SLA_DTPS2C

Plate centre from ξ, η and α, δ

ACTION:
From the tangent plane coordinates of a star of known [α, δ], determine the [α, δ] of the tangent point (double precision)
CALL:
CALL sla_DTPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)
GIVEN:

XI,ETA

D

tangent plane rectangular coordinates (radians)

RA,DEC

D

spherical coordinates (radians)


RETURNED:

RAZ1,DECZ1

D

spherical coordinates of tangent point, solution 1

RAZ2,DECZ2

D

spherical coordinates of tangent point, solution 2

N

I

number of solutions:

  0 = no solutions returned (note 2)

  1 = only the first solution is useful (note 3)

  2 = there are two useful solutions (note 3)


NOTES:
(1)
The RAZ1 and RAZ2 values returned are in the range 0 2π.
(2)
Cases where there is no solution can only arise near the poles. For example, it is clearly impossible for a star at the pole itself to have a non-zero ξ value, and hence it is meaningless to ask where the tangent point would have to be to bring about this combination of ξ and δ.
(3)
Also near the poles, cases can arise where there are two useful solutions. The argument N indicates whether the second of the two solutions returned is useful. N = 1 indicates only one useful solution, the usual case; under these circumstances, the second solution corresponds to the “over-the-pole” case, and this is reflected in the values of RAZ2 and DECZ2 which are returned.
(4)
The DECZ1 and DECZ2 values returned are in the range ±π, but in the ordinary, non-pole-crossing, case, the range is ±π/2.
(5)
RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
(6)
The projection is called the gnomonic projection; the Cartesian coordinates [ξ, η] are called standard coordinates. The latter are in units of the distance from the tangent plane to the projection point, i.e. radians near the origin.
(7)
When working in [x, y, z] rather than spherical coordinates, the equivalent Cartesian routine sla_DTPV2C is available.