To build a sundial that keeps accurate time is not an easy task. A sundial is more than merely a statue that casts a shadow on numbers as the sun moves across the sky. It requires that we understand and take into account the equation of time. It took two millenniums and necessitated the development of a great deal of sophistication in our understanding of what time is and how to keep track of it.

If the earth moved at a constant speed in a perfect circle around the sun, and if its axis were not tilted with respect to its orbit around the sun, then sundials would always keep perfect time.

Sun time is based on the passage of the sun across the meridian, an imaginary line that passes directly overhead connecting the north and south poles. “Noon” in sun time is the instant that the sun crosses the meridian from a.m. (literally: ante meridian — before noon) into p.m. (post meridian — after noon. Just for the record: Noon is neither 12 a.m. nor 12 p.m. It is 12 noon, or just noon.)

Clock time, on the other hand, divides each day into 24 hours. It is based upon the regular intervals of mechanical clocks, as Sir Isaac Newton envisioned and defined it in the late 17th century.

Although the time from one clock noon to the next will always be exactly 24 hours, the time from one solar noon to the next might be slightly more or less than 24 hours. The difference is small but significant: A solar day in January is more than a minute shorter than a solar day in July. This is not due to changes in the earth’s rotation speed, which varies only a few microseconds from one day to the next.

The differences in the length of the solar day are small, but they add up over the months. They reach their maximums in February, when sun time is 14 minutes slower than clock time, and November, when sun time is 16 minutes faster than clock time.

They do not accumulate from one year to the next because they cycle back and forth as the seasons change. The sun clock runs slow a little more than half the year, so there are exactly four days every year when clock time and sun time are synchronized.

The equation of time is the totality of differences between sun time and clock time throughout the year. Two factors determine it. One is the tilt of Earth’s rotational axis; the other is its elliptical orbit.

As the sun heads northward from the March equinox, the sun first lags behind the clock, catches up to it at the June solstice, then races ahead of the clock until the September equinox. From there the sequence repeats through the December solstice until the following March equinox when the cycle begins again.

The elliptical orbit affects the equation of time because the earth moves at different speeds in different portions of its orbit, moving faster when closer to the sun and slower when farther away.

If the earth moved around the sun in a circular orbit at a constant speed, then it would move the same fraction of the orbit with each rotation. In the elliptical orbit, when it moves faster it also moves through a larger portion of the orbit in the time of one rotation. The result is that the earth has to turn a little farther before the meridian comes under the sun again. Clock noon thus arrives before the sun crosses the meridian, so the sun appears to be slow.

The equation of time accounts for the fact that the earliest sunrise and latest sunset do not occur on the same day in summer. The sun is way behind the clock in late summer, making those August days seem the longest of the summer.

Richard Brill is a retired professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.