era.tpors.md

eraTpors

rv = ERFA.tpors(xi, eta, a, b)

In the tangent plane projection, given the rectangular coordinates of a star and its spherical coordinates, determine the spherical coordinates of the tangent point.

Given:

   xi,eta     double  rectangular coordinates of star image (Note 2)
   a,b        double  star's spherical coordinates (Note 3)

Returned:

   *a01,*b01  double  tangent point's spherical coordinates, Soln. 1
   *a02,*b02  double  tangent point's spherical coordinates, Soln. 2

Returned (function value):

              int     number of solutions:
                      0 = no solutions returned (Note 5)
                      1 = only the first solution is useful (Note 6)
                      2 = both solutions are useful (Note 6)

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". If the spherical coordinates are with respect to a right-handed triad, (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. The angles a01 and a02 are returned in the range 0-2pi. The angles b01 and b02 are returned in the range +/-pi, but in the usual, non-pole-crossing, case, the range is +/-pi/2.

5. Cases where there is no solution can arise only near the poles. For example, it is clearly impossible for a star at the pole itself to have a non-zero xi value, and hence it is meaningless to ask where the tangent point would have to be to bring about this combination of xi and dec.

6. Also near the poles, cases can arise where there are two useful solutions. The return value indicates whether the second of the two solutions returned is useful; 1 indicates only one useful solution, the usual case.

7. The basis of the algorithm is to solve the spherical triangle PSC, where P is the north celestial pole, S is the star and C is the tangent point. The spherical coordinates of the tangent point are [a0,b0]; writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), side c is then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be found) is (pi/2-b0). Angle C is given by sin(C) = xi/rho and cos(C) = eta/rho. Angle P (to be found) is the longitude difference between star and tangent point (a-a0).

8) This function is a member of the following set:

       spherical      vector         solve for

       eraTpxes      eraTpxev         xi,eta
       eraTpsts      eraTpstv          star
     > eraTpors <    eraTporv         origin

Called:

   eraAnp       normalize angle into range 0 to 2pi

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.

This revision: 2018 January 2

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