Having Fun with the Equation of Time

That funky figure eight [on a globe] is what’s known as an analemma, and it traces out the course of the Sun in the sky through the year as measured from a daily point fixed in apparent solar time.

Solar Noon occurs when the Sun stands at its highest elevation (also known as its altitude) above the local horizon when it transits the north-south meridian. The trouble is, the passage apparent solar time doesn’t exactly match what we call solar mean time, or the 24 hour rotation of the Earth. In fact, this discrepancy can add up to as much as more than 16 minutes ahead of solar noon in late October and November and over 12 minutes behind it in February. This is worth bringing up this week because this factor, known as “The Equation of Time” — think “equation” in the sense that sundial owners must factor it in to make solar mean and apparent time “equal” — reaches its shallow minimum for 2014 this Saturday at 7:00 UT/3:00 AM EDT with a value of -6.54 minutes.

You can make your own analemma simply by photographing the position of the Sun at the same time each day. Just remember to account for the shift on and off of Daylight Saving if you live in an area that observes the archaic practice,[emphasis added] residents of Arizona need not to take heed. Otherwise, you’ll end up with a “split analemma…” Wintertime near the December Solstice is the best time to start this project, as the Sun is at its lowest noonday culmination and this will assure that your very own personal analemma won’t fall below the local horizon.

From Cornell University...

What is sidereal time?

Mean time is the sort of time we’re used to, where a day is 24 hours, the time it takes for the Sun to complete one trip around the sky and return to its original position. Sidereal time is measured according to the positions of the stars in the sky. A sideral day is the time it takes for a particular star to travel around and reach same position in the sky. A sidereal day is slightly shorter than a mean day, lasting 23 hours, 56 minutes, and 4.1 seconds. A sideral day is divided into 24 sideral hours, which are each divided into 60 sidereal minutes, and so on.

The reason that sidereal days are shorter is that while the Earth rotates on its axis, it is also moving around the Sun. Both motions are counter-clockwise as viewed from the north pole. You may find it helpful to draw a diagram. The sun can be represented with a point. Draw the Earth. Let it be noon for an observer on the Earth, so sketch a little stick person with his feet on the Earth and his head pointed at the Sun, because at noon, the Sun is directly overhead. Draw a line from the Earth to the Sun, and let it extend far beyond the Sun. Draw a star on this line. From the observer’s point of view, the star is also overhead, although of course it would be hidden behind the Sun. Now, imagine that the observer is carried for one mean day on the Earth as it makes a rotation while also moving through space. Draw the Earth at its new position in the orbit (it’s okay to exaggerate this motion for purposes of illustration) and notice that when you add the person pointing at the Sun, he’s no longer pointed toward the star! More than one sideral day has passed!

You might ask whether the star’s distance would affect the length of the sideral day. Try moving the star farther from the Sun, and you’ll notice that as the star gets very far away, the differences become quite small. Even the closest star to us is so far away that the sidereal day is the same, no matter what star you use to measure it.”

http://curious.astro.cornell.edu/question.php?number=110

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