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    Re: lunars with and without altitudes
    From: Henry Halboth
    Date: 2006 Nov 14, 17:08 -0500

    I was really waiting for you or Frank to provide the further words of
    wisdom. I'm just a poor illiterate sailor.
    My interest in Lunars originated in the pre-electronic navigation days, when
    even a gyro compass was considered a luxury, and we had to fall back on the
    radio direction finder or radio compass in making a thick weather landfall.
    I experimented with the method in the hope that it might provide some backup
    under circumstances where accurate time or other requirment of celestial
    navigation might be lacking, even potentially as respects lifeboat
    navigation. My experimentation, at that time, found the method too
    cumbersome and essentially to inaccurate to deserve ongoing consideration.
    Understand that at the time in question, there was no distribution of
    information, no published lunar tables that were known to me, no pocket
    calculators, and no internet with guys like you and Frank available in an
    electronic second.
    ----- Original Message -----
    From: "George Huxtable" 
    Sent: Tuesday, November 14, 2006 12:49 PM
    Subject: [NavList 1714] Re: lunars with and without altitudes
    > 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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