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    Re: AP terminology, WAS: 2-Body Fix -- take three
    From: Frank Reed
    Date: 2009 Nov 13, 19:58 -0800

    Douglas Denny, you wrote:
    "Because you are not comparing altitudes with the St Hilaire method but 
    you are comparing zenith distances."
    That doesn't really matter. We know both. Once its corrected for refraction, 
    dip, etc., the altitude is nor more nor less than the complement of the 
    zenith distance. 
    And you wrote:
    "What you can do however is imagine you are at position you _do_ know and work 
    out a zenith distance for that position. Then you can compare the difference 
    between them because they will be close together in value."
    Well, that's a good description of the intercept method, yes. But it's not the 
    only way to proceed. What you can do instead is directly calculate one (or 
    probably many) locations on the Earth where the altitude *should be* exactly 
    what we have measured, which is how the original Sumner line algorithm 
    worked. These days, we don't do this and we use the St. Hilaire intercept 
    method instead because it's a lot less work computationally (for paper 
    computations, that is; for computer calculations the difference is quite 
    And again, these few historical methods are not the only ways to proceed! 
    Here's another way you could work the calculation:
    I measure the altitude of Aldebaran to be 45 degrees. I know my position is 
    "somewhere" in the box bounded by 30N,60W and 31N,61W. So I calculate the 
    altitude of Aldebaran at the corners of the box. At the northwest corner, I 
    find 44.5. At the southeast, I find 45.5. At the southwest corner, I find 
    45.1. At the northeast corner, I find 44.9. You can visually (or by 
    calculation) interpolate the LOP based on those four points. The LOP runs 
    diagonally across that square from just north of the southwest corner to just 
    south of the northeast corner. And if your initial position estimate was way 
    off, you have direct information on the rate of change of altitude with 
    respect to lat and lon and can easily find your way to the correct "square" 
    of lat/lon by repeating the calculation. You can work out the entire circle 
    of position to whatever level of accuracy you choose by working along the 
    lat/lon grid at whatever grid spacing is required. The advantage of this sort 
    of procedure is that it can also be applied to more exotic types of position 
    line data.
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