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    Re: Lunar Distance in Wikipedia
    From: George Huxtable
    Date: 2007 Aug 16, 10:16 +0100

    Renee Mattie wrote-
    
    | Clive Sutherland's illustration has now been incorporated into the
    wikipedia
    | article
    | http://en.wikipedia.org/wiki/Lunar_distance_%28navigation%29
    
    =====================
    
    Those attentions are doing a power of good to that Wikipedia article on
    Lunar Distance (Navigation).
    
    I have a few suggestions, that she might consider at the next iteration, if
    she isn't fed-up yet.-
    
    Is there any way that Clive Sutherland's name could be inserted as an
    attribution, to that illustration? Perhaps he should have put it into the
    corner of the pic. itself.
    
    Renee's caption runs- "Observing Lunar Distance at Sea. Measure the height
    of the star, the height of the moon, and the distance between them." I
    wonder if this gives a misleading notion of what's important? And the first
    part is superfluous, being stated on the pic. itself.
    
    So, can I suggest something like- "The slanting angle between the Moon and a
    star (or the Sun) is measured precisely. The altitudes are needed for making
    corrections."
    
    Ref.4 gives a somewhat misleading impression, in my view, when it states-
    "Chronometers were not regularly supplied to the Royal Navy till about
    1825". As I recall (but can't quote references), it wasn't until 1825 that
    home-waters Naval vessels were routinely supplied with a chronometer, but
    for many years before that, chronometers were available to ships on foreign
    service, in numbers which depended on the nature of their duty.
    
    There's no mention, as yet, of the business of clearing the measured lunar
    distance of corrections. Something ought to go in about that.
    
    Is my previous suggestion , made in NavList 3069, 2 August, considered
    suitable as a first-draft, or do others have better ideas? It's a bit wordy.
    
    ==================
    [edit] Errors and corrections.
    
    A lunar distance changes with time at a rate of roughly half a degree, or 30
    arc-minutes, in an hour. An error of just one arc-minute, then, will give
    rise to an error of about 2 minutes in Greenwich Time. The Earth spins at 15
    degrees per hour, so that would lead to an error of half a degree, or 30
    arc-minutes, in the resulting longitude; near the Equator; that corresponds
    to 30 miles. So lunar distance can never be a precise way to determine
    longitude, but nevertheless, to a navigator approaching a continent from the
    ocean, even such a rough figure was of great value. Thirty minutes in
    longitude was the target set by the famous Longitude Prize, which was won in
    the end, not by the lunar method, but by Harrison with his chronometer.
    
    In the early days of lunars, predictions of the Moon's position were good
    only to half an arc-minute, so to obtain the required overall precision of
    one arc-minute, only half a minute could be allowed for errors in measuring
    the lunar distance, and in calculation, combined. The best sextants could
    indicate angle to one-sixth of a minute, but in practice at sea, actual
    errors were somewhat larger, good observers typically achieving overall
    accuracy within half a minute in favourable conditions. From the unstable
    deck of a small vessel, in bad weather, with the sextant elevated and tilted
    at an awkward angle to get both objects simultaneously in view in its small
    mirrors, and with much of the sky obscured by square sails, it became a
    severe test of a navigator's skill.
    
    Almanac tables predicted lunar distances between the centre of the Moon and
    the centre of the Sun, as would be seen by an imaginary observer placed at
    the centre of a transparent Earth. In an observation, the centre of the Moon
    can not be estimated with sufficient accuracy. Instead lunar distances were
    always measured to the sharply lit, outer edge ("limb") of the Moon, and an
    allowance then made, from the almanac, for the Moon's "semidiameter", for
    that day; and similarly for the Sun. That was the first step in the
    correction process.
    
    The second step, always referred to as "clearing" a lunar, was in allowing
    for the effects of parallax and atmospheric refraction on the observed lunar
    distance. These vary, depending on the altitudes of the two bodies.
    Parallax, which changes the apparent position in the sky depending on the
    perspective of just where it's seen from, is especially important for the
    Moon, because it is so close to the Earth. It can shift the Moon's position
    by up to a whole degree, and has to be corrected for with great precision.
    In most celestial observations, measuring up from the horizon, correction
    for these effects would be a simple addition or subtraction. Not so for a
    lunar, however, because of its skewed angle. Instead, additional
    measurements are made of altitudes of the two bodies, close to the same
    moment as that of the lunar distance, high accuracy not being needed for
    those altitudes, in themselves. Great precision was required in the
    resulting calculations, however, which called for five-figure log tables of
    trig functions.
    
    In some circumstances, that additional measurement of Sun or star altitude
    could also be used to derive local time, bypassing the need for a separate
    observation.
    
    ========================
    
    Finally, there needs to be a historical note, giving credit where it's due.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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