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    Re: Almanac accuracy, WAS: Re: Hughes Tables.
    From: Douglas Denny
    Date: 2009 Jul 17, 17:47 -0700

    The accuracy of almanac data depends on the source(s) of the algorithm(s) used 
    for the computation; the source data for the computations and the 
    computational platform used.
    
    The official almanac offices are charged with promulgating the most accurate data available.
    The US and London Almanac Office produce data for different users to different 
    degres of acuracy.  In simple terms, the The Astronomical Almanac publishes 
    the most accurate data to seconds of arc or time; next,  the Nautical 
    Almamanac, which will have the largest error with GHA of the Sun no more than 
    0.'25; with less than 0.'2 for the Sun or Moon to be expected, and, it 
    states: the quantities are generally correct to the nearest 0.'1  
    
    The Air almanac has data rounded to the nearest minute of arc.
    
    For a full detailed explanation see the "Explanatory Supplement to the 
    Astronomical Ephemeris and the American Ephemeris and Nautical Almanac"  
    published jointly be the American and UK Nautical Almamac Offcies.
    
    Also, Jean Meeus' book 'Astronomical Algorithms' gives a very good appraisal 
    of accuracy to be expected using the fundamental algorithms on computer or 
    hand calculators (which are available in the 'Explanatory Supplement' as 
    above and Meeus' book).
    It would appear computer almanacs available on te hinternet use these algorithms and data.
    
    Some almanacs published are not necessarily going to give "accurate" data if 
    they do not use sufficient number of significant digits, or round-up errors 
    appear, or the built-in trig functions are not accurate in themselves.  Early 
    computers only had six or eight sig digits of computation available.  Modern 
    calculators appear to use nineteen digits but can still trip-up with trig 
    functions or use of long parameters e.g. with Julian centuries being used.
    
    For navigational use an acuracy of 0.'1 arc is more than adequate. However, if 
    you want to study the occultation of a star behind the Moon then 1" of arc at 
    least would be needed for the Moon and star.   The number of harmonic 
    parameters required in the algorithm to accurately calculate the accurate 
    position of the Moon for this kind of work is in the hundreds.  This is not 
    needed for navigational use where a few dozens will be adequate.  Meeus' book 
    is excellent for an explanation of this.
    
    I use 'ICE' Version 0.51 (the last version available) on computer for accurate 
    data which was published by the US Almanac Office in the 80's I believe. It 
    gives full accuracy to Nautical Almanac standards I believe.  Initially 
    developed as a free resource, the US Office must have come under pressure 
    from somewhere (?) to stop this being available free (my guess is the UK 
    almanac office) as it was suddenly withdrawn, nor was it further developed 
    for free use.  They now have 'MICA' which is the same thing but with updated 
    interfacing for modern computer - and you _pay_ for it of course , which I 
    think is a bit of a cheek when you consider the information itself is 
    universal and is a universally needed and used resource , and has already 
    paid for to be obtained by the taxpayer through the science and research 
    councils, MOD and other government agencies - i.e agencies owned by the 
    taxpayer.  It is an information source I believe that in the interests of 
    safety at sea should be totally free.
    
    ICE is still available from various sites. It is not particularly 
    user-friendly; nor does it give HP for the Moon but is still very good and 
    gives full Nautical Almanac accuracy. There is another I use which appears 
    good for navigational use and seems acurate but I cannot vouch for its 
    accuracy as I do not know the source or algorithms used.
    
    I also use an HP 50g calculator with the standard algorithms I entered from 
    'Explanatory Supplement' and in Meeus' book which is more than accurate 
    enough for navigation.
    
    Douglas Denny.
    Chichester England.
    
    
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