SLA_REFZ - Apply Refraction to ZD

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/node169.html | 275 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 275 insertions(+) create mode 100644 src/slalib/sun67.htx/node169.html (limited to 'src/slalib/sun67.htx/node169.html') diff --git a/src/slalib/sun67.htx/node169.html b/src/slalib/sun67.htx/node169.html new file mode 100644 index 0000000..6180ab0 --- /dev/null +++ b/src/slalib/sun67.htx/node169.html @@ -0,0 +1,275 @@ + + + + +SLA_REFZ - Apply Refraction to ZD + + + + + + + + + + + + +

+ +

+
+ Next: SLA_RVEROT - RV Corrn to Earth Centre +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_REFV - Apply Refraction to Vector +

SLA_REFZ - Apply Refraction to ZD + +

ACTION: +: Adjust an unrefracted zenith distance to include the effect of +atmospheric refraction, using the simple + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model. +
CALL: +: CALL sla_REFZ (ZU, REFA, REFB, ZR) +

GIVEN: +

+
+ + + + + + + + + + + + + +

ZU	D	unrefracted zenith distance of the source (radians)
REFA	D	$\tan \zeta$ coefficient (radians)
REFB	D	$\tan^{3} \zeta$ coefficient (radians)

RETURNED: +

+
+ + + + + +

ZR	D	refracted zenith distance (radians)

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 formula used here is based on the + Newton-Raphson method. For the utmost numerical consistency + with the refracted to unrefracted model, two iterations are + carried out, achieving agreement at the 10^-11 arcsecond level + for $\zeta=80^\circ$ . The inherent accuracy of the model + is, of course, far worse than this - see the documentation for + sla_REFCO for more information. +

2. +

At $\zeta=83^\circ$ , the rapidly-worsening + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model is abandoned and an empirical formula takes over: +

$\begin{displaymath} +\Delta \zeta = F \left( + \frac{0^\circ\hspace{-0.37em}.\hspa... + ...hspace{0.02em}00202 E^2} + {1 + 0.28385 E +0.02390 E^2} \right) \end{displaymath}$

+where $E=90^\circ-\zeta_{true}$ and F is a factor chosen to meet the + $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ formula at $\zeta=83^\circ$ . 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

$80^\circ$	$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$
$81^\circ$	$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$
$82^\circ$	$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$
$83^\circ$	$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$
$84^\circ$	$4\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.9$
$85^\circ$	$5\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$
$86^\circ$	$6\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$
$87^\circ$	$7\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$
$88^\circ$	$11\hspace{-0.05em}^{'\hspace{-0.1em}'}$
$89^\circ$	$21\hspace{-0.05em}^{'\hspace{-0.1em}'}$
$90^{\circ}$	$43\hspace{-0.05em}^{'\hspace{-0.1em}'}$
$91^\circ$	$92\hspace{-0.05em}^{'\hspace{-0.1em}'}$	< high-altitude
$92^\circ$	$220\hspace{-0.05em}^{'\hspace{-0.1em}'}$	< sites only

3. +