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    Re: Almanacs, theory and use.
    From: Bill Wells
    Date: 2007 Nov 23, 00:29 -0800

    With all due respect for the previous entries, I would like to suggest
    a different approach. Let's not lose sight of the objective - Mike
    wants to demonstrate to his kids that the Earth is in fact spherical
    (or close to it). We are not told the age of the children, but the
    following suggestion applies to students of all ages.
    
    Mike could begin with the method used by Eratosthenes around 200 BC to
    calculate the circumference of the Earth. It is also a clear and
    intuitive demonstration of the curvature of Earth. There is no point
    in repeating here details of the method he used; there are plenty of
    websites the kids will easily find which show the concept in a
    straightforward way.
    
    The kids could conduct their own experiments, at local apparent noon
    holding a meter stick vertically on a level surface near their home in
    Scotland, then measuring its shadow. This time of year in Edinburgh
    they will see a shadow about 400 cm long, with a sun altitude of 14
    degrees. A call to grandmother near London, where the sun altitude
    will peak at 18.5 degrees, and the kids will find that she sees a
    shadow of 300 cm. This is a dramatic difference, and a simple sketch
    with or without trigonometry will go a long way to demonstrating the
    curvature (and oblate spheroid shape) of our Earth. Their actual
    locations in England and Scotland will, of course, produce different
    results, but the numbers will be meaningful. After this demonstration,
    move on to elevations of Polaris at both locations with the Ebbco,
    followed by determination of positions using the almanac.
    
    Let's keep in mind this is about the children, and developing in them
    an interest in the sciences. Better not start out with rocket science,
    or they will go back to the Google on the PC.
    
    By the way, this is my first post; I am likely the new member of the
    group.
    
    Regards, Bill
    
    
    
    
    On Nov 20, 3:39 am, Isonomia  wrote:
    > We live in Scotland and my mother lives in England, so I thought it
    > would be  pretty simple to prove to my kids using a sextant that the
    > world was  spherical - so I bought an EBBCO on eBay. Whilst I've
    > proved to myself I can  use a sextant to find out where I am, I'm
    > still to convince the children either that you can, or that you would
    > want to.
    >
    > I started by using some software into which I put the time,
    > approximate  longitude, latitude and sextant reading, and (after
    > working out I had to  subtract half the sun's diameter) I finally got
    > something average on our  location on average about 3 miles from our
    > location. Unfortunately, as far  as a kid is concerned, if you have a
    > PC, you may as well look up  google/streetmap rather than waste time
    > with a sextant, so I need to find a  PC-less way to find out where I
    > am.
    >
    > So, using a bit of trig (with some software from the web) I created my
    > own  single-page weekly tables (the sun don't shine everyday!), giving
    > altitude  and direction of the sun for a given location for each
    > minute of the day.  This allows me to create a table for any given
    > place which most children who  can add two digit numbers, and use a
    > ruler/protractor could use by  themselves (with instructions) to plot
    > a line giving their location (to  within 10miles I hope!), which if
    > repeated twice in a day should give an  "exact" location.
    >
    > Now, I know how my "Almanac" works, but even having figures for every
    > minute  of the day, for a known location and interpolating results for
    > seconds, I  will still be pushing it to get tabular errors less than
    > 1'. From what I  have been able to discern about real almanacs they
    > contains a fraction of  this information with only hourly figures for
    > every location in the world.  Although, I've downloaded a few
    > worksheets to "calculate" the figures, I  can't understand how these
    > are used (I neither have a worked example, nor do  I have an almanac,
    > nor do I have a theoretical explanation for the tables -  but I don't
    > see that as a fundamental problem!) Surely getting from these  figures
    > in the Almanac to one at any time for a particular location but
    > involve some complex trigonometry and rather hectic sinusoidal
    > interpolations - neither of which are apparent on the worksheets!
    >
    > What I really want to know is how my "almanac" relates to a real
    > almanac,  and how, could and should I make my "almanac" more like a
    > real almanac and  still have it useable by children? I've tried
    > searching the internet, for  any explanation of how to use an almanac
    > (with the theoretical background) -  any help would be greatly
    > appreciate (remembering I am not familiar with  SHA, GHA, and whilst I
    > learnt spherical geometry at University, I'm a little  rusty)
    
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