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    Re: Astronomical Refraction: Computational Method for All Zenith Angles
    From: Marcel Tschudin
    Date: 2005 Aug 23, 11:53 +0300

    Refering the comments made to this subject:
    > 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.
    Thanks god! It works now. Comparing with Frank's code showed me that the in
    the Auer Standish algorythm the air density has to be relative and not
    absolute. After correcting this the calculation of refraction values works
    now excellent.
    Refering to the Auer Standish paper, it is for me still questionable how
    they could arrive with their atmospheric model to the results they compare
    with the analytical formula using the indicated input data.
    Comparing the algorythm with the results Garfinkel (1967) obtained using a
    lapse rate of 6.5degK/km (see Table IV):
          Z.D. Garfinkel Calculated Difference
          85 10.233 10.239 0.006
          86 12.200 12.205 0.005
          87 14.967 14.961 -0.006
          88 19.033 19.034 0.001
          89 25.400 25.394 -0.006
          90 36.050 36.050 0.000
    A  very special thankyou to you, Frank, for all your help you provided to
    obtain this tool. Without your help, I would not have been able to do it. To
    all of you in the mail list, who are not so much interested in this subject,
    I would like to thank you for your comprehension.

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