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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.

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?

Bill

```
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