Facts of the Matter
Richard Brill
The equation of time
explains why summer’s
dog days seem longerA sundial is much more than a statue that casts a shadow on numbers as the sun moves across the sky.
It is that, but to build a sundial that keeps accurate time is no easy task. It requires that we understand and take into account the equation of time.
No coincidence, then, that it took 2,000 years and the 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.
Time keeping is based on the movement of the earth as it spins on its axis and revolves around the sun. But these motions are not as regular as they appear, and there is no reason, anyway, to expect that they should be either regular or synchronized.
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 is based on dividing each day into 24 hours. It is based upon the regular intervals of mechanical clocks, as it was envisioned and defined by Isaac Newton 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 may 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, however, caused by changes in the earth's rotation speed. The daily rotation of the earth is relatively constant, changing 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 maxima in February -- when sun time is 14 minutes slower than clock time -- and in 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 totality of differences between sun time and clock time throughout the year is called the equation of time, and there are two factors that determine it. One is the tilt of earth's rotational axis, the other is its elliptical orbit.
The tilted axis results in the sun oscillating throughout the year between the Tropic of Cancer and the Tropic of Capricorn at 23.5 degrees North and South of the equator respectively. As it 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 further away.
If 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 further 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.
Aside from being a puzzle that drove the development of science and the concept of time, the equation of time accounts for the fact that the earliest sunrise and latest sunset don't occur on the same day in summer. Another effect is the sun is way behind the clock in late summer, making those August days seem the longest of the summer.
The equation of time was important to those curious and inventive folks who wanted to make accurate sundials to keep solar time before the middle of the seventh century saw the invention of mechanical clock time. Today we can keep atomic time accurate to nanoseconds and the equation of time is just another piece in the puzzle that is our physical universe.
We could all be a little smarter, no? Richard Brill picks up
where your high school science teacher left off. He is a professor of science
at Honolulu Community College, where he teaches earth and physical
science and investigates life and the universe.
He can be contacted by e-mail at rickb@hcc.hawaii.edu