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From: Bill (no email)
Date: Mon Apr 18 2005 - 20:10:58 EDT
> 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.
Frank
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,
Bill
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