sidereal time

A system of timekeeping used by astronomers, useful because a star rises and sets at the same sidereal time every day, but not at the same solar time.

References such as star charts and tables give a star's right ascension and declination. Adding the right ascension to the local sidereal time gives the hour angle. Adjusting the telescope's mount so that its setting circles indicate the hour angle and the declination from the table should point the telescope at the star's present position.

The meaning of a sidereal day is most easily understood by comparing it with a solar day.

Imagine a line running from north to south through the sky and passing through the point directly overhead. This line is called the meridian. The length of time between the instant when the sun crosses the line and the instant when it crosses it again is a solar day.

Instead of the sun, we could perform the same procedure with a star, say the star Sirius, starting the timer when Sirius crossed the meridian and stopping when it crossed again the next night.

Actually, astronomers don't use a star as their reference point for sidereal time. Instead, they use the point on the celestial sphere where the sun crosses from the half of the celestial sphere that is below the plane of the earth's equator into the half that is above the plane of the earth's equator. This point is called the true vernal equinox. It is one of two points where two great circles on the celestial sphere intersect: one circle (the true Equator) found by projecting the plane of the earth's equator onto the celestial sphere, and the other (the ecliptic) by similarly projecting the plane of the earth's orbit. The true sidereal day is the time interval between the instant when the true vernal equinox crosses the meridian one night, and the instant when it crosses on the following night.

As with solar days, there is both an apparent sidereal day and a mean sidereal day, which is the average of the apparent (see day). 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 4 minutes earlier each day. Irregularities in the earth's rotation also affect the length of sidereal days; unlike atomic time, sidereal time is not absolute.

Why do the lengths of the solar and sidereal days differ? 

Try this little demonstration. 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. Even if the earth didn't rotate, there would be one day per year. The number of rotations earth makes in a year will be one less 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. It has no special name or use.

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.

Actual measurements of sidereal time depend on the use of some particular catalog of stars, and the point observed crossing the meridian is the “catalog equinox.” For a complete explanation, refer to one of the references.

Kenneth Seidelman, editor.
Explanatory Supplement to the Astronomical Almanac.
Mill Valley, CA: University Science Books, 1992.

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