES Subroutine

  1. astro_module.f90
  2. astro_module
  3. TPXES

public subroutine TPXES(a, b, a0, b0, xi, eta, j)

In the tangent plane projection, given celestial spherical coordinates for a star and the tangent point, solve for the star's rectangular coordinates in the tangent plane.

Status: support routine.

Notes

  1. The tangent plane projection is also called the "gnomonic projection" and the "central projection".

  2. The eta axis points due north in the adopted coordinate system. If the spherical coordinates are observed (RA,Dec), the tangent plane coordinates (xi,eta) are conventionally called the "standard coordinates". For right-handed spherical coordinates, (xi,eta) are also right-handed. The units of (xi,eta) are, effectively, radians at the tangent point.

  3. All angular arguments are in radians.

  4. This routine is a member of the following set:

     spherical       vector       solve for

    TPXES < TPXEV xi,eta TPSTS TPSTV star TPORS TPORV origin

References

  • Calabretta M.R. & Greisen, E.W., 2002, "Representations of celestial coordinates in FITS", Astron.Astrophys. 395, 1077

  • Green, R.M., "Spherical Astronomy", Cambridge University Press, 1987, Chapter 13.

History

  • IAU SOFA revision: 2018 January 2

Arguments

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

star's spherical coordinates
real(kind=wp), intent(in) :: b

star's spherical coordinates
real(kind=wp), intent(in) :: a0

tangent point's spherical coordinates
real(kind=wp), intent(in) :: b0

tangent point's spherical coordinates
real(kind=wp), intent(out) :: xi

rectangular coordinates of star image (Note 2)
real(kind=wp), intent(out) :: eta

rectangular coordinates of star image (Note 2)
integer, intent(out) :: j
  • 0 = OK
  • 1 = star too far from axis
  • 2 = antistar on tangent plane
  • 3 = antistar too far from axis

Contents

Source Code

TPXES

Source Code

    subroutine TPXES ( a, b, a0, b0, xi, eta, j )

    implicit none

    real(wp),intent(in) :: a !! star's spherical coordinates
    real(wp),intent(in) :: b !! star's spherical coordinates
    real(wp),intent(in) :: a0 !! tangent point's spherical coordinates
    real(wp),intent(in) :: b0 !! tangent point's spherical coordinates
    real(wp),intent(out) :: xi !! rectangular coordinates of star image (Note 2)
    real(wp),intent(out) :: eta !! rectangular coordinates of star image (Note 2)
    integer,intent(out) :: j !! status:
                             !! * 0 = OK
                             !! * 1 = star too far from axis
                             !! * 2 = antistar on tangent plane
                             !! * 3 = antistar too far from axis

    real(wp),parameter :: tiny = 1.0e-6_wp

    real(wp) :: sb0, sb, cb0, cb, da, sda, cda, d

    !  Functions of the spherical coordinates.
    sb0 = sin(b0)
    sb = sin(b)
    cb0 = cos(b0)
    cb = cos(b)
    da = a - a0
    sda = sin(da)
    cda = cos(da)

    !  Reciprocal of star vector length to tangent plane.
    d = sb*sb0 + cb*cb0*cda

    !  Check for error cases.
    if ( d > tiny ) then
       j = 0
    else if ( d >= 0.0_wp ) then
       j = 1
       d = tiny
    else if ( d > -tiny ) then
       j = 2
       d = -tiny
    else
       j = 3
    end if

    !  Return the tangent plane coordinates (even in dubious cases).
    xi = cb*sda / d
    eta = ( sb*cb0 - cb*sb0*cda ) / d

    end subroutine TPXES