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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.


next up previous
Next: SLA_TPV2C - Plate centre from and x,y,z
Up: SUBPROGRAM SPECIFICATIONS
Previous: SLA_TP2V - Tangent Plane to Direction Cosines

SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk