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    Equation of Time Simplified?
    From: George Brandenburg
    Date: 2013 Mar 11, 09:46 -0700

    I have always been intrigued by the Equation of Time, especially at the time of year when the earliest sunset and the latest sunrise occur a couple of weeks before and after the shortest day. When I took Frank's course a few years ago I learned how to use the EoT and what it looked like plotted as a function of time, and at some point I learned that it resulted both from the elliptical shape of the earth's orbit and the tilt of the earth's axis. But I had the impression that the EoT was the result of a fairly complicated calculation that couldn't be written as an actual equation. And a quick look through the Wikipedia entry for EoT didn't dispel this notion.

    So recently a favorite pastime has been to try and visualize the effects that lead to this time shift and how they change over the course of the year. (It's actually been a great way to get to sleep after I go to bed!) I found I could come up with relatively simple explanations for the two contributions that only depended on basic geometry and physics. In fact the only part I couldn't work out in my head was the spherical geometry needed for the axis tilt effect - somehow this was never included in my education as a physicist. But a quick look in Bowditch provided the necessary spherical trig formula.

    Once I had a formulas for both effects in mind I put them into excel together with a calculation of the EoT from NOAA, and I was pleased to see that they agreed almost perfectly! So my next exercise was to write up what I had done in case any other Cel Nav geek might be interested:-). I also generated a couple of figures to help explain what I was doing. The end result is attached, and yes it does conclude with a relatively simple formula for the EoT.

    If this is of interest to any NavListers I'd love to hear your comments, criticisms, etc.

    George B
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