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    Re: Latitude of prime vertical sight
    From: Gary LaPook
    Date: 2007 Aug 01, 10:08 -0700

    Gary writes:
    
    Remember, "the sun rises in the east" that you learned as a child. Of 
    course we then learn that it doesn't rise exactly due east  but 
    sometimes north and sometimes to the south depending on the season. At 
    44� of latitude the azimuth at sunrise varies from 56� to 124� which is 
    never more than 34� from due east. At lower latitudes the azimuth 
    changes even less, at the equator its maximum difference form due east 
    is only 23.5�, the maximum declination of the sun.
    
    
    So advancing an LOP derived from a sunrise observation would provide a 
    maximum angle of cut of about 30� or less which we know will at least 
    double the possible error in the latitude determined. Figure in  the 
    error due to variable refraction of a low altitude sight and you end up 
    with what would only be a very approximate latitude.
    
    
    George Huxtable wrote:
    
    >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---.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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