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    Re: Angular Distance Between Stars
    From: Frank Reed
    Date: 2012 Sep 14, 10:40 -0700

    Greg, you wrote:
    "a pair of stars differing in azimuth by 45 degrees with the altitude of star A at 45 degrees and star B at 65 degrees."

    Sure. Let's do it both ways. Using the calculator that I linked before (but any will do), I enter 45.0, 0.0 for one lat/lon, 65.0, 45.0 for the other and find a great circle distance of 1893.1 minutes of arc or 31d 33.1'. Direct application of the cosine formula in a spreadsheet, of course, agrees. Since both objects are above 45 degrees, the refraction is almost linearly proportional to zenith distance and therefore any distance is compressed by the same amount: 0.1' per 5 degrees so the refracted distance is shorter by 0.6'. The refracted distance then is about 31d 32.5'. Slightly more work (but easy if any computing capability is available), you calculate the refracted altitudes which I find are 45.016 and 65.008 degrees and enter them as "latitudes" in the great circle distance calculator with the same 45.0 degree difference in azimuth. The result is the same as the short calculation, 31d 32.5', though round-off differences might shift it by 0.1'.

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