In my last post I described a program that could be used to calculate the angular separation of two celestial objects using their equatorial coordinates. I now want to revisit my calculation of the separation of the double stars Mizar and Alcor. I previously gave the coordinates of Mizar A as RA 13h 23m 55.543s Dec. +54 deg. 55' 31.30" and Alcor as RA 13h 25m 13.538s Dec. +54 deg. 59' 16.65". I previously found that their separation to 4 decimal places was 0.1968 degrees. Now using my own program I find that inputting the same coordinates I get the separation as 0.196820915 degrees which to four decimal places is the same value as before.
Unfortunately, as often happens on the web, the tool that I used previously to calculate the separation of these two stars is no longer accessible and so I can't compare the values to higher decimal places.
However I have found some other online calculators. For example, inputting these coordinates in Clear Sky Tonight I obtain the separation as 11 minutes and 48.56 seconds which corresponds to 0.196822222 in decimal degrees and this differs from mine at the 6th decimal place. Another online calculator is this one by the Russian-Turkish 1.5m telescope. If I enter the coordinates here I get a separation of 0.196837 degrees which differs from mine at the 5th decimal place.
To be honest, this is more than I expected, so rounding obviously is an issue. However, 1 arc second is 0.00028 degrees so we are talking about a tenth of an arc second error or so at most.
All text and images © Duncan Hale-Sutton 2025
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