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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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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:

>
>| 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?
>
>
>"The local sunrise had been determined in retrospect by an astronomical
>program.
>
>===================
>
>
>No, it's not possible.
>
>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,
>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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