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Subject: Re: Calculated Altitudes for Lunars
From: George Huxtable (george@XXX.XXX)
Date: Mon Oct 21 2002 - 12:30:16 EDT
Much as I respect Bruce Stark's thoughts about lunars, questions come to
mind about part of his latest mailing, in which he said-
>you
>only have to have the altitude within 6' of the truth to get the correction
>within 0.'1. Furthermore, only about half of that 0.'1 will, on average,
>>show up in the distance. There's only one case in which the whole 0.'1
>could >show up. That's when the two bodies and your zenith are in one,
>straight, >vertical line.
First, I suggest that the word "vertical" is superfluous, and indeed rather
misleading. From the tropics, the Moon may be on one side of the sky, the
other body on the other side, and the zenith somewhere between. In that
case, also, the full effect of refraction and parallax errors for both
bodies added would show up in the lunar distance, though one wouldn't
describe the line-in-the-sky joining the three as "vertical", more like
"horizontal".
Second, I regard his use of an "average" effect of half the maximum as
unsound. Take a navigator on the equator. The Moon will pass within
twenty-odd degrees of overhead, and so will any of the usual comparison
bodies. So, in general, he will NEARLY ALWAYS see somewhere near the
maximum possible effect of parallax + refraction on the lunar distance.
It's little consolation to him to tell him that when averaged with
observers in higher latitudes, the effect is only half as much. No, it's
the worst-case situation that has to be considered, not the average, and
that occurs in the tropics under a high Moon.
However, I agree with Bruce's conclusion that altitudes known to within 6
arc-minutes allow one, using the Almanac, to compute corrections that add
no more than 0.1 minutes error to the corrected lunar distance.
Finally, Bruce concludes-
>I don't see how errors of 6' or so in the altitudes could be a serious
>problem.
I am not sure what Bruce means here. If he means that knowing altitudes to
a precision of 6' is quite sufficient to make the necessary corrections to
the observed lunar distance, then I agree. If he means that it's not a
serious problem to estimate the altitudes, using the Almanac, within 6',
then I disagree. It can be done, but it involves an accurate recent
measurement of the Hour-angle of the true Sun, and a knowledge of the
difference between the Greenwich Hour Angles (or the Right Ascensions) of
the Sun and Moon (and of the Sun and other-body) at the moment of the lunar
measurement. If Bruce offers an easy way through this thicket we will all
be delighted.
George Huxtable.
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george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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