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Subject: Re: Questions
From: Bruce Stark (Stark4677@XXX.XXX)
Date: Thu Feb 28 2002 - 13:00:15 EST
You've got a good grip on it, Arthur, and have laid things out clearly. The
only thing that SHOULD make a difference between what you get with your
method and with mine is the correction for temperature and pressure. I don't
include that correction. As you've suggested, rounding error buildup could be
a part of the difference. My method is designed to avoid such buildup as far
as possible.
Table 4, augmented semidiameter, is an example. The Almanac gives the moon's
HP to the nearest 0.'1 every hour. The moon's SD has to be in the same ratio
to HP as her diameter is to the earth's equatorial diameter: 0.2725. By using
HP to inter table 4 you get SD to the nearest 0.'03, and get it for the hour,
not just the day's average.
Rather than have a separate table for augmentation, which would mean and
extra step in the calculation, augmentation is built in to the values in
table 4. As I expect you know, augmentation is zero when the moon's on the
horizon, and 100% when she's overhead. It's a matter of distance. On the
horizon you see her from the distance her center is from the center of the
earth. Overhead you see her from that distance shortened by half the diameter
of the earth, so she looks bigger.
She looks bigger according to the ratio of her distance from the earth's
center to her distance from the earth's surface. That ratio is the cosecant
of her HP. You may want to make a sketch to see why. And in case you don't
deal in cosecants, the ratio is the inverse of the sine of HP.
As the moon rises from the horizon her augmentation increases as the sine of
her altitude. So the formula I used to make table 4 is:
(0.2725 HP)/(1-sin HP sin altitude)
In case that doesn't show up on your screen in understandable form, here it
is in words: Take 0.2725 of HP and divide it by unity less the product of the
sine of HP and the sine of altitude.
As to where the greatest leverage for increasing accuracy is, it's in the
reliable accuracy of your sextant and the skill you develop in using it. But
among the lesser stuff what counts most is the semidiameters you apply to the
distance.
Hope this helps. I think George has answered your other questions.
Bruce
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