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    Re: Precomputed lunar distances
    From: Bill B
    Date: 2005 Apr 18, 19:10 -0500

    > Bill you wrote:
    > "Two sides of a spherical  triangle meeting at the
    > zenith. Both start off almost perpendicular to the  horizon and progressively
    > arc in to the zenith.  So from the *observers*  frame of reference,
    > refraction is acting up and in, less up and more in the  higher the bodies."
    Frank replied:
    > I have a hunch that you're picturing a sort of  "perspective drawing" of a
    > spherical triangle in which it might appear as if the  refraction is acting
    > "in"
    > or sideways.
    Yes, that is my image.  A two-dimensional representation of three
    dimensions.  What a camera would see.
    > It's important to picture a spherical  triangle from the
    > perspective of the observer. The arcs (sides) of a spherical  triangle are not
    > curved. If you draw a spherical triangle with corners at the  zenith and two
    > arbitrary stars, all three sides look *exactly* straight as seen  by the
    > observer.
    > Gou outside tonight and point at Spica. Now trace the side of  the spherical
    > triangle that connects Spica to the zenith. You finger should  trace a line
    > across the sky that looks (to you) exactly straight and exactly  vertical.
    > Next
    > point at Antares. Trace the side of the triangle from Antares to  the zenith.
    > Your arm should rise straight and vertical. Finally trace the side  from
    > Antares
    > to Spica. Your finger should move straight across the sky. How does
    > refraction affect these triangle sides?? It lifts each star entirely
    > vertically  and so
    > entirely within the two sides that lead to the zenith. There's no  component
    > perpendicular to those sides. Make sense?? And of course, the distance
    > between the stars is reduced by refraction even through the refraction is
    > completely in the vertical  direction.
    Understood.  While there are no "straight" lines on the surface of a sphere,
    if the segment of the great circle is on the axis the eye is directed
    toward, it will appear to the observer as a straight line.  The sextant has
    the ability to look in two directions at once--two straight lines.  Now if I
    used a finger for each body and looked between them while tracing both the
    great circle segments to the zenith, would I still observe two straight
    lines?  In any case a triangle is formed.
    What deeply confuses me is as follows. Using two hypothetical stars with
    equal declinations and an LHA between them, I calculate true separation as
    34d 27.7'.  I raise the equal Hc's of the two stars from a staring point of
    1d 36.8' in increments of 11d 02.9' (11d 02.8 for last step) and calculate
    refraction separation correction.  The results are as follows:
    Hc           Refraction   Correction
    1d 36.8'     -18.2'       -0.31796
    12d 39.7'     -4.1'       -0.57133
    23d 42.6'     -2.2'       -0.59930
    34d 45.5'     -1.4'       -0.60260
    45d 48.4'     -0.9'       -0.57422
    56d 52.3'     -0.7'       -0.64021
    67d 54.2'     -0.4'       -0.64310
    78d 57.1'     -0.2'       -0.63534
    89d 59.9'      0           0
    They do not seem to reflect refraction moving along a straight line to me,
    where I might expect the corrections to be similar to a curve derived from
    refraction values at those altitudes.
    Another hypothetical scenario.  If I take the same two stars, calculate true
    separation of 34d 27.7', they have identical Hc's of 1d 36.8', and
    hypothetical refraction is -88d, what separation might I expect to measure
    with a sextant?
    Thanks for your continuing help,

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