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    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.
    
    
    
    
    
    
    
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