Physics 155: Sidereal Time

Sidereal Time and Solar Time

Careful observation of the sky will show that any specific star will cross directly overhead (on the meridian) about four minutes earlier every day. In other words, the day according to the stars (the sidereal day) is about four minutes shorter than the day according to the sun (the solar day).

If we measure a day from noon to noon - from when the sun crosses the meridian (directly overhead) to when the sun crosses the meridian again - we will find the average solar day is about 24 hours. If we measure the day according to a particular star - from when that star crosses the meridian to when that star crosses the meridian again - we will find the average sidereal day is 23 hours and 56 minutes.

The reason for this is illustrated below. On the first day, point A points directly toward the sun at exactly twelve noon. After a full rotation of the Earth, point A is pointing in the same direction in space, but since the Earth has also proceeded along its orbit, point A is no longer facing the sun. It takes another 4 minutes of rotation for point A to again face the sun. (The effect is exaggerated in the picture.)

To Find the Sidereal Time

The right ascension of a star is equal to the sidereal time when that star crosses the meridian (is directly overhead). Using a star globe, you could find the sidereal time by finding the star pattern for a particular date and time and then reading off the right ascension of stars passing the meridian. By observation, you could find the sidereal time by locating a prominent star that is passing directly overhead (crossing the meridian) and then looking up its right ascension on your star finder or in a star atlas.

For example, the star Capella in the constellation Auriga has the coordinates RA 5h 13m DEC 46deg. When Capella is directly overhead, the sidereal time is 5:13.

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