NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: karl appendix
From: George Huxtable
Date: 2010 Jun 26, 11:31 +0100
From: George Huxtable
Date: 2010 Jun 26, 11:31 +0100
Dave Walden wrote about John Karl's book "Celestial Navigation in the GPS Age", about curiosities he had discoved in the predicted sextant angle between Antares and Nunki- "i see the major error has been corrrected without comment in the second printing" =================== This is a matter that cropped up some time ago, after the first edition appeared, in Navlist [3984] of 25 Nov 2007, in which I wrote- "With the discussion about inter-star differences, I remembered that John Karl's new book, "Celestial Navigation in the GPS age", devoted several pages to helping users to calibrate or check their own sextants that way. He selected 12 pairs of bright stars (with rather a Northern-hemisphere bias), to provide a suitable spread of angles to calibrate, ranging from Bellatrix to Betelgeuse, at about 7 deg 30', as far as Betelgeuse to Spica, at over 113 deg. For each such pair, he provides a table, showing how the refraction alters the odd minutes and fractions of that separation, based on the observer's latitude, and on the altitude of the first-named star. In the explanation he claims- "Since the observer's latitude and the star's altitude determine the altitudes of any other star ... the altitude of the second star is not needed". On the face of it, it seems a good simple scheme, dead easy for a user to implement. But on reflection, I'm not convinced. I have been worrying about that statement. I don't think it is true. It's all a bit more complicated than that, I fear. Given a latitude, and a star with known declination, and an observed altitude, it's true that one can deduce a local hour angle. That local hour angle will be the same in amount, corresponding to that altitude, whether the star is rising or falling in the sky, before or after culmination, but will be opposite in sign. And there will therefore be two completely different Greenwich hour angles. And therefore two completely different possible values for the local hour angle, and thus the altitude, of the second star. Therefore, as I see it, there should be two different tables for the refraction correction, depending on whether the first star is to the East or the West of the observer. The table as given, for, say, Bellatrix to Betelgeuse, tells only half the story. I haven't investigated the matter deeply enough to discover which half." =================================== Subsequently, John and I discussed the matter off-list. We realised that, though the predictions were correct for when the first star was rising, in the eastern sky, refraction of the second star was miscalculated when the first was falling, in the West, after culmination. This applied to all star-pair tables in that appendix. It's the discrepancy that Dave Walden noticed in his first posting.. The result has been that for the second edition, that appendix has been completely rejigged, to avoid the problem, as Dave has noted.. But Dave, and other observers wishing to work to high precision, should note that stellar aberration, which varies between star-pairs and cycles over the year, has not been taken into account, which can cause a maximum error of just over half an arc-minute, either way, in the case of the worst-affected pair, Betelgeuse - Spica. John explains this in some detail on page 240 of the second edition, and describes how a more precise calculation can be made in another way, if necessary In the first edition, however, aberration was treated in such a way that the maximum errors for certain star-pairs at certain times of year could have been doubled, so a significant improvement has been made for the second edition. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.