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    Re: Shape of the Sun's daily motion
    From: Frank Reed
    Date: 2022 Feb 9, 06:59 -0800

    Each day of the Sun's motion is one loop of a rising spiral from December 21 to June 21. Followed by a descending spiral for the next six months. Then repeating year after year. On any single day, the Sun's path is nearly a circle, but not quite. From any one location on the Earth, if you trace its motion for a full day, you'll see something almost perfectly circular around the celestial sphere (and for detail, it's close to a "small circle" on most dates and only close to a "great circle" on the equinoxes, when the Sun is closest to the celestial equator).

    If you look very closely at one day's "near-circle" in the Sun's motion, you find that the circle doesn't close. Instead the latitude is rising or falling all day long. Right now, for example, in early February, the latitude is climbing all day long at a rate of 0.8 knots (the maximum rate at the equinoxes is just about one knot). At the same time, you'll discover that the daily near-circles don't quite close in another way. On some days, the Sun gets a little ahead of itself. In exactly 24 hours, it may have travelled, as seen from the perspective of an observer on the ground, a half-dozen miles past its starting longitude 24 hours earlier. Or on other days, the Sun is slow and has not quite returned to its starting longitude after exactly 24 hours. All of this motion is summed up quite neatly in a useful diagram called the analemma, and I recommend reading about it here: analemma.com. Today we happen to be quite close to a significant point on the analemma; we're coming up on "Sun Slow Day".

    Frank Reed

       
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