Sundials, Mean Time, and the Equation of Time.

One of the first applications of astronomy in the ancient world was keeping track of time and the seasons.  For agricultural societies, knowing when to plant and reap crops was extremely important; in addition, you will notice that many holidays are celebrated near or on days of astronomical events (e.g., the winter solstice or the first moon after the spring equinox).

The first time used was Apparent Time, which is based on the position of the sun (i.e., where the sun appears in the sky).  This is the time that you would read on a sundial.  The basic defining characteristic of Apparent Time is noon, which occurs when the sun is on the meridian.

A slight problem arises with Apparent Time, however, once you begin using a watch: every day is not exactly the same length (although the average is still 24 hours).  This is due to a number of reasons, two important ones being that the Earth's motion as it orbits the sun is non-uniform and that Apparent Time is assumed to be measured from the equator.    (You would also have to adjust for the fact that Storrs is not at the center of the Eastern Time Zone, but 11 minutes east.)

So if you wanted to use Apparent Time, you would have to adjust your watch every day.  To avoid these problems the concept of Mean Time is used.  (Here "mean" refers to the arithmetic mean: an average.)  The Mean Time is based on the mean, or average, position of the sun, and assumes that each day is exactly 24 hours long.  In other words, it assumes the Earth travels uniformly around the sun.  Mean Time is the time you use every day.

So if you read the time from a sundial, how do you know what the Mean Time is? The Equation of Time is a function that shows the difference between Apparent Time and Mean Time.  The Equation of Time takes into account all the small adjustments for the Earth's movement and provides one amount to add or subtract from the sundial reading.

Equation of Time

The figure of the Equation of Time above may look familiar: it is also on a plaque on the base of the sundial behind the UConn Student Union.  An astronomical almanac or ephemeris will give the Equation of Time down to about 1 second.

For example, if the sundial reads 12:00 noon on May  14, when the Equation of Time is about +4 minutes, then the adjustment would be:

MT = AT - E/T - (Distance from Center of Time Zone)  + Daylight Savings

MT = 12:00 nn - (4 min) - (11 min) + 1 h = 12:45 pm

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 This page was last updated on 27 March 1998
and is © 1998 by Jim McDonald.