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Re: Time of meridian passage accuracy
From: George Huxtable
Date: 2009 Sep 26, 17:27 +0100
From: George Huxtable
Date: 2009 Sep 26, 17:27 +0100
Posting [9939] concludes with these words- "There is a vast difference between practical navigation and theoretical astronomy. That is the point which you have academically and pedantically missed." Well, thank you, Douglas Denny, for those few kind words. No doubt they were intended to disparage, but "academic and pedantic" is a badge I will wear with some little pride. It's a standard I hope to maintain... =================== When he wrote those words, Douglas was taking the Sun's declination to be changing at 0.8 arc-minutes per day, which he then revised in a suibsequent posting to be 0.8 arc-minutes per hour. Does that factor of 24 lead him to reassess any of the statements he made in [9939], I wonder, or does he still maintain that the effect of changing declination is "very small as to be of no practical concern to practical navigators."? How much, if any, of that posting does he now wish to retract? This question, of the time-difference between meridian passage and maximum altitude (= culmination) has been discussed in some detail in the "Admialty Manual of Navigation, vol III". My edition is 1938, where it's on pages 146 to 156. Thanks to list member Jim Wilson, for pointing that out. Jim has also written about the matter in "Position from observation of a single body", in Navigation, 32(1) Spring 1985. Antoine's posting [9938] explains the matter rather better than I could. Jim derives the formula for the amount of the correction in time, between meridian passage and culmination, due to changing declination, as- correction (in seconds of time) = rate of change of declination (in arc-minutes per hour) x (tan lat - tan dec) x 48 / pi. For the observations quoted by Douglas Denny, with dec changing at 0.8 minutes per hour, lat = 50�, dec = 14.5�, this amounts to a time-error of about 11.3 seconds. That is, indeed, very significantly less than both my earlier rough-guesses. Perhaps, Douglas and I are now starting to converge... Nevertheless, if he is hoping to establish the time of meridian passage with any precision, that correction should certainly be taken into account, and not dismissed out of hand. It amounts to a systematic error in deduced longitude of nearly 3 arc-minutes, in every such observation made at that time of year. Use of bubble sextant, on land, for such a purpose isn't in itself conducive to high precision, and observations made with a better tool for such a job, sextant or theodolite, would give a more precise result. The better that is, the more necessary it is to take such time-correction into account. Of course, the same correction would become much larger if the observation was being made from a moving vessel, with a North-South component of speed which can be tens of knots, not limited to a knot as is the motion of Sun declination. That matter has been discussed, in great detail, in recent postings about longitude-around-noon on Navlist. Some additional points- Douglas wrote- "I am aware of the changing declination of the Sun - it is changing constantly, hence a meridian passage curve such as the one I gave is actually skewed - in theory." Not "skewed", actually. The shape, near noon, is a parabola. It remains a parabola, of just the same shape, when the changing declination is allowed for; but is simply displaced a bit in time from being centred on LAN, as I've indicated. And he added- "The differences between actual (appareent) max Altitude and true Mer passage of the Sun are so small as to be negligable if max altitude is calculated near to the apparent Mer Passage... ". Which is indeed correct, as far as altitude is concerned. The small difference in altitude between LAN and culmination can often be neglected. However, navigators of vessels that possessed chronometers, particularly if they were steaming fast in a North-South direction, were advised to measure the noon altitude, not at its peak value, but at the moment of calculated LAN, to arrive at a correct latitude.. But that's not what we've been discussing. It's not a change in altitude, but a shift in time-of-peak, to obtain longitude, that concerns us here. It's not a matter that was much discussed in navigational texts. That's because longitude-around-noon was never a standard tool in the navigator's box, though it has achieved great prominence on Navlist. Navigators were aware of its many drawbacks, as have been discussed by us at length; one of which is the need for such time-corrections to be made. Instead, they relied for longitude on observations made as far as possible from meridian passage, which implied, if their timepiece was good, that longitudes could then be almost as precise as latitudes were. ============== In response to my pointing-out that he had made no allowance for time-offset, between LAN and maximum altitude, Douglas wrote, in [9932]- "The difference is 0.000737068 degrees, or 0.04422408 minutes, or 2,6 seconds of arc. Utterly negligable " Does he still maintain that statement? Otherwise, I invite him to withdraw it now. I don't know what it was based on; perhaps he will explain. It was on that basis that I wrote that he had missed the point. Was that wrong? 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 -~----------~----~----~----~------~----~------~--~---