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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@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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