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    Re: Calculated Altitudes for Clearing
    From: George Huxtable
    Date: 2002 Mar 25, 00:30 +0000

    Bruce Stark wrote-
    
    >George has a point about calculated altitudes. But the explorers and
    >surveyors of the past routinely left the altitudes to be calculated. They
    >were using a different kind of nautical astronomy and a different kind of
    >Nautical Almanac. It was only in the twentieth century, with the advent of
    >the GHA Almanac, that navigators came to need accurate Greenwich time to work
    >their observations. I've tried to show how the old system worked in a series
    >of papers on Lewis and Clark's observations, published by the Navigation
    >Foundation.
    
    Response from George-
    
    Well, I don't see that the change from Right-ascension to GHA made any
    difference to the difficulty of working lunars from calculated (as opposed
    to measured) altitudes. The altitude of the Moon (and therefore its
    contribution to lunar parallax) changed just as fast, no matter how it was
    tabulated in the almanac. Perhaps Bruce will explain this "old system" for
    us.
    
    Bruce is quite right that in the past the use of calculated altitudes, if
    measurements couldn't be made, was recommended, as far back as Maskelyne in
    the "British Mariner's Guide" of 1762, and then in the first Nautical
    Almanac for 1767. However, Maskelyne is nowhere very specific about the
    details of how to do it.
    
    With certain positions of the Moon in the sky, the GMT may well converge
    quickly, and if the initial guess of Greenwich time for the observation was
    a good one then reiterations might not be necessary. But how can an
    observer tell without enough iterations to show that he is converging on a
    precise result? If Bruce has access to the calculations made by (say) Lewis
    and Clark, perhaps we can find out when they used calculated altitudes for
    the Moon, and if they did so when the Moon was high in the sky, and if they
    then recorded their successive iterations for time, and how these
    converged.
    
    It's starting to dawn on me that the serious effects of Moon parallax on
    the calculations for GMT  have not been properly appreciated by lunar
    navigators in the past. It has just been though of as just "one of those
    corrections we have to allow for".
    
    It depends on whether my own investigations about "parallactic retardation"
    have any validity, which is quite a big if. The conclusions remain somewhat
    tentative, but I am gradually gaining some confidence in their relevance as
    nobody yet has had a go at shooting them down. A challenge would indeed be
    appreciated: there's nothing as effective as having to explain and defend
    your ideas to clarify the mind. If there's a big hole in its middle, the
    sooner it is discovered, the better.
    ===========================
    
    >But the point I particularly want to make is that people should observe
    >distances wherever they are, without taking the time or going to the trouble
    >of dealing with an artificial horizon. That way they will take hundreds of
    >observations, not just one or two, and they will become familiar with their
    >sextants.
    
    I agree with Bruce here, to some extent. As long as those measurements made
    with calculated altitudes are understood as being for their value as
    sextant practice. Unless a series of successively more accurate iterations
    for time is obtained, they should not be considered as a valid measure of
    GMT.
    
    On the other hand, if instead a measurement of lunar altitude can be
    obtained, the observer can ensure that this was taken at the same time as
    that for the lunar distance, and the measured altitude must then be
    appropriate to that time, whatever it turns out to be.
    
    ==========================
    
    >Artificial horizons are an important topic on their own. I've read some good
    >advice, and done a bit of experimenting, but would not take many observations
    >if it were mandatory to set one up every time.
    
    Well, if an artificial horizon is necessary, then it's necessary. It's no
    argument to say that it is too awkward. Is it such a big deal, anyway, to
    keep a tray of liquid in your garden, with a cover over to stop you putting
    your foot in it? (My wife is the family gardener, and I won't quote her
    response to that proposal.)
    
    >Haven't tried it yet, but I think we can figure out how to use our present
    >Almanac the same way the old navigators used theirs.
    >
    >Bruce
    
    Please do, Bruce.
    
    George Huxtable.
    
    ------------------------------
    
    george---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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