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    Re: angles betwqeen lines of position
    From: Bill B
    Date: 2012 Jul 18, 01:09 -0400

    On 7/17/2012 11:53 PM, Alan S wrote:
    > Possibly I should have mentioned it, I was shooting using a Davis
    > Artificial Horizon. Does that effect the thing?
    No dip for the AH. Assuming you corrected for IE and refraction and
    remembered the altitude is 2x what you would measure from the horizon,
    (IE and random error are cut in half) you are good to go.
    Assuming we were looking at the same sun on the same day, or close to
    it, declination will be similar, so time of observations from LAN (or
    any other time) and latitude tell the tale.
    On Tuesday of this week at lon 86d 14!9 W and lat 41d 45!5 N LAN was
    13:51:17 EDT.  From 1 hour before LAN to LAN the azimuth changed from
    144d to 180d. A change of 36d per hour. Nominally the same on the other
    side of LAN.
    Sunrise was 6:51:21.  From 20 minutes after sunrise to 1hr 20 minutes
    after sunrise the azimuth changed from 64d to 73d.  A change of only 9d.
    If I change the date to near the winter solstice, the above figures
    change quite a bit.
    A 2D thought experiment. Imagine a horizontal line passing through the
    hub of a bicycle wheel.  We are not measuring along the circumference of
    the wheel/tire, we are measuring a along a vertical from the outside of
    the tire to the imaginary horizontal line.
    The best 3D mental image I give you--imagine your celestial horizon.  It
    meets your horizon due east and ends due west.  Its peak is 90d minus
    your latitude. At 0 declination the sun follows that arc. At +23d the
    the sun describes an arc 23 larger than the 0d arc/circle.  In winter at
    -23 declination the sun forms a circle smaller your celestial horizon's
    circle/arc. Three concentric circles.
    End result--sun is higher in the summer, sunrise and set are north of
    east or west.  Sun is lower in the winter, sunrise and set south of east
    or west.
    To the crux of the biscuit (as Frank Zappa might say): We are not
    directly measuring the movement of the sun along its arc/circle.  We are
    measuring as distance between the sun and the horizon along is meridian,
    which appears as a straight line from directly overhead through the
    sun/body to the visible horizon when facing the body.
    In the time it took me to be verbose, Brad posted a brief and concise
    answer. Hope one or the other syncs up with you perception.
    Bill B

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