### SLA_DTPS2C

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

ACTION:
From the tangent plane coordinates of a star of known $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$, determine the $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ 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 $0\phantom{\rule{0.3em}{0ex}}-\phantom{\rule{0.3em}{0ex}}2\pi$.
(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 $±\pi$, but in the ordinary, non-pole-crossing, case, the range is $±\pi /2$.
(5)
RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
(6)
The projection is called the gnomonic projection; the Cartesian coordinates $\left[\phantom{\rule{0.3em}{0ex}}\xi ,\eta \phantom{\rule{0.3em}{0ex}}\right]$ 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 $\left[\phantom{\rule{0.3em}{0ex}}x,y,z\phantom{\rule{0.3em}{0ex}}\right]$ rather than spherical coordinates, the equivalent Cartesian routine sla_DTPV2C is available.