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    Re: Sunrise, Sunset, LAN, LMT
    From: George Huxtable
    Date: 2004 Aug 5, 00:08 +0100

    Andrew Corl first wrote-
    I downloaded a problem from the website
    >www.oceannavigator.com entitled "Navigating without a clock."  This
    >problem deals with a noon sight to determine latitude but there is no
    >clock on the ship.  Lest anyone get to worried, the author of the
    >problem does make several assumptions to make the problem solvable.
    >I have looked in a number of places for a paper and pencil method to
    >determine GMT as well as sunrise and sunset.  I have found a basic
    >computer program from Sky and Telescope magazine in 1994 which shows how
    >to determine sunrise and sunset at a selected position, but so far no
    >way to determine noon GMT.  I know that this information is provided in
    >the nautical almanacs on the daily pages, but I am looking for a way to
    >calculate this number using a pencil and paper.
    Later, in response to a call to clarify his question, Andrew added-
    >Is there a way to use the GHA for the sun from the daily page from one
    >of the online almanacs to calculate noon GMT, and then use the table
    >"Convert Arc to Time" to calculate LAN?  Is that possible?
    His question still leaves mu puzzled, and to judge from the responses that
    have been posted, I'm not the only one to be confused.
    Andrew, please tell us what you want to know the local apparent noon FOR.
    If it's just to establish the time for taking a latitude sight, then you
    don't need to know LAN at all (except, perhaps, on board a very high-speed
    Just measure the highest altitude that the Sun reaches, without bothering
    about exactly what that time is. As soon as you detect that the Sun has
    started to fall from its highest point, note what the maximum sextant
    reading was. That will give you a perfectly good figure for latitude, and
    no clock was needed at all, nor any precise knowledge of longitude. You can
    forget about LAN.
    On the other hand, if you are trying to determine longitude (without a
    clock) please say so clearly. You are now in much deeper waters. and the
    solution to the problem (by means of lunar distance, the skew
    angle-across-the-sky between the Moon and another body) is not a matter for
    a beginner. If that's the problem you wish to tackle, we can help. But I
    suspect you are asking a simpler question.
    Now foe some comments on the various responses to Andrew's request. Some of
    these are my usual nit-pickings, but others are more serious-
    Mike Boersma wrote-
    >You could try a time sight. If you have very accurate latitude, the
    >altitude of the sun and the declination of the sun, you can solve for
    >the meridian angle, which is then converted into LHA. The difference
    >between GHA and LHA is the longitude. Longitude = time. See table 20 in
    >the online Bowditch. This method is VERY prone to error due to latitude
    >errors. Small errors in latitude lead to large errors in longitude.
    >Meridian angle = t; h = altitude; d = declination; L = Latitude:  cos t
    >= (sin h - sin L*sin d) / cos L * cos d
    >Z = sin t  * cos d * sec h
    >t = LHA. GHA - LHA = longitude.
    >A less error prone method, and perhaps the preferred for determining GMT
    >in the circumstances that you describe, is by means of lunar distance.
    No matter how accurate your latitude may be, if you don't know the time,
    and don't know the longitude, there's no way of finding either from a
    time-sight. You need to know one to discover the other, using a time-sight.
    That leaves lunar distance as the only option for discovering longitude, if
    you have no timepiece.
    Chuck Taylor wrote-
    >In theory, if you had an accurate timepiece and could
    >observe the exact instant that the sun crosses your
    >meridian (when it reaches its highest point), you
    >could  then calculate your longitude by converting
    >time to arc.
    The exact instant at which the Sun crosses your meridian is NOT the same as
    the moment that it reaches its highest point. There's a correction to be
    made, to account for any North-South component of the observer's speed, and
    also to allow for changing declination of the Sun. For the non-critical
    timing of the moment to measure altitude (for latitude), that correction is
    unnecessary, but for any determination of longitude it has to be included.
    Zorbec Legras wrote-
    >Attention de greatest sun altitude is Not the instant of transit for a
    >mobile observer.
    Nor is the instant of greatest Sun altitude (quite) the same as the instant
    of meridian transit, even for a stationary observer (except at the
    solstices), due to the changing declination of the Sun. But it's close.
    Robert Gainer wrote-
    >If you are at 23 degrees north
    >latitude or greater the sun is never due east or west.
    I wonder if that was really what Robert meant to say. For half the year,
    from Spring equinox to Autumn equinox, for those of us who are above 23
    degrees North, the Sun passes through due East every morning, and due West
    every evening. Robert's stament is true only in the Winter months.
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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