# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Time of meridian passage accuracy**

**From:**George Huxtable

**Date:**2009 Sep 27, 10:36 +0100

Andres wrote- "BOWDITCH says this: 1801. Equation of Time To calculate latitude and longitude at LAN, the navigator seldom requires the time of meridian passage to accuracies greater than one minute. Therefore, use the time listed under the "Mer. Pass." column to estimate LAN unless extraordinary accuracy is required. Pub. No. 9 THE AMERICAN PRACTICAL NAVIGATOR. 2002 BICENTENNIAL EDITION Any opinion? ============== That's an interesting question. I can't find those words in my earlier 2-volume edition of 1977 , not in para 1801 or in para 1809, which it devotes to equation of time. It's certainly true that to calculate LATITUDE from Sun altitudes at LAN, there's no need to know Sun-time to better than a minute. But in the (unusual) situation of trying to deduce LONGITUDE from altitudes-around-noon, knowing Sun-time only to the nearest minute adds an unnecessary error of +/- 7.5 arc-minutes to the result. Perhaps Bowditch presumes that in general, attempts to deduce longitude that way are going to be rough-and-ready ones, in which such an additional error wouldn't matter. And that any attempts to do better come into the "extraordinary accuracy" category. But it seems silly to me, to introduce such unnecessary error by taking the predicted "mer pass", given only to the nearest minute, when right alongside it is the prediction for equation of time, given to the nearest second. Why not use that? Or, if needing to be even more precise, why not use the Sun GHA prediction for noon that day at Greenwich, and convert the difference from 0-degrees into time? Of course, all those predictions are for noon that day at Greenwich, and as equation-of-time is continually changing, though slowly, by the time it's local noon where you happen to be, the EoT will be a bit different. It's pretty easy to allow for this by using the tabulated value in the almanac for that day, and also for the previous day or the next (depending on whether you are East or West of Greenwich), and interpolating accordingly. There are other ways to get Equation of Time. It can be computed from "first principles", in a similar way to that described by Douglas Denny, who wrote, in [9923]- "The Equation of Time is quite rigorously dealt with in W.M. Smart's book 'Textbook on Spherical Astronomy'. A formula is quoted based on the mean longitude of the Sun." I have the 5th edition of Smart's textbook, printed in 1971, which gives the equation of time in equation 32 of chapter VI, "Time". And yes, the calculation of equation of time has been treated rather carefully. However, if precise results are needed, it needs to be taken with a pinch of salt. Smart treats the tilt of the Eart's axis, the eccentricity of the Earth's orbit, and the longitude of perihelion as constants, adopting their values as they were in 1931. In fact, all three change slowly over the years, altering the shape of the curve of equation of time quite dramatically when taken over several hundred years, as Meeus illustrates in his chapter 28. Over the ensuing 78 years after 1931, those changes will be less dramatic, but will be there. For any precise work, that Smart formula should not be used blindly, without taking some care to check whether it still remains valid (I haven't done so). 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 unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---