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    Re: Can I Navigate Without an Assumed Position?
    From: Bill Lionheart
    Date: 2017 Aug 26, 14:24 +0100

    Probably this is well known to navigators, it is just something I know
    from geometry.
    
    If you know the GP of a heavenly body and its altitude that means you
    are on a  known "small" circle centred on the GP. On a map projection
    that is conformal circles are taken to circles, so you have a position
    circle on such a chart. If you have two such position circles you know
    you are at one of the (typically two) places that they intersect.  If
    you have three and they more or less agree at one point of
    intersection you have your position. This does not use an assumed
    position (other than you are on the surface of the earth).
    
    The reason we need an assumed position is that we usually work on a
    chart on the scale where we can approximate the small circles by
    straight lines. This is easier and if you had a big enough chart to
    draw the circles it would not be so accurate.  You would probably then
    zoom in and do it with the conventional method using the circle method
    as your GP. You can do it all computationally rather than graphically
    of course.
    
    [The more knowledgeable NavList members will no doubt reply with the
    history and terminology of such methods in navigation]
    
    Bill
    
    
    --
    Professor of Applied Mathematics
    University of Manchester
    http://www.maths.manchester.ac.uk/bl
    

       
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