NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Time of meridian passage accuracy, Smart, and Cotter.
From: George Huxtable
Date: 2009 Sep 28, 09:54 +0100
From: George Huxtable
Date: 2009 Sep 28, 09:54 +0100
Good. Douglas Denny and I appear to have converged to the point where our differences are resolved. Two by-products of that discussion have emerged, which it may be profitable to explore further- =============================== The first relates to Smart's predictions for Equation of Time in chapter 6, on "Time", in his Text-book on spherical astronomy. Smart gives a general formula, in his equation 29, in my 1971 edition. That equation has also been reproduced in Meeus, as eq. 28.3. Meeus quotes Smart's 1956 edition, presumably the copy that was on his shelf. I expect it's also in the same form in Douglas Denny's 1977 edition of Smart, as it applies always. Meeus gives a way to calculate precisely the "constants" in that equation, as they are not actually constant, but vary slowly with time. In my 1971 edition, Smart also provides , in equation 32, a simpler expression, in which he has substituted the values of those "constants", as they happened to be in 1931. Douglas tells us that in his 1977 edition, those values had been updated to epoch 1975. It matters, to use up-to-date values, if any precision is being attempted. Meeus shows that over the century from 1900, the July value of EoT changed by all of 13 seconds of time. That would be enough to throw Sun GHA positions out by over 3 arc-minutes. Not a lot, perhaps, but in order to predict Sun positions to within "Almanac accuracy" of 0.1 arc-minutes, you can put up with no more that half a second of error in EoT. If you tried to use the Smart equation 32 for that purpose, it would already be that far out within 3 years of the 1975 epoch. Douglas tells us he has updated the parameters accordingly, which is the right thing to do. Otherwise, those 1975 predictions would be out of date by 34 years already, in 2009. So my warning stands. Do not take the values from Smart equation 32, if you want precise answers for Equation of Time. Instead, go to Meeus, where you will find all the details to get it exactly right. ============================== The second topic relates to Charles H Cotter, and his book, "History of Nautical Astronomy", (1968). In an earlier posting, responding to Douglas' reference to Cotter's "Complete Nautical Astronomer", (1969), I wrote- "Thanks for bringing that Cotter book to my attention. I hadn't come across it before. Cotter also treats these questions in his "History of Nautical Astronomy",(1968), but some aspects are confused, and several of his equations are wrong. Perhaps he had got things clearer by 1969." To which Douglas Denny replied- "I have not yet looked to compare Cotter's 'History of Nautical Astronomy' with his 'Complete Nautical Astronomy' and check your claim that he was inaccurate in some way. I have all of his books, some with personal annotations to me as I knew him from my Cardiff student days. It is due to Charles Cotter that I have an interest in navigation and nautical astronomy today. He was a most charming and generous man and an excellent teacher. I would be very surprised indeed if he is in any way "Confused" or with "wrong equations" as he was a recognised expert in the theroy of nautical astronomy." Douglas should consider the attached list of perceived errors which list members have discovered in "History of Nautical Astronomy", and which have been disseminated on this list and elsewhere. He may find it useful to keep as an errata list with that volume; that's what it was intended for. A few of those defects noted may be rather trivial, but many others are certainly not so. If he can shoot any down, we would be pleased to make amendments. If he discovers other errors, no doubt he will pass them on, and we can add them. As a former student of Cotter, I would be interested in any comments he may have about the matter. 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. --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---