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    Re: A Lunar alternative?
    From: George Huxtable
    Date: 2003 Oct 2, 09:54 +0100

    Peter Fogg wrote-
    >In his book 'Along the Clipper Way' Francis Chichester includes the story of
    >how the ship 'Alert' found its way, with difficulty, around Cape Horn in
    >mid-winter sometime before 1840. He then muses about the difficulties of
    >observing and working a "lunar" then goes on:
    >"...and then suddenly thought of a simple solution which I will explain
    >briefly: make a simultaneous observation of the sun and the moon for
    >altitude when the moon is nearly east or west. From this compute a sun-moon
    >fix, using a guessed-at GMT. Now compute a second fix from the same
    >observation but using a GMT which differs from the first by half an hour or
    >an hour. Now establish the latitude by a meridian altitude of the sun or any
    >other body as it crosses the meridian. This observation does not require
    >accurate time. Now join the two sun-moon fixes and the point where the line
    >joining them, produced if necessary, cuts the known latitude must be the
    >correct longitude at the time of the observation. Knowing the longitude
    >enables you also to know the correct GMT at the time of the sun-moon fix.
    >    I fear the accuracy of this method, which depends on the rate of
    >movement of the moon in its orbit, would be poor, but it could be a most
    >valuable observation ...."
    George Huxtable replies-
    Peter has reintroduced an old friend to this list, who pops up at regular
    Best I can do is to refer him to section 4.6, "Longitudes without lunar
    distances?", in the latest of my (regrettably still incomplete) series,
    "About Lunars, part 4a", which appeared on 11 Jan 03. A pointer can be
    found to its archived address on Arthur Pearson's website
    To save the trouble, however, I will copy that section again below. If
    questions or doubts remain in Peter's mind (or anyone else's) I hope they
    will be voiced on this list.
    Why is it necessary to measure lunar distabces at all? It's an unfamiliar
    and awkward process to many navigators. Can the same information be
    obtained just by the familiar process of measuring altitudes? This question
    arose recently on the Nav-L mailing list, and I will tackle it here by
    quoting (edited) versions of Chuck Griffith's question and my own reply.
    Chuck asked-
    >Consider an alternative approach to finding GMT. Why can't we
    >observe the altitude of the moon and one other body and, using our assumed
    >latitude, solve for  the meridian angle of both bodies. The difference between
    >the two angles should change by the rate at which the moon moves through
    >the sky
    >faster than another body. If that's true, can't we find the meridian angle
    >between the two bodies for the even hours, say on either side of what time we
    >think it is, and use the same inverse linear interpolation approach to find the
    >time of our sight?
    >Of course, I can think of a couple issues with this approach worth discussion.
    >First, this only works when the altitude of the moon and the other body change
    >reasonably with time, i.e., we can't do it when either body is close to being a
    >meridian sight. Second, we need both altitudes simultaneously. I think this
    >could be solved by alternately observing one body then the other several times
    >and graphing the sights so that we could derive an averaged simultaneous
    >altitude from the graph.
    My response is as follows-
    The question is a very fair one. It has been asked before, however;
    starting in 1674. Francis Chichester, the famous single-handed
    circumnavigator, proposed such a method in 1966, and a spate of
    publications followed, on similar lines. These were answered in an
    authoritative article by David Sadler, then director of HM Nautical Almanac
    Office, in the RIN's "Journal of Navigation", 31, 2 May 1978, page 244,
    entitled "Lunar Methods for 'Longitude Without Time' ".
    From my point of view, the drawback of Sadler's article is that it is
    illustrated by a diagram of such devilish cunning and complexity that I am
    quite unable to make head or tail of it. If any reader manages to penetrate
    its mysteries, I would be grateful for an explanation.
    It's important to bear in mind that in any measurement that uses the Moon's
    motion to provide time and hence longitude, accuracy in determining the
    Moon's position is all. This follows from the fact that each minute-of-arc
    error results in an error in the final position of the vessel of 30 minutes
    of arc (which near the equator corresponds to 30 miles) or sometimes more.
    It is FAR more demanding that the normal run of astronavigation.
    The main virtue of a lunar is that the all-important measurement in which
    so much accuracy is required, the angle-in-the-sky between the Moon and the
    Sun (or other body) does not involve the horizon AT ALL. True, the
    altitudes of Sun and Moon do have to be measured up from the horizon as an
    auxiliary measurement, but this is only to get a correction to a
    correction, and an imprecise value for those altitudes will be perfectly
    Why is the accuracy so degraded whenever the horizon is involved?
    First, if there's any haziness in the air, the first thing to become
    indistinct is the line of the horizon.
    Second, even if the horizon is really sharp, it isn't exactly a
    well-defined straight line (except in millpond conditions), especially from
    a small craft. The horizon-line is made up from the peaks of overlapping
    waves and swell, and the vessel, too, is riding on those waves. The
    observer does what he can by timing his shots when he judges his vessel to
    be on the top of its "heave", but it is inevitably a compromise.
    Third, even if the horizon is both sharp and straight, its angle  can be
    affected by anomalous refraction, which causes the dip to vary from its
    predicted value. Air layers at different temperatures near the horizon can
    cause the sun's image to be distorted as it rises and sets, and can in
    extreme cases cause mirage effects when a distant vessel is observed as
    floating well above the horizon, sometimes even inverted. Where none of
    these objects is there to give a clue to the odd behaviour of light on its
    path from skimming the horizon to the observer's eye, anomalous dip may
    nevertheless be present, quite unsuspected and undetectable. An error in
    dip of 1 minute may be quite usual, and 2 or 3 minute errors can also occur
    occasionally. There is no way for the observer to correct for it. (Special
    instruments to measure the dip-of-the-moment have been devised but are very
    These errors may present no real problems in normal astronavigation. After
    all, what significance has an error of 2 or 3 miles in an astro position?
    However, to the lunar observer, where any such errors are multiplied 30
    times or more in calculating his longitude, they are intolerable.
    When objects lie in opposite parts of the sky, the Moon to the East, say,
    and the Sun to the West, such horizon errors would actually add when
    comparing the positions of the two objects.
    This was well-known to eighteenth-century navigators, who accepted the
    practical and arithmetical difficulties of measuring lunar distance up in
    the sky, rather than altitudes up from the horizon, to cling on to all the
    precision that they possibly could.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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