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    Re: Sun near zenith sight
    From: David Pike
    Date: 2016 Sep 22, 14:44 -0700

    Francis you wrote:  I got the same as Greg, but previously thought you could not get a fix from a single sight  (well + Az). Do you have any ground rules to cover this situation? Is it only when very close to equator or what? In what situations can you do this kind of fix?

    Just off the top of my head, and at the risk of being shot down by the experts, I would say you are correct except in one or two unique situations where the PZX triangle turns into a straight line.  For an observer at the pole, P and Z are coincident, so the height of the sun will change only by the change in declination all day, which around the summer solstice, will not be very much.  After allowing for the change in declination, the difference between shots 12 hours apart will be twice the distance from the pole (Hinks 1944).
    The other occasion is the case in point when the height of the Sun is within a few minutes of arc of 90.  This time Z and X are near coincident. 
    The Sun can only have one zenith at a particular time, so if you have accurate time and GHA and Declination Sun you can work back to get the Sun’s position, and you will be on a circle of position radius from it equal to the difference between the height measured and 90
    The smart-phone azimuth and altitude is something of a red herring, because that is only produced because the smart-phone already knows where it is from GNSS
    .
    You could of course join the Sun’s zenith to your DR position to produce some sort of most probable position, but that’s all it would be, an MPP.  DaveP

       
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