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    Re: Eqn. of time
    From: Bill B
    Date: 2007 Jan 09, 00:16 -0500

    > 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?"
    
    Frank replied:
    
    > 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.
    
    Thanks Frank
    
    I do have a basic understanding of the underlying reasons for this, but
    certainly lack the skill sets to parse them into a precise result.
    
    I had, many years ago, graphically merged the effects, but that yielded only
    a basic understanding.  I do calculate the equation of time yearly thanks to
    the information you provided a couple of years ago, and do graph the
    results.
    
    I guess my question may have been more historical in nature. The First Point
    of Aires appears to have shifted over 2000 years (mainly due to precession I
    presume), the distance of our pole star has shifted and will continue to on
    a 26,000-year cycle for the same reason, and the calendar we now use has
    been revised. That caused me to wonder if at some time in the past there was
    a conscious effort to link the equation of time to some celestial event.
    
    Looking at it from a purely (modern) calendar event, the central zero point
    occurs close to the midpoint of a calendar year in June, but is past that
    calendar midpoint.
    
    Looking at it using a half year in modern calendar days from perihelion it
    comes a bit closer. The rub here, as you pointed out, is that the earth's
    speed is greater when closer to the sun, so it may travel a greater distance
    as a result of higher speed (Johannes Kepler), therefore any effort to place
    it at "midpoint" prior to Kepler was may have been empirical in relation to
    today's mathematics.
    
    If the list will indulge me a few questions:
    
    When was the equation of time first understood and mapped?
    
    At that point, was there an attempt to link it to a celestial event that may
    now be lost in change?
    
    On a related issue: If I understand it the pole star will--within a
    generation or two--come as close to earth's rotational axis as it will come
    for 26,000 years. All things being equal, will the winter solstice occur
    during June in approx. 13,000 years?
    
    If yes to the above, will the northern hemisphere (like Australia now) pick
    up a bit more heat by virtue of proximity in the summer, and a bit less in
    the winter?
    
    Bill
    
    > 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.
    
    
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