When does a day begin?

In the Western civil calendar, the day begins at midnight local time. For astronomers, the day begins at noon, which conveniently avoids dividing the night's events between two dates. Astronomers' dates are 12 hours ahead of the civil date; an occurrence on the afternoon of May 8 would have happened on May 9 as astronomers see it.

In many cultures the day begins at sunset, a division observed for religious purposes by Jews and Moslems.

Where does a day begin?

According to present notions of timekeeping, the day begins along the International Date Line. The exact location at which the first sunrise of the day (or year, or millennium) could be seen became a matter of controversy during preparations for the celebration of the second millennium ce.

The Royal Greenwich Observatory calculated that sunrise is first seen at Balleny Island in Antarctica; next at Caroline Island, part of the Republic of Kiribati; and third on New Zealand's Pitt Island. In 1996, the Millennium Adventure Company leased the highest hill on Pitt Island, claiming the site would be “the first terrestrial, accessible and populated place to usher in the next 1,000 years.”

The length of the day

The simplest definition of a day's duration, and the one used in most sciences, including astronomy, is that it is 86,400 seconds as the second is defined in SI. The rotation of the Earth is not explicitly mentioned in this definition, but of course that is where the “86,400” comes from.

Solar days

The apparent motion of the sun defines a day for most people. A good way of timing its coming and going (sunsets and sunrises are messy because light is bent more near the horizon) is to imagine a line running from north to south and passing through the point directly overhead. Such a line is called a meridian. Start your stopwatch when the sun crosses the line and stop it at the instant when it next crosses it again (such a crossing is called a transit). You have recorded the length of an apparent solar day. If you did this for an entire year, you would find that some days–remember, we are talking about 24-hour days here–are longer than others. To even things out, we can average the lengths of all the apparent solar days during a year and get the mean solar day.

Sidereal days

Imagine however, that instead of using the sun, we begin timing when some particular point on the celestial sphere, say the star Sirius, crosses the meridian, and stop when it crosses again. To our surprise, we would find that the duration is shorter than the mean solar day. What we have measured is the apparent sidereal day. The sidereal day is subdivided in the same way as the solar day, into 24 sidereal hours; each sidereal hour into 60 sidereal minutes, and each sidereal minute into 60 sidereal seconds. As with solar days, the length of sidereal days is subject to irregularities in the Earth's rotation (see below), and so there is both an apparent sidereal day and a mean sidereal day.

Actually, the point on the celestial sphere that is used for measuring sidereal time is not a star, but the true vernal equinox, the point where the sun crosses from the southern celestial hemisphere into the northern celestial hemisphere each year. The true vernal equinox is one of two points where two great circles on the imaginary celestial sphere cross:

The true sidereal day is the time interval between two successive instants when the true vernal equinox crosses the meridian.

In 1991, one mean solar day = 1.00273790935 mean sidereal days. The mean sidereal day is 23 hours, 56 minutes, 4.09054 seconds long, about 3 minutes 55 seconds shorter than the mean solar day. In other words, the stars rise about four minutes earlier each day.

Why do the solar and sidereal day differ?

Try this: Place a cent and quarter face up on the table before you, with the penny on the left. Abe and George will be facing each other. The penny represents earth and the quarter the sun. Abe is our observer on the earth; he sees the sun directly in front of him.

Move the penny around the quarter in a clockwise direction. When the penny is above the quarter, the quarter passes out of Abe's view and remains hidden until it appears overhead when the penny is below the quarter. The sun has risen and set, but the penny hasn't rotated at all; Abe has continued to look at the same point on the wall all this time. In other words, the number of sidereal days in a year is one more than the number of solar days.

Because the vernal equinox itself moves (due to the precession of the Earth's axis), the sidereal day is not quite the same as the period of earth's rotation with respect to a fixed direction in space. That period is 0.0084 seconds longer than a sidereal day. Oddly enough, this, the true period of the Earth's rotation, has no special name or use.

The Erratic Earth

One of the great frustrations of 19th century astronomy was that it could predict the motion of everything but the Moon. Using Newtonian mechanics, astronomers should have been able to predict exactly where the Moon would be at a given moment, but the predictions were repeatedly wrong.

Towards the end of the century, it began to dawn on them that it wasn't the Moon's motion that was irregular, but the clock they were using: the rotation of the earth, which affects the length of the apparent solar and sidereal days and the time assigned to observations. The problem showed up first in studies of the Moon because the Moon moves against the background of distant stars more quickly than anything else. As a result, smaller intervals of time are visible in its motion than in that of slower moving objects. Several different causes for irregularities in the Earth's rotation have been discovered:

By the 1860s astronomers generally agreed that over the very long term, days are getting longer as the Earth's spin slows due to tidal friction and the transfer of some of its energy to the moon. The length of the day increases by about 0.001 second each century. This is called the secular variation.

In the 1930s a seasonal variation in the length of days was discovered. Days in March are about 0.001 second longer than days in July. The pattern more or less repeats each year. This seasonal variation is thought to be due to the action of winds and tides. [N. Stoyko, 1937]

Recently abrupt, irregular changes of several thousandths of a second have been discovered, which are thought to be due to interactions between motions in the Earth's outer layers and core.

Dennis D. McCarthy and J. D. H. Pilkington (eds.)
Time and the Earth's Rotation: Proceedings of the 82nd symposium of the International Astronomical Union held at San Fernando, Spain, 8-12 May 1978.
Dordrecht, Holland: Reidel, 1979.

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