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    Re: Refraction
    From: Fred Hebard
    Date: 2005 Aug 4, 13:33 -0400

    Here's the answer to your original question from the Intro to Volume 2
    of HO249:
    "A useful feature of these tables is the provision for low and even
    negative altitudes; this enables sights of the Sun, or other bodies, to
    be reduced when actually below the horizon as seen from sea level.
    Refraction at such low altitudes is large and variations from the
    standard values are too great to be ignored; provision is thus made in
    Table 6 for the application of a temperature correction in such cases."
    So they're using a different refraction table for Volumes 2 & 3 than
    for Volume 1.  That different table (Table 6) is found in the file
    "SRTA_flier.pdf" for Volume 2's directory on the link I sent earlier.
    Note there are two "SRTA_filer.pdf" files, one for Volume 1 and one for
    Volume 2 (don't know about Volume 3).  Volume 2's Table 6 includes
    negative sextant altitudes down to about -3.5 degrees.
    You can correct the refraction values given by Table 6 for temperature
    in a subsection of the table, which is to what the above quotation
    refers in its last sentence.
    As far as the formula used to calculate Table 6, it may be somewhere in
    HO249.  I assume you have Meeus' formula for normal observations.
    Meeus' formula, as transcribed by G. Huxtable, is:
    tan(90-0.99914*S-(7.31/(S+4.4)), where S is the sextant altitude in
    degrees.  I don't know whether this formula blows up at 0, but you
    could try it and see whether it gives the same results as HO249's Table
    6.  It's pretty close to the Nautical Almanac's refraction table.  As I
    recall, the Nautical Almanac recently revised their refraction formula
    slightly, so it might be off by a hair.
    As indicated in a previous post, I have no idea how Meeus' formula was
    Frederick V. Hebard, PhD                      Email: mailto:Fred@acf.org
    Staff Pathologist, Meadowview Research Farms  Web: http://www.acf.org
    American Chestnut Foundation                  Phone: (276) 944-4631
    14005 Glenbrook Ave.                          Fax: (276) 944-0934
    Meadowview, VA 24361
    On Aug 4, 2005, at 12:20 PM, Marcel E. Tschudin wrote:
    > Fred,
    > Yes, how do I get in this? Just trying to cover in a self-made program
    > the
    > situation from an object at the horizon (over sea level) as seen from a
    > mountain or air craft.
    > The "real" calculation is done via integration. But since this is not
    > very
    > practical one uses approximative formulae like e.g. the one from
    > Bennett
    > which Meeus mentions in his book Astronomical Algorithms. All tables on
    > refraction I found so far do end at 0? elevation and for none of the
    > approximative formulae I could find an indication that they also would
    > be
    > valid for negative elevations.
    > I also was wandering whether the approximate formulae could be used by
    > calculating the Refraction R for e.g. -2? the follwing way:
    > R(-2?)  =  R(0?)  +  (  R(0?) - R(+2?)  )
    > If this would be correct then one would not need separate formula for
    > negative elevations.
    > Greetings from Marcel

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