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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

882.0. "Equation of Time - information sought." by BIRGP1::TURRELL (I will not Reason and Compare:) Fri Jun 03 1988 12:35

    	Hi,
    
       A friend and I are interested in designing/building a sundial
    and have come across a problem which we hope someone out there can
    help with.
    
       What we are looking for is a mathematical formulation of the
    "Equation of Time". As far as I am able to make out the expression
    merely consists of two sine waves added together. However, despite
    the fact that tables providing approximate values are readily
    available, we seem unable to find the actual formula used.
    
        Grateful for any and all help.
    
    			Pete_T.
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882.1CTCADM::ROTHIf you plant ice you'll harvest windFri Jun 03 1988 16:0713
    Look in the Nautical Almanac; the expression is actually very
    complex, involving an expansion in Chebyshev polynomials.
    It results from a hairy perturbation analysis of the orbits
    of the planets, etc.

    There is a version of the Almanac that does have the series
    expansions - it's the one commonly used by astronomers.

    For a sundial, you don't really need the accuracy though.  It may
    be simpler to look in one of the Dover paperbacks that explains
    the theory of sundials.

    - Jim
882.2CTCADM::ROTHIf you plant ice you'll harvest windFri Jun 03 1988 16:084
    One other note - the Almanac is available in diskette form nowadays.
    That may be more useful than the paper copy...

    - Jim
882.3Keep horology nuclear free, bring back sundials.BIOMIC::TURRELLI will not Reason and Compare:Mon Jun 06 1988 16:058
    	Jim,
    
    Thanks for the reference, I'll see if I can dig it out. I take your 
    point re the accuracy but you know how these things can get under the 
    skin when you get going. Also I rather liked the idea of coding a
    short simulation program.
    
    		Pete_T.
882.4From the Mills Book...SDOGUS::DRAKEDave (Diskcrash) Drake 619-292-1818Mon Jun 13 1988 05:3725
    There is a good reference to be found in,
    "Positional Astronomy and Astro-Navigation Made Easy"
    H.R. Mills  Halsted Press, John Wiley and Sons  of New York
    ISBN 0-470-99324-3
    
    From page 218
    
    assume w=(360 * number of days from January 1st / 365.25)
                 
    assume RA= sun's right assention on the given date
    
    The approximate Equation of Time
    
    E= -7.64 sin (w)  +  9.863 sin (2 * RA)
    
    another approximation
    
    L= sun's longitude from Norton's Star Atlas or similar
    
    E = -7.64 sin (L +78)  +  9.863 sin (2 * L)
    
    page 220 discusses  analemmatic noon marks for sundial fabrication.
    
    Hope this helps.