From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node168.html | 276 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 276 insertions(+) create mode 100644 src/slalib/sun67.htx/node168.html (limited to 'src/slalib/sun67.htx/node168.html') diff --git a/src/slalib/sun67.htx/node168.html b/src/slalib/sun67.htx/node168.html new file mode 100644 index 0000000..c695ed9 --- /dev/null +++ b/src/slalib/sun67.htx/node168.html @@ -0,0 +1,276 @@ + + + + +SLA_REFV - Apply Refraction to Vector + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_REFZ - Apply Refraction to ZD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFRO - Refraction +

+

+

SLA_REFV - Apply Refraction to Vector +   +

+
+
ACTION: +
Adjust an unrefracted Cartesian vector to include the effect of +atmospheric refraction, using the simple + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model. +

CALL: +
CALL sla_REFV (VU, REFA, REFB, VR) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + +
VUDunrefracted position of the source ($[\,Az,El~]$ 3-vector)
REFAD$\tan \zeta$ coefficient (radians)
REFBD$\tan^{3} \zeta$ coefficient (radians)
+

+
RETURNED: +
+
+ + + + + +
VRDrefracted position of the source ($[\,Az,El~]$ 3-vector)
+

+
NOTES: +
+
1. +
This routine applies the adjustment for refraction in the +opposite sense to the usual one - it takes an unrefracted +(in vacuo) position and produces an observed (refracted) + position, whereas the + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model strictly + applies to the case where an observed position is to have the + refraction removed. The unrefracted to refracted case is + harder, and requires an inverted form of the text-book + refraction models; the algorithm used here is equivalent to + one iteration of the Newton-Raphson method applied to the + above formula. +
2. +
Though optimized for speed rather than precision, the present + routine achieves consistency with the refracted-to-unrefracted + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model at better than 1 microarcsecond within + $30^\circ$ of the zenith and remains within 1 milliarcsecond to + $\zeta=70^\circ$. The inherent accuracy of the model is, of + course, far worse than this - see the documentation for sla_REFCO + for more information. +
3. +
At low elevations (below about $3^{\circ}$) the refraction + correction is held back to prevent arithmetic problems and + wildly wrong results. Over a wide range of observer heights + and corresponding temperatures and pressures, the following + levels of accuracy are achieved, relative to numerical + integration through a model atmosphere: +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
$\zeta_{obs}$error 
   
$80^\circ$$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$ 
$81^\circ$$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$ 
$82^\circ$$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$ 
$83^\circ$$3\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$84^\circ$$7\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$85^\circ$$17\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$86^\circ$$45\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$87^\circ$$150\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$88^\circ$$340\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$89^\circ$$620\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$90^{\circ}$$1100\hspace{-0.05em}^{'\hspace{-0.1em}'}$ 
$91^\circ$$1900\hspace{-0.05em}^{'\hspace{-0.1em}'}$< high-altitude
$92^\circ$$3200\hspace{-0.05em}^{'\hspace{-0.1em}'}$< sites only
+
4. +
See also the routine sla_REFZ, which performs the adjustment to + the zenith distance rather than in $[\,x,y,z\,]$. The present routine is faster than sla_REFZ and, + except very low down, + is equally accurate for all practical purposes. However, beyond + about $\zeta=84^\circ$ sla_REFZ should be used, and for the utmost + accuracy iterative use of sla_REFRO should be considered. +
+
+ +next + +up + +previous +
+ Next: SLA_REFZ - Apply Refraction to ZD +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFRO - Refraction +

+

+

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