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From: Frank Reed (no email)
Date: Sat Apr 02 2005 - 05:35:16 EST
Jim T wrote:
"The oblateness correction accounts for the distortion of the earth into an
oblate spheroid (spinning ellipse) from a true sphere (spinning circle),
caused by its spin around the polar axis. As a result, parallax in altitude
can vary by less than 20 seconds of arc between the spherical and oblate
spheroid models. This correction is not enough to worry about in most
practical CN, even for lunar distance sight reduction."
The angle Bill was puzzling over is unrelated to the oblateness correction,
but no matter, this is still a topic worth addressing.
In the majority of the historical methods, the Earth's oblateness was
ignored. But today, it *is* worth worrying about since most people who are
interested in lunars seem to be interested in the theoretical best case of minimum
error. In my own experience, I can get results consistently that match the
theoretical expectations to 0.2' in typical cases. If we were to ignore
oblateness, this would appear to significantly increase the error.
And you wrote:
>>On page 280 of the Nautical Almanac (2004): "If an error of 0.2' is
significant (then the) expression for the parallax in altitude for the Moon
should include a small correction OB for the oblateness of the Earth...".<<
I realize that you're aware of this, but just to be doubly sure it's worth
noting that that correction in the NA is the oblateness for an observed
altitude only. For lunars, where the arc is measured at an angle across the sky,
the correction is a little different.
And you wrote:
>>"On http://www.clockwk.com/lunars/easylun.html
Frank wrote, "The method I've described here does not include a correction
for the oblateness of the Earth. This can be added easily but it's a fairly
minor issue."<<
Right. For a hand method or a calculator method as in "easy lunars", it's
probably not worth bothering over. But if you're coding it up, it's easy to add.
For those interested in the calculational nitty-gritty, the oblateness
correction calculation is described fully in Chauvenet. It's not complicated, but
you have to watch the signs. A nice thing about it is that it's not
"method-dependent". If you want to clear your lunars using Witchell's method from the
late 18th century or Airy's method from the late 19th or Bruce Stark's from
the late 20th [I am assuming for the last case as I haven't tried it], you can
apply the oblateness trick in exactly the same way in each method.
Incidentally, the calculator on my web site formerly labeled an item in the
results as "oblateness correction". I decided this was a little misleading
since the correction enters in two ways during the calculation. So now, instead,
the analysis is marked simply 'corrected for oblateness'. In any given
scenario, if you want to find out how much of a difference the oblateness makes,
just go back to the data entry page and toggle on or off the checkbox for
oblateness. Then you can compare the cleared distance directly.
-FER
_www.HistoricalAtlas.com/lunars_ (http://www.HistoricalAtlas.com/lunars)
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