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)

XI,ETA	D	tangent plane rectangular coordinates (radians)

RA,DEC	D	spherical coordinates (radians)

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 $0 - 2 π$ .
(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 $\pm π$ , but in the ordinary, non-pole-crossing, case, the range is $\pm π / 2$ .
(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.