From: Frank Reed
Date: 2020 Sep 23, 10:04 -0700
I understand that you realize the difference is tiny, but for some others reading this topic, it may be worth emphasizing.
A tenth of a minute error in the GHA or Dec of a star near the celestial equator, like Mintaka, for example, corresponds to a tenth of a nautical mile error in position on the ground. As we climb to higher latitude, the lines of longitude converge, as we all know, and therefore 0.1' in GHA is a smaller distance than 0.1' in Dec, which is essentially the same tenth of a mile at all latitudes. We can work out the scaling by multiply by cos(Dec). The declination of Polaris is close to 89.33°. The cosine of that Dec is approximately 0.011 or about 1/86. That means a difference of 0.1' in GHA at that latitude corresponds to a distance on the ground of roughly 71 feet (22m). A one minute of arc error in the GHA of Polaris is actually slightly better than a one second of arc error for a star near the equator. Unfortunately, the Q tables in many navigation works create the illusion that we need minute of arc accuracy in GHA/LHA in order to work up a Polaris sight. That's just an argument against critical tables.
I wasn't quite sure from your post, Sean, but it sounds like you might be saying that you missed the factor of 15 in the conversion from proper motion in RA. That could do it. The standard astronomical value PM_in_RA is given in second of time (right ascension). That has to be multiplied by 15 to get to seconds of angle. Proper motion has little impact on the positions of most stars. You should also check Rigil Kentaurus (alpha Cen) and Arcturus. Those are the two navigation stars for which proper motion matters most.
By the way, if you missed that factor of 15, you certainly wouldn't be the first. For some years the popular TI-calculator-based "StarPilot" app, created, written, and developed with great care and attention to detail by Luis Soltero, had this wrong, and it showed up clearly in the positions of Arcturus and Rigil Kentaurus after some decades from the year 2000 baseline epoch (which made it untrustworthy for historical analysis of lunars, for example).