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    Re: lunars with and without altitudes
    From: George Huxtable
    Date: 2006 Nov 14, 17:49 -0000

    A thoughtful contribution fro Henry Halboth states-
    
    " ... you both ignore the fact that one of the observations in the
    Lunar set is also intended for the purpose of establishing the Local
    Apparent Time, for ultimate comparison with the GAT deduced from the
    GMT established by the distance cleared...."
    
    He is right to point out that determining a longitude involves
    comparing LAT (Local Apparent Time) with Greenwich time, and both
    those quantities are needed. Most of the discussion about lunars
    concentrates on the lunar-distance measurement itself, because it's so
    difficult to get sufficient accuracy. That is mostly because of the
    slow motion of the Moon with respect to the stars, only about half a
    degree in an hour, so that a measurement of lunar distance to 1
    arc-minute determines GMT to no better than 2 minutes of time, and
    therefore longitude to 30 arc-minutes.
    
    In contrast, determining LAT involves measuring the altitudes of
    bodies which move across the sky at 15 degrees in an hour, so that
    measuring altitude under optimum conditions to an arc-minute can
    determine LAT to (roughly speaking) four seconds of time, which will
    have an effect on the resulting longitude of only 1 arc-minute.
    
    Because getting LAT to sufficient precision is so easy, then, it's
    rather taken for granted when lunars and longitude are being
    discussed. That doesn't mean that it can be neglected.
    
    Henry continued-
    
    "An error in the Altitude or Latitude employed for that purpose will
    affect whatever accuracy in Longitude or Chronometer Error may be
    expected from the observations as a whole. The Latitude induced error,
    of course, being dependent on the distance off the Prime Vertical of
    the body employed for the purpose of establishing the LAT."
    
    All that is perfectly true, but for the reasons given above, any such
    contribution to the overall error will usually be small, compared with
    the errors in the lunar-distance part of the process.
    
    and further-
    
    "In response to my previous comments, George has taken issue with my
    statement to the effect that computed altitudes were dependent upon
    knowledge of "position/time", but seems to go right on to prove my
    point by citing a prior knowledge of LAT to assist in the altitude
    computation."
    
    I don't recall having taken issue with such a statement at all.
    Indeed, I agree with Henry that a measurement of LAT is necessary.
    
    He had written-
    
    "... yes, I know it's possible to calculate the altitudes - however,
    does not that require a position/time of reasonable accuracy - some
    authorities stating these calculated altitudes should be within four
    arc minutes of the truth,..."
    
    and I hadn't disagreed with that, but answered "no" to his follow-up
    question-
    
    " ...and does not such accuracy require a position/time accuracy
    better than is ultimately determinable by the Lunar Distance. "
    
    The iteration method, as I explained it, requires a precise value of
    LAT, which is a time that doesn't depend on lunar distance for its
    measurement, combined with a guessed initial value for longitude. That
    guess is improved at each iteration, and that process does indeed rely
    on the measured lunar distance. That was my only point of disagreement
    with Henry's analysis.
    
    If altitudes of the two bodies involved in a lunar are measured,
    rather than calculated, it can often be convenient to use one of those
    observations as a time-sight also, to obtain LAT. This is handy,
    because it's  a measure of LAT or very near the same moment as the
    lunar. Especially handy, in the early days when a ship might not have
    carried any timepiece at all; not even a hack-watch.
    
    Often, however, LAT is determined from a time-sight taken at some
    other moment in that day from the lunar, in which case the elapsed
    time between the two must be accounted for, including any known error
    in the rate of the timepiece, and an allowance must also be made for
    any change in longitude over that period., derived from
    dead-reckoning. You can see the circumstances in which this procedure
    must apply. If a Moon-star lunar distance is measured in the dark of
    night, with no horizon visible, then altitudes of the two bodies can't
    be observed, and must be found by calculation. And neither can a
    time-sight be taken; that has to await some light on the horizon, and
    the difference between the times of the two observations has to be
    allowed for.
    
    Henry has described those possibilities well in his last posting,
    which ends "but that is probably a subject for later discussion." I
    await his words of wisdom with some interest.
    
    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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