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Re: Time of meridian passage accuracy
From: Douglas Denny
Date: 2009 Sep 25, 15:29 -0700
From: Douglas Denny
Date: 2009 Sep 25, 15:29 -0700
The declination on the example was calculated for the time of Mer Passage at Greenwich for simplicity and because there is practically no difference from here at 51 minutes West to Greenwich. Mer Passage at my location at Long 51.2 minutes West is three minutes 24.8 seconds later than Greenwich. On the 29th April 2009. By my calculator, programmed with Smart's formulae for Equation of time; and formulae from Meeus and Explanatory Supplement for the Astronomical Almanac: At Greenwich, at Mer Passage the Declination was 14.4398056824 Degrees N. At Bosham (three min 24.8 sec later) it was 14.4405427504 Degrees N. The difference is 0.000737068 degrees, or 0.04422408 minutes, or 2,6 seconds of arc. Utterly negligable - unless you are concerned with the time of an occulting star with the Sun (if you could see it), or checking Einstein's Special relativity. ---------- The comment asked for, was concerned with _practical navigational_ use: the quote from Bowditch. More specifically mentioned:- if the Equation of Time within one minute is adequate. It has long been the case in Marine navigation that Mer Passage can be adequately useful in practical navigation with simple calculation using Mer Passage for Greenwich for the day (which is why it is still given in the Nautical Alamanac for each day), and an allowance for local longitude. This is more than adequate for navigational use. --------- You will also note from the graph of my example, that the maximum altitude was within one minute of arc for approx plus and minus ten minutes of time. This is the main point in question here I believe - that obtaining Mer passage at the location to within one minute of time using an Equation of Time within this limit is _more_ than adequate. Correction for declination change in practical navigation for Mer Passage is, I think, academic. It might be useful perhaps for the sake of better accuracy, with times of the year with maximum change of rate of declination, and local longitudes approaching 180 degees from Greenwich. Still negligable for marine navigation. One minute of arc accuracy is the best one would normally expect anyway. Douglas Denny. Chcihester. England. Throughout his posting [9923], Douglas Denny appears to presume that Meridian Passage of the Sun occurs at the same moment as the maximum altitude of the Sun, at the peak of the curve of altitude with time. But it doesn't, except at the solstices, because of the Sun's changing declination. On the 29th April, the Sun's declination is increasing (Northward) by about 0.8 arc-minutes per hour. By a bit of rough guesswork, that's enough to delay the moment of peak altitude, to be somewhere between 1 and 2 minutes later than Meridian Passage. Which will throw out his assessments by that amount. To set up a precise North-South line, it's a factor that must be allowed for. For star observations, there's no such problem, as the declination stays constant. George. contact George Huxtable, at george---me.uk -------------- Also:- I just wrote- "On the 29th April, the Sun's declination is increasing (Northward) by about 0.8 arc-minutes per hour. By a bit of rough guesswork, that's enough to delay the moment of peak altitude, to be somewhere between 1 and 2 minutes later than Meridian Passage. Which will throw out his assessments by that amount." However, that guesswork was a bit too rough. On second thoughts, I would reassess that time offset, due to changing declination of the Sun, to be about half a minute of time. Still well worth correcting for, however. George. contact George Huxtable, at george---me.uk --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---