More Precisely 1.3 - Astronomical Timekeeping

Posted by Andri Fadillah Martin on Saturday, February 11, 2012

Astronomical Timekeeping


The motions of Earth and the Moon define the basic time units—day, month, and year—by which we measure our lives. Today the SI unit of time, the second, is defined by ultra-high-precision atomic clocks maintained in the National Bureau of Standards in Washington, D.C., and in other sites around the world. However, the time they measure is still based on the time determined by astronomical events. Let’s take a moment to consider in a little more detail how days, months, and years are defined and measured.

At any location on Earth, a solar day may be simply defined as the time between one noon and the next. Here, "noon" means the instant when the Sun crosses the meridian—an imaginary line on the celestial sphere through the north and south celestial poles, passing directly overhead at the given location. This is the time that a sundial would measure. Unfortunately, this most direct measure of time has two serious drawbacks—the length of the solar day varies throughout the year, and the definition of noon varies from place to place on Earth.

Recall that the solar day is the result of a "competition" between Earth’s rotation and its revolution around the Sun—Earth’s revolution means that our planet must rotate through a little more than 360º between one noon and the next (see Figure 1.10). However, while Earth’s rotation rate is virtually constant, the rate of revolution, —or more specifically, the rate at which the Sun traverses the celestial sphere as it moves along the ecliptic, —is not, for two reasons (illustrated in the exaggerated diagrams below).




First, Earth’s orbit is not exactly circular (see Chapter 2), and our orbital speed is not constant—Earth moves more rapidly than average when closer to the Sun, more slowly when farther away—so the speed at which the Sun moves along the ecliptic varies with time. Second, because the ecliptic is inclined to the celestial equator, the eastward component of the Sun’s motion on the celestial sphere depends on the time of year (and note that this would be the case even if Earth’s orbit was circular and the first point did not apply). At the equinoxes, the Sun’s path is inclined to the equator, and only the Sun's eastward progress across the sky contributes to part of the motion. At the solstices, however, the motion is entirely eastward.

The combination of these effects means that the solar day varies by roughly half a minute over the course of the year—not a large variation, but unacceptable for astronomical and many other purposes. The solution is to define a mean solar day, originally cast in terms of a fictitious mean Sun that moves around the celestial equator at constant speed, but which in effect is just the average solar day over an entire year. This is the day our clocks (atomic or otherwise) measure, and it is by definition constant. One second is 1/24  1/60  1/60 = 1/86,400 mean solar days.

Now all of our clocks tick at a constant rate, but we are not quite out of the woods in our search for a standard of time. The above definition is still local—observers at different longitudes see noon at different times, so even though their clocks keep pace, they all tell different times. In 1883, driven by the need for uniform and consistent times in long-distance travel and communications (the railroads and the telegraph), the continental U.S. was divided into four standard time zones. Within each zone, everyone adopted the mean solar time corresponding to a specific meridian within the zone. Since 1884, standard time has been used around the world. The global standard time zones are shown below.
By convention, the reference meridian is taken to be 0º longitude (the Greenwich meridian). In the United States, Eastern, Central, Mountain, and Pacific time zones keep the mean solar time of longitudes 75º W, 90º W, 105º W, and 120º W, respectively. Hawaii and Alaska keep the time of longitude 150º W. In some circumstances, it is even more convenient to adopt a single time zone: universal time (formerly known as Greenwich mean time) is simply the mean solar time at the Greenwich meridian.

Having defined the day, let’s now turn our attention to how those days fit into the year—in other words, to the construction of a calendar. The "year" in question is the tropical year, tied to the changing seasons. It is conventionally divided into months, which were originally defined by the phases of the Moon. The basic problem with all this is that a synodic (lunar) month does not contain a whole number of mean solar days, and the tropical year does not contain a whole number of months or days. Many ancient calendars were lunar, and the variable number of days in modern months may be traced back to attempts to approximate the 29.5-day synodic month by alternating 29- and 30-day periods. The modern (Western) calendar retains months as convenient subdivisions, but they have no particular lunar significance.

One tropical year is 365.2422 mean solar days long, and hence cannot be represented by a whole number of calendar days. The solution is to vary the number of days in the year, much as early calendars varied the number of days in the month, to ensure the correct average length of the year. In 46 B.C. the Roman emperor Julius Caesar decreed that the calendar would include an extra day every fourth year—a leap year—ensuring that the average year would be 365.25 days long. This Julian calendar was a great improvement over earlier lunar calendars, which had 354 (= 12 x 29.5) days in the year, necessitating the inclusion of an extra month every three years!.

Still, the Julian year was not exactly equal to the tropical year and, over time, the calendar drifted relative to the seasons. By A.D. 1582, the difference amounted to 10 days, and Pope Gregory XIII instituted another reform, first skipping the extra 10 days (resetting the vernal equinox back to March 21), then changing the rule for leap years to omit the extra day on years that were multiples of 100, but retain it in multiples of 400. The effect of this is that the average year became 365.2425 mean solar days long—good to one day in 3300 years. The idea of "losing" ten days at the behest of the Pope was unacceptable to many countries, with the result that the Gregorian calendar was not fully accepted for several centuries. Britain and the American colonies finally adopted it in 1752. Russia abandoned the Julian calendar only in 1917, after the Bolshevik revolution, at which time they had to skip 13 days to come into agreement with the rest of the world.

The most recent modern correction to the Gregorian calendar has been to declare that the years 4000, 8000, etc., will not be leap years, improving its accuracy to one day in 20,000 years—good enough for most of us to make it to work on time!

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