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    Re: Latitude of prime vertical sight
    From: George Huxtable
    Date: 2007 Aug 1, 09:11 +0100

    Paul Lee asked-
    
    | Hi everyone,
    | I'm new to navigation, and am doing some work on the usage of prime
    | vertical sights. I know it gives longitude, but if you knew the time
    | of sunrise, is it possible to obtain a value for lattitude too?
    
    Later, he added-
    
    "The local sunrise had been determined in retrospect by an astronomical
    program.
    The prime vertical sight would be taken about this time."
    
    ===================
    
    Reply from George.
    
    No, it's not possible.
    
    The comments about unpredictable low-level refraction, though true in
    themselves, are missing the point. (True, I might add, except for Bill's
    lower limit of 30 degrees, which would exclude half the sky, and most
    observations. Lower limits of 5 or 10 degrees are more appropriate,
    depending on the level of precision that's sought)
    
    You are only making one measurement, presumably an altitude of the Sun, at a
    moment when you have calculated (not observed), that it will be exactly to
    your East. You are not observing the time of local sunrise, simply taking it
    from some program, which will have asked for both latitude and longitude
    before predicting that time. Your longitude could have been derived from the
    prime vertical observation, but how did you provide the latitude, to feed
    into the program? If you have had to tell it the latitude, you can't then
    expect a prediction that it provides to tell you the latitude.
    
    As a a general rule, if you have two quantities to find (such as latitude
    and longitude) you have to make two independent observations to do so.
    Calculating the time of sunrise, from a program, is not observing it. IF you
    could allow precisely for the low-level refraction (which you can't, because
    it's so variable), you could TIME the moment when (say) the Sun just peeped
    over the horizon, and then due to refraction, its centre would be at an
    altitude of about 50'  below the true horizon. If you timed that moment, it
    would be just like measuring a sextant altitude at a particular moment, and
    from it, and an almanac for the Sun, you could derive a position line at
    that moment. Then you could cross that with a North-South position line from
    the prime vertical observation, and where these lines meet is where you are,
    in lat and long.
    
    But beware; even that would not work well in the circumstances you describe,
    when you say "The prime vertical sight would be taken about this time."
    Unless the Sun's azimuth has had plenty of time to change, between sunrise
    and your prime vertical observation, then the two resulting position lines
    would not have a decent angle between them, and latitude of the crossing
    would be found very imprecisely. That would exclude such a procedure at
    dates anywhere near the equinox. Of course, prime vertical observations of
    the Sun are themselves impossible throughout the Winter half of the year.
    
    If both the azimuth and the altitude of the Sun (or any other body) could be
    precisely measured at sea, at the same instant, they would comprise the two
    independent observations that are called for, to determine latitude and
    longitude, in one go. That's true at the moment of prime vertical, or any
    other moment. So if you could observe (not predict) that the Sun really was
    exactly on the prime meridian, to your East, and simultaneously measure its
    altitude, you could get both latitude and longitude. That's possible for a
    surveyor on land, with a firmly-planted theodolite, knowing his direction of
    due North, but not for a mariner at sea, who has only his compass.
    
    I am puzzled, though, why Paul is interested in prime vertical observations.
    Is it for historical studies? When the Sumner method came in, improved by St
    Hilaire in the mid 19th century, a position line could be determined from an
    observation of any body at any time. Two such observations provide two
    position lines. Where they cross is where you are. Simple as that. It's a
    method which applies everywhere, at all times. Then, such special-cases as
    prime-vertical became irrelevant, though noon sights lingered on, because of
    their arithmetic simplicity.
    
    Prime vertical observations are no more than a special case of a Sumner
    line, providing a North-South position line (longitude), which has to be
    crossed with a different observation (often, near noon) to provide a
    position in lat and long.
    
    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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