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Thank you Frank, that helps a lot.

> Bill you wrote:
> "My next query, will there be horizontal refraction as well?"
>
> Luckily no. Consider: which way would it go? North, South?

I considered there was a downward vertical correction for refraction from
observed to actual of both bodies, and a possible lateral correction from
the body's observed separation.  In the case of two bodies, the observed
positions would be closer than the actual positions.

> By the symmetry
> of the atmosphere alone, there shouldn't be any "sideways" refraction, it has
> to  be all in the vertical direction (except under "weird" atmospheric
> conditions  which would probably guarantee cloudy weather, too). Refraction
> lifts all
> stars.  It compresses the constellations towards the zenith.

I think the key in your explanation was, " Refraction lifts all stars. It
compresses the constellations TOWARDS THE ZENITH."

My usual fault in creating a mental image/model is using the wrong frame of
reference.  With your indulgence, let me take a stab at seeing if I have a
useable model.

Any body I view is on a great circle that passes through the body, my zenith
and nadir.  These great circles meet at my zenith and nadir.

When I observe one body (my only real experience to date) and if I could see
the great circle through the body, my zenith and nadir it would appear as a
straight line segment perpendicular to my horizon.  All refraction would be
linear and vertical.

Let's again assume the great circles are visible. If I look at two bodies
(say 45d apart) and point a camera at a point midway between them, the great
circle through that midpoint would appear to be a straight line.  The great
circles to the left and right through the bodies would appear as arcs from
the horizon to my zenith.  Refraction along those great circles would no
longer be linear as it is moving along the arc of the great circle to the
zenith, and would have x and y components.

What prompted my question was a set of experiments using Spica and Arcturus
May 6 04:00 UT.  I calculated the angle by formula.  Then I determined the
Hc and azimuth of each star.  Using plane trig and a right triangle, I used
the difference in Hc as the opposite leg, and the difference in azimuth
(corrected by midpoint of Hc's using cosine) as the adjacent leg.  When I
calculated the hypotenuse, it was approx. 10% over the calculated distance.
This caused me to question if there was horizontal component to refraction
or if the opposite side was not indeed perpendicular, but rather slanted
toward the zenith.  Again, "towards the zenith" is the key.

> By the way, parallax, for the Moon, Sun etc. is also an entirely vertical
> correction so you can go immediately to the case of lunar distance
> calculations
> from you star-star calculations, if you want.

I see vertical and horizontal components to parallax.  Ignoring refraction
for the moment, if at any given time I keep the observer's longitude
constant and shift latitude, the Sun or Moon semidiameter will change.  If,
again at the same moment, I keep the observer's latitude constant and shift
longitude, the Sun or Moon semidiameter will change. But since it is one
body, the great circle appears as a straight vertical line, so through the
wonders of math the parallax can be expressed as a vertical for any given
observation point. Yes no?

> There's one small issue: the
> Earth's oblateness yields a slightly non-vertical component to parallax but
> that  can be dealt with separately.

Can't wait. 

Bill

   

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