Sidereal Time, Civil Time and Solar Time

Sidereal time is a method astronomers use to locate objects. Using sidereal time its possible to point a telescope to an object in the sky.

Civil time is based on the position of the Sun in the sky. The 24 hours on a clock represent an apparent solar day. The apparent solar day is the time between successive transits of the Sun across an observer's meridian.

Apparent solar time, as measured by clocks, is not a very accurate system for measuring actual solar time. This is because the Earth's orbit is elliptical and the Earth's rotation axis is inclined by 23.5° from the orbital plane. Using this system would require clocks to run faster on some days and slower on others. To get around this, civil time uses an average solar time, which means that a solar day is an average of 24 hours and this is constant throughout the year. The difference between average solar time and apparent solar time is called the equation of time and varies by up to 16.25 minutes throughout the year. This average time gives rise to the Greenwich Mean Time.

Sidereal Time for Astronomers

During a year, the Sun appears to move around the sky along the ecliptic, and if we look at the night sky each month at midnight we will see that the constellations also appear to move around the sky (albeit much slower). Consequently, the time as measured by the distant stars and the solar time measured by the Sun cannot be equal.

Astronomers' time is best measured concerning the background stars and is referred to as sidereal time.

The normal definition of a sidereal day is "the time between successive transits of the First Point of Aries whereas the mean solar day is defined as the average time between transits of the sun.

The Earth has a normal rotation rate of 365 times per year, so we expect the sun to transit 365 times in the year, compared with 366 transits of our chosen star. The extra transit occurs after the final transit of the Sun. This accounts for the difference between solar time and sidereal time.

By dividing the "extra" day into 365 parts, we can calculate that a sidereal day is about 4 minutes shorter than a solar day. Consequently, stars appear to rise 4 minutes earlier each evening.

The zero point used for sidereal time is the transit of the First Point of Aries at Greenwich, England, also known as Greenwich Sidereal Time (GST). It is 0 hours at solar noon at the time of the March equinox (approximately March 21). It is also 0h at midnight at the time of the September equinox (approximately September 21) in Greenwich.

Greenwich Sidereal Time is the local sidereal time for observers at Greenwich. Observers at other longitudes will also have their own local sidereal time (LST). This is calculated from GST using the following formula.

Equation 14 - Local Sidereal Time

Where λ is the observer's longitude expressed in hours:minutes.

Worked Example

Assume Greenwich Sidereal time is 12:30. What is the local sidereal time at an observatory located at +20° (or 20° E)?

Longitude needs to be converted into hours and minutes. Since 24h = 360°, 20° corresponds to:

Equation 15 - Calculate Local Sidereal Time

1.33 hours is the decimal form of 1h 20 minutes.

Equation 16 - Local Sidereal Time Calculation

Hour Angle, Sidereal Time and Right Ascension

The hour angle (HA) of a celestial body is defined as the angle measured westwards in units of time along the celestial equator from the observer's meridian to the hour circle passing through the celestial body. It, therefore, represents the sidereal time that has elapsed since that object was on the meridian.

It follows directly from this definition that the LST is the hour angle of the First Point of Aries.

The following equations illustrate the relationships between Local Sidereal Time, Right Ascension and Hour Angle.

Equation 17 - Relationship between LST, HA and RA