Mean solar time

If the length of the apparent solar day (the time between two successive passages of the Sun across the observer's meridian) is measured by an accurate sidereal clock it is found to vary throughout the year. There are two main reasons for this:

(i) The Sun's apparent orbit about the Earth is an ellipse in which equal angles are not swept out by the radius vector joining Sun to Earth in equal times.

(ii) The path of the Sun is in the ecliptic which is inclined at an angle of approximately to the equator (along which the Sun's hour angle is measured).

Astronomers overcame these irregularities to obtain mean solar time by the following devices.

(i) A fictitious body called the dynamical mean sun is introduced which starts off from perigee with the Sun, moves with the mean angular velocity (mean motion) of the Sun and returns to perigee at the same time as the Sun. It also moves in the plane of the ecliptic.

(ii) When this dynamical mean sun, moving in the ecliptic, reaches the vernal equinox IP, a second fictitious body called the mean sun starts off along the equator with the Sun's mean motion, returning to ^ with the dynamical mean sun.

Since the mean sun increases its right ascension at a constant rate of about 1°/day and increases its hour angle by 24h in one sidereal day, the time between successive passages of the mean sun over the observer's meridian is constant. This interval is called a mean solar day.

The relationship between sidereal time and mean solar time is given below.

1 mean solar day = 24h 03m 56-5554s of sidereal time. 1 sidereal day = 23h 56m 04-0905s of mean solar time.

Some astronomical almanacs give tables for the conversion of mean solar time to or from sidereal time. The Astronomical Almanac published in Great Britain and the United States demonstrates how Universal Time (Greenwich Mean Time) may be converted to sidereal time and vice versa.

In order to relate the positions of the mean sun and the real Sun, a quantity called the equation of time is defined as the difference between the hour angle of the Sun (O) and the hour angle of the mean sun (ms), or

The equation of time E is related to the time of ephemeris transit T, tabulated for every day of the year in the Astronomical Almanac, by the equation

Greenwich Mean Time (gmt) or Universal Time (ut) is based on mean solar time such that

Equation (2.23) implies that a civil day begins when it is mean midnight. gmt (ut) is a convenient time system used in most observatories throughout the world. In civil life, unless the longitude concerned is near the Greenwich meridian, local time systems are used, the surface of the Earth having been divided into standard time zones for this purpose.

This convention gives a clock time related approximately to the Sun's position in the sky and also avoids the necessity of a moving observer continually adjusting his watch.

Within each zone the same civil mean time called Zone Time (zt) or Standard Time is used and the zones are defined by meridians of longitude, each zone being 15° (1h) wide. The Greenwich Zone (Zone 0) has bounding meridians 0h 30m W and 0h 30m E, and keeps the time of the Greenwich meridian, namely gmt (ut). Zone + 1 has boundaries 1h 30m W and 0h 30m W, keeping the time of meridian 1h W. Zone -1 has boundaries 1h 30m E and 0h 30m E, keeping the time of meridian 1h E. The division of the Earth's surface in this way is continued east and west up to Zones +12 and -12. According to the previous definition both these zones would keep the time of 12h W which is also 12h E. The convention is made that the zone from 11h 30m W to 12h W is Zone +12, while the zone from 11h 30m E to 12h E is Zone -12. The meridian separating them is called the International Dateline where a given day first begins.

It should be added that the actual dateline, for geographical reasons, does not follow faithfully the 12h meridian but makes local detours to include in one hemisphere parts of countries that would be placed in the other if the Line did not deviate this way. It should also be added that ships crossing the dateline from east to west omit one day, while others crossing from west to east add one day.

In large countries, such as the USA and China, more than one zone is involved. In the United States four time zones are used; the mean times are called Eastern, Central, Mountain and Pacific Times, based on the meridians 5h, 6h, 7h and 8h west of Greenwich.

The relation between Zone Time and gmt is where the longitude of the meridian involved is added when west and subtracted when east (in agreement with the previous rule—see equation (2.20)).

The year used in civil life is based on the tropical year, defined as the interval in time between successive passages of the Sun through the vernal equinox. This is 365 2422 mean solar days. For convenience the calendar year contains an integral number of days, either 365 or 366. Every fourth year (called a leap year) has 366 days, excepting those century years (such as 1900 ad) whose number of hundreds (in this case 19) are indivisible by four exactly. These rules give a mean civil year equal in length to 365-2425 mean solar days, a figure very close to the number of mean solar days in a tropical year.

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