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    Re: Lunars using Bennett
    From: George Huxtable
    Date: 2008 Jul 3, 22:58 +0100

    I wrote, about clearing a lunar to get Greenwich time.-
    
    "Solving that problem calls for a different approach, because when the exact
    time is as yet unknown, neither are the exact positions of the bodies in the
    sky. That's why additional observations of the altitudes of the bodies were
    called for; or another technique, that of iteration, might be possible."
    
    and Ken Muldrew responded-
    
    "Two altitudes were needed, but there was no need for them to be of the
    bodies used for the lunar distance. The practice of land navigators in the
    18th and 19th centuries seems to have been to take an altitude of a body
    that was either rising or setting for local time and a meridian altitude for
    latitude."
    
    What (I think) Ken is referring to here is the process of deriving your
    position, in lat and long, once Greenwich time is known, from a lunar or
    from a chronometer. Then you need a meridian altitude, for latitude, and an
    altitude of a body somewhere near East or West, for longitude.
    
    Either of those altitudes might (or might not) have been observed as
    altitudes taken of the bodies involved in the lunar, which needed to be
    measured for clearing purposes. We agree about that
    
    I might not have expressed myself clearly, but the altitude measurements I
    was referring to were those necessary for clearing the lunar, to get
    Greenwich time
    
     "Even when the lunar was a sun-moon measurement (so that the time sight
    used a sun altitude), the lunar was cleared with a calculated altitude for
    the sun (i.e. no effort was made to extrapolate the measured sun altitude to
    make it coincident with the measured lunar distance)."
    
    Could Ken explain further, please? I think I can see how that might arise,
    especially if a Sun-Moon lunar was taken near noon in Summer, inland. In
    that case, with no sea horizon, altitudes would have to be measured by
    reflection, and the doubled Sun altitude might well put it out of range of
    an octant, or even of a sextant.
    
    It was, as Ken implies, possible to work a lunar by calculating the two
    altitudes, rather than measuring them. The problem arises that in order to
    do that, you have to make an initial guess at your GMT, by making a guess at
    your longitude. Then, if you work the lunar on that basis, it will give you
    a better GMT, and therefore a longitude, that's much closer to your initial
    guess (about 30x closer, I think). That's fine if you have a good idea of
    your longitude already, as a land-navigator might well have. If your initial
    guess was a bad one, you could revise it, and redo the calculation; that was
    the "iteration" that I referred to. At sea, a navigator might well have been
    subject to storm conditions and obscured skies for several days on end, so
    may well lose track of longitude and DR.
    
    Ken raises the intriguing possibility (if I understand him right) that for
    the lunar, perhaps only the Moon altitude might be measured, and the Sun
    altitude could be calculated instead. I've not come across that notion
    before, but perhaps it would work. The Sun's contribution to correcting the
    lunar, mainly the effect of refraction, is small, especially when the Sun is
    high. The Moon's contribution, mainly its parallax, is much greater. and
    more dependent on its altitude. Perhaps, then, a precise value for Sun
    altitude isn't really needed, and it can be estimated instead. I haven't
    quite convinced myself of the validity of that argument, and offer it up,
    for what it's worth, for someone else to knock down.
    
    George.
    
    contact George Huxtable at george@huxtable.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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