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Meesus et al gave formulas for calculating star-to-star angular distance
given declinations and SHAs.

I am looking at the reverse case.  Measuring the angular difference between
two stars at different altitudes.

For discussion purposes only, I suggest the following theoretical example:

Star 1 Hs (altitude)   50d
Star 2 Hs (altitude)   10d
Measured distance      56d 34'.1

Given STP and 0 dip and IC, and adjusting for vertical refraction:

Star 1 Ho              49d 59'.2
Star 2 Ho              09d 54'.7
Angular distance        ?

The vertical component of the difference between the two has gone from 40d
to 40d 04'.5.  Now the distance measured along the Hs diagonal will be less
than the distance between the Ho positions in the above example (ignoring
other factors).
Correct?

My next query, will there be horizontal refraction as well?

In Meesus's chapter on refraction he gives an example of the reduction of
the Sun's vertical observed measurement when near the horizon due to
refraction.  He then states, "...the horizontal diameter of the solar disk
is very slightly contracted by reason of the refraction.  This is due to the
fact that the extremities of this diameter are raised along vertical circles
that meet at the zenith."  He goes on to mention Danjon, "...writes the
apparent contraction of horizontal diameter of the Sun is practically
constant and independent of altitude, and  that this contraction is
approximately 0".6."

Perhaps I am comparing apples to oranges, but the star viewed through the
horizon glass is straight on and would not exhibit horizontal refraction?
As the other star is viewed at an angle (relative to the first) through the
index and horizon mirrors, would there be horizontal refraction affecting
the horizontal component of the diagonal between the two?  If so, how would
that correction be calculated?

Confused in Indiana

Bill

   

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