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    Re: Question re. A and B factors (corner cosines) lunars
    From: Frank Reed
    Date: 2012 Jan 24, 20:42 -0800

    Jaap vd Heide, you wrote:
    "as in case Paris would have been due east from Chicago, Chicago is on a great "circle of equal distance to Paris" and Waukegan - being due North - isn't."

    I'm not entirely sure what you were getting at here. Are you saying that if the great circle course to some (suitably distant) city is exactly due east from one location, it won't be exactly due east if we move to a location 60 miles north? That's true (unless the distant city is 90 degrees away). This is accounted for by the next term in the series expansion, the "Q" or quadratic term.

    And you wrote:
    "The difference obviously depends on the ratio between the distance North of Chicago considered in respect to the distance (tied to the radius of the mentioned circle) to the far reference point. (in the example Paris)"

    Or to put in terms of lunars, it works because the altitude corrections are small and the lunar distance is relatively large. These series expansion methods don't work as well when the altitude corrections become large, as when both objects are below 15 degrees altitude, or when the lunar distance is short, say, less than 15 degrees. As it happens, this isn't really a problem for lunars since those cases were traditionally avoided for other reasons.


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