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Subject: Re: Lunars and the Astra IIIb
From: George Huxtable (george@XXX.XXX)
Date: Sun Dec 16 2001 - 05:26:09 EST
Eric Haberfellner asks-
>I have acquired a copy of Bruce Stark's "Tables for Clearing the Lunar
>Distance and Finding G.M.T. by Sextant Observation" and am planning to try
>this ancient and noble art some time in the new year.
>
>Is the Astra IIIB a reasonable instrument to attempt this with? In the
>preface, Mr. Stark mentions that "0.1' of error in the distance causes about
>twelve seconds of error in Greenwich time". Now, I do not know of a sextant
>with a guaranteed accuracy of 0.1' (6"). The best that I know of is the
>Cassens and Plath with a guaranteed accuracy of +/- 9" (0.15'). The Astra
>IIIb has a stated accuracy of +/- 20" (.33'). Does this mean that it is
>reasonable to attempt to determine GMT to an accuracy of about 50 seconds
>with an Astra IIIb?
>
>I would also be interested in hearing from others who have tried using Mr.
>Stark's tables.
>
>Eric Haberfellner
===============
I have never measured a "lunar" at sea, but I will have a shot at answering
Eric's question.
It is true that observing a lunar requires a high accuracy in the sextant.
It is a demanding test and the reason why the brass sextant, with its
precisely-engraved scale, was developed from the old wooden octant. The
reason is that the errors in the resulting longitude are, in general, about
30x greater than any error in the measured lunar distance. The reason for
that factor of 30 is because the Moon moves around the sky about 30x slower
than the Sun appears to move around the Earth. So an error of 1 minute in
lunar distance gives rise to an error of half a degree in longitude. That's
why such high accuracy is called for in a lunar distance measurement.
( Note: at certain times, when the Moon is high in the sky, the effects of
rapidly-changing parallax can increase this factor from 30x to nearly 60x:
this is a good reason for restricting lunars to Moon altitudes of less
than, say, 30 degrees, if possible, though more than 10 degrees to limit
the effects of refraction.)
In terms of determining Greenwich time, rather than longitude (and that is
what Eric asked about), the motion of the Moon is about half a minute of
arc in a minute of time, so an error of 1 minute of arc corresponds to an
error in time of two minutes. With a Moon that's high in the sky, the
effect of changing parallax can nearly double this, to a time-error of four
minutes.
With an accurate sextant, the limit of what an observer can achieve is
normally limited by the resolution of his eye, which is for most people
estimated to be about 1 minute of arc. By using the telescope in his
sextant, an observer can improve this somewhat, but the motion at sea
limits the magnification that can be used to, say, 2.5. This is especially
true on a small vessel. As a result, with the most perfect sextant, I doubt
whether even the best observer on a small vessel could claim an overall
precision of lunar distance to be better than about half a minute of arc.
My own opinion is that if an observer on a small vessel can measure lunars
to within a minute of arc, he is doing very well indeed. In rough weather,
such measurements become considerably degraded.
Is the astra 3b calibrated, to provide, in the box, a table of
scale-corrections to make for different values of arc reading? If so, it's
worthwhile making those corrections. But even if not, the quoted accuracy
of 20 seconds of arc is sufficient to provide a worthwhile measurement.
I am not familiar with Stark's tables, so I am not in a position to comment
on their claimed precision. When taking into account all the many
corrections that need to be considered, all measurements and corrections
are usually estimated to the nearest 0.1 minute of arc. This does not imply
that each one has to be known to that accuracy, or that the result is to
that accuracy: far from it. It's to ensure that when adding up all the
corrections, the errors do not accumulate in a way that puts the end-result
seriously in error.
The result of all this, to answer Eric's question, is that I would not
expect an accuracy in Greenwich time of 50 seconds to be achievable from a
small craft, with even the best sextant. Maybe, from on land, that might be
possible. But with a careful observer, in good conditions, afloat, I would
estimate an accuracy of two minutes of time to be achievable with a
not-too-high Moon, either with his Astra or with a more expensive sextant.
As I said, I have no practical experience of measuring lunars from a small
craft, and would welcome comments from those that have.
Lunar distance tables, of the angle-in-the sky between the Moon and the
Sun, or a planet, or a star near the Moon's path, were tabulated at 3-hour
intervals in the Nautical Almanac until the early 1900's, but not since.
However, it's quite easy to calculate lunar distances for yourself, from
the predicted GHA and declination of these bodies, using a programmable
pocket-calculator or a computer. If anyone asks, I will explain how. That
is only part of the problem, though. Making all the corrections and
reducing the result to a measurement of GMT is a complex matter.
George.
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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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