NavList:

Looks like the distance from Merak to Polaris is 34.0699 degrees or 34° 4' 12". This is the value for today without refraction. You can calculate this if you know the stars' coordinates in RA (or GHA or SHA) and Dec. Let me know if you're interested. You can read out coordinates from the free software Stellarium (available from stellarium.org). While Stellarium has some bugs, you can usually count on things like stellar coordinates. Just click on each star, and the exact coordinates are displayed in the upper left. There is also an angle-measuring tool available in Stellarium and with careful clicking and zooming in and out, you can measure angles between stars with an accuracy of at least 1' of arc.

This star-to-star distance will vary slightly during the year due to aberration, and it will vary significantly with the stars' altitudes due to refraction. For example, if you're in latitude 41 N and the Dipper is low in the sky with Merak almost directly below the pole star, Polaris will be lifted by refraction by 1.1 minutes of arc while Merak (at an altitude of about 7 degrees) will be lifted by about 7.3 minutes of arc so the angular separation will be reduced by 6.2' to 33° 58.0'. If instead Merak is high above Polaris, then the distance will be 34° 3.4' reduced by refraction by only 0.8'. In the latter case, we're nearly in the situation where the change in distance due to refraction follows the simple rule "0.1' for every 5 degrees of distance" which applies with good accuracy for any orientation of the pair of stars and any altitude as long as both stars are above 45 degrees altitude.

-FER

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