# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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? Thanks for your continuing help, Bill