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    Re: Eqn. of time
    From: Frank Reed CT
    Date: 2007 Jan 8, 20:37 EST
    Bill, you wrote:
    "How was a zero point(s) originally arrived at so the extremes in difference
    to either side of zero are roughly equal?  Is/was it tied to some event, or
    more or less arbitrary?"
    The zeroes in the equation of time are not tied to an event. But if you split the EqT into its two constituents, the zeroes and extreme points are then meaningful.
    If the Earth had no tilt with respect to its orbit, the equation of time would have one and only one cause: the eccentricity of the Earth's orbit. Since the Earth travels faster around the Sun at perihelion (which happens on January 4 in the current epoch), the Sun is crossing the sky faster in January than it is six months later. So that makes the Sun a "bad clock" if we use it to tell time from noon to noon each day. Graph out the equation of time that results from the eccentricity only and it's a nice symmetrical sine curve with the zeroes in logical places. This sine curve has an amplitude of about 460 seconds (of time)
    Now suppose that the Earth's orbit is almost exactly circular, like the orbit of Venus. In this case, there is no change in the Earth's speed in its orbit during the year. But if the Earth's axis is tilted by 23.5 degrees (as it is in this era) then there will be a different source for the equation of time. The Sun moving on its path at a steady pace along the ecliptic reaches the observer's meridian sooner or later depending on its declination (this is easiest to see if you imagine a hypothetical case where the inclination of the ecliptic is 89 degrees, then when the Sun is near the celestial pole it will cross many meridians of right ascension in just a couple of days). This second source of the equation of time has zeroes and extreme values at the dates of the solstices and equinoxes. It, too, yields a nice symmetrical sine curve (nearly at least). It has an amplitude of about 592 seconds of time.
    The two "sine" curves are added up to give the total equation of time. We're adding two sine curves with similar but not identical amplitudes and different phases. Try putting this together in a spreadsheet where you can vary the amplitudes and the phase difference. The shape of the equation of time is the natural result of this addition. The zeroes have no particular significance, but you can see how the arise from significant dates in the two underlying causes.
    42.0N 87.7W, or 41.4N 72.1W.

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