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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Astronomical Refraction: Computational Method for All Zenith Angles
From: Marcel Tschudin
Date: 2005 Aug 23, 01:52 +0300

```Frank, you wrote

> Today, I coded  up a much better way of dealing with all of this
> atmospheric
> structure. I  generate a density table directly from the temperature
> profile
> of the atmosphere  (this is the principal independent variable) and the
> condition of hydrostatic  equilibrium and the ideal gas law which is how
> atmosphere
> models are  derived usually. While these equations can be integrated
> analytically in  important special cases you then have to do a lot of work
> patching
> together the  pieces. But if you do the integration numerically from the
> ground
> up, it's  trivial to modify the temperature profile, generate new
> atmosphere
> data, and  then re-run the refraction tables.

Added what you proposed. Density values look resonable, BUT ...

> And that's it. This model can then be used  as input to the refraction
> integration. Using a lapse rate of 5.70 deg C per  kilometer below 11km
> altitude and
> a rate of zero above that altitude, I was able  to replicate almost
> exactly
> the refraction tables in the Auer-Standish article.  The differences were
> mostly less than one-tenth of a second of arc.

I would have wished to get such results, mine are substancially higher...
I checked and checked and can still not findout why.

Further you wrote
> By the way, Marcel, thanks for raising this  issue. It's led me to all
> sorts
> of interesting things.
...and I did not imagine that I finally would spend so much time on it. Your
"interesting things" gave me courage and the input to start writing a
program for it. At the moment, it looks as I am stuck half way.

Marcel

```
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