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    Longitude by altitudes. was Re: How Many Chronometers?
    From: George Huxtable
    Date: 2009 May 8, 10:47 +0100

    I have switched the threadname to make it more relevant
    Geoffrey Kolbe wrote-
    "List member John Karl, in his book "Celestial Navigation in the GPS Age",
    has a nice little section on page 73 entitled Time from a Lunar LOP and a
    Star Fix. The essence of the method is the LOPs from a number of star fixes
    will cross neatly at a given point on the chart, but that point will in
    error in longitude due to the error in the chronometer. The longitude error
    in a lunar LOP will be slightly different due to the faster motion of the
    moon across the sky. The trick then is to adjust the time so that all LOPs -
    including the lunar LOP - cross at the same point. The amount of adjustment
    required gives the error in the chronometer.
    I had not seen this described before and thought it quite neat."
    andMike Burkes added-
    "Hi folks, yes indeed this method also discussed in "Self Contained
    Celestial Navigation" by John Letcher Chap 17 pgs 96-105. Pretty neat
    A sceptic  writes-
    This reappears in our columns from time to time, and was proposed, 40 years
    or so ago, by Francis Chichester, in an article entitled "longitude without
    time", or something similar. It has two serious snags, which tend to be
    glossed-over by its proponents.
    Consider, first, the standard lunar distance method, which is perfectly
    valid in principle, but has its own serious drawbacks, as follows-
    1. The biggest problem is its inherent inaccuracy. Every minute of error in
    the measured distance gives rise to about 30' of error in longitude.
    2. Corrections for parallax and refraction are very demanding and need to be
    made to high precision.
    3. The observation itself can be tricky because the sextant has to be used
    in an unfamiliar way. It call for much practice and high precision.
    The alternative way that Chichester, Karl, and Letcher, and perhaps many
    others, propose to do this job, is basically by measuring the ALTITUDE of
    the Moon and in some way comparing it with what that altitude should be from
    a position determined by altitudes of other bodies. Any difference relates
    to an error in the presumed time, and therefore in the longitude.
    Because this involves only the familiar process of measuring altitudes, it
    avoids drawback 3, above. It calls for quite a lot of calculation, but that
    too is familiar stuff, so it avoids most of drawback 2. However, everything
    still needs to be done to very high precision, because the result depends on
    small discrepancies between different altitude measurements. But this method
    has drawbacks of its own, which may explain why it has never caught on.
    1. Except in or near the tropics, the Moon's changing altitude is less
    affected by its changing position with respect to the star background, of
    about half a degree an hour. Near Moon's meridian passage, it's hardly
    affected by it all, so measuring Moon's altitude becomes a rotten way to
    determine the Moon's motion against the stars. At high latitudes, and low
    Moon declinations, the effect of the Moon's motion against the stars, on the
    altitude, is never more than a fraction of that half a degree an hour,
    because the Moon is never rising or falling vertically, but only at a
    shallow angle. So the inherent weakness of a lunar observation for time, its
    insensitivity, calling for such extreme precision in observation, becomes
    amplified when measured by means of altitude, except in special
    circumstances. On the other hand, measurements of the lunar distance
    directly, with respect to Sun or star, are always in line, or nearly so,
    with the actual motion of the Moon, so the full sensitivity of half a degree
    an hour (or near) are achieved.
    2. The inherent error in a normal sextant observation is not so much in
    establishing the position of the object itself, but in assessing the true
    line of the horizon below it, especially from the deck of a vessel. Horizons
    are seldom straight sharp lines. Dip may vary from one day to another.
    That's why a lunar distance has the potential for such high precision in
    measured angle, because it doesn't involve the horizon at all (except for a
    subsidiary, and insensitive, correction). In the Moon-altitude measurement,
    errors in determining altitudes of Moon and other-bodies combine, and can
    amount to a few arc-minutes, each minute giving rise to a longitude error of
    at lease 30', and in some circumstances much more.
    So, if anyone tries to persuade you of the virtues of such a method, look at
    their arguments with a leary eye before taking such claims at face-value. To
    be fair, John Karl does mentions some of these difficulties. But his
    example, on page 77, must be in error when he states- "..also we see that
    the Moon's altitude only changed by 31.3' in an hour (about 0.5' per
    minute)". That's the rate of change of motion of the Moon with respect to
    the stars, not the rate of change of altitude, which will be much greater.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Navigation List archive: www.fer3.com/arc
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