A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Sean C
Date: 2020 Sep 23, 02:57 -0700
Just after Frank posted the link to his USNO app clone, I was comparing the app's data to the output of my Excel almanac. Everything matched well enough ... except Polaris. The declination was fine, but the GHA was off by about an arcminute. I know this is a tiny difference - and the effect it has on the computed altitude is even smaller. But I find it odd that Polaris would be the only problem. Every other star I tried was within 0.1 arcminutes of GHA. And the further I got from J2000, the bigger the discrepancy with Polaris. I got the same results with a few other apps.
So, I decided to re-read the pertinent chapters of Meeus' Astronomical Algorithms, double check my J2000 position and PM figures and take a close look at what I had done in the worksheet. At first, I thought maybe my PM or position data was wrong. I'm pretty sure I got it from SIMBAD. Their site gives a value of 44.48 mas/yr for Polaris' PM in RA - and that's what I was using. Wikipedia gives 198.8 mas/yr. I tried that, but the output was still off.
Next, I thought maybe I had made some calculation mistake - like forgetting to include the effect of aberration. But apparently I did account for that. I also read that one of the formulas Meeus suggests for calculating stellar positions should be modified depending on whether one is using FK4 or FK5 positions. So I downloaded the FK5 catalogue to see if SIMBAD's position data was close to that, and it was - meaning I was using the right formula. Hmmm ...
During all of this investigating, I had been playing around with the PM value in my spreadsheet to see if I could get consistent matches over long time periods. And I did find a value which seemed to work rather well: 3100 mas/yr. But that seemed crazy considering it is orders of magnitude larger than the other sources I checked. But it did work ...
Well, just now I was going over the chapters in Meeus' book again and I got to the examples for converting stellar positions between epochs. Lo and behold, there was an example using Polaris. Meeus gives position and PM values for the exercise. The value given for PM in RA is +0.19877s (that's "seconds" as in "h:m:s"). My spreadsheet uses decimal degrees, so I converted it and ... surprise!: it is equal to 2.98155 arcseconds or 2981.55 mas - very close to the 3100 mas I had settled on earlier.
Now ... my question(s) for all of you: What is going on here? Am I missing something? How can three different sources have such different values for Polaris' PM in RA? Did I make a mistake in reading the units used or frame of reference? And which one really is correct (or at least more correct)? I'm so confused.
Thanks in advance for any insights.