SLA_TPS2C - Plate centre from $\xi,\eta$ and $\alpha,\delta$

ACTION:

From the tangent plane coordinates of a star of known $[\,\alpha,\delta\,]$, determine the $[\,\alpha,\delta\,]$ of the tangent point (single precision)

CALL:

CALL sla_TPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)

GIVEN:

XI,ETA	R	tangent plane rectangular coordinates (radians)
RA,DEC	R	spherical coordinates (radians)

RETURNED:

RAZ1,DECZ1	R	spherical coordinates of tangent point, solution 1
RAZ2,DECZ2	R	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 $0\!-\!2\pi$.
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 $\xi$ value, and hence it is meaningless to ask where the tangent point would have to be to bring about this combination of $\xi$ and $\delta$.
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 $\pm\pi$, but in the ordinary, non-pole-crossing, case, the range is $\pm\pi/2$.
5. RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
6. The projection is called the gnomonic projection; the Cartesian coordinates $[\,\xi,\eta\,]$ 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_TPV2C is available.