Relating coordinate systems to each other can be done through time systems. Astronomical time systems are constructed on the principle of tracking a reference point on the celestial sphere relative to an observer's celestial meridian. Thus time is measured basically by Earth's rotation. A convenient reference position from which to mark the passage of time is an observer's celestial meridian. Since both the vernal equinox and the Sun are carried westward by the rotation of the sky, each can serve as an "hour hand" on the celestial clock.
Sidereal Time
One sidereal day is equal to the interval between two successive crossings of an observer's celestial meridian by the vernal equinox. This corresponds to one complete rotation of Earth on its axis. The local sidereal time (LST) is given by the local hour angle of the vernal equinox (LHAVE), which is equal to the sum of any object's right ascension and hour angle. Local sidereal time progresses uniformly at the rate of 15o to the hour and can be read from a sidereal clock whose rate is that of Earth's rotation. The clock is set to read 0h0m0s at the instant the vernal equinox crosses the celestial meridian, 1h0m0s when the vernal equinox has moved 15o west of the meridian, corresponding to a local hour angle of 1h, and so on around the sky through 24h, when a new sidereal day begins.
Solar Time
Apparent solar time is given by the local hour angle of the Sun, (LHAS) + 12h, to start the solar day at midnight. One apparent solar day is equal to the interval between two consecutive passages over an observer's meridian by the Sun. Time measured by the apparent or real Sun is slightly variable for two reasons: First, the Sun's annual motion along the ecliptic varies a little because of Earth's orbital eccentricity (as we will see in a study of Kepler's law of areas). Second, the projection of the real Sun's motion along the ecliptic onto the celestial equator, where hour angle is measured, varies slightly over the course of a year. A more suitable clock time is one that does not change in an irregular manner from day to day.
This is accomplished by introducing an imaginary sun called the mean sun. It moves uniformly eastward along the celestial equator at a daily rate that is equal to the average daily rate of the real Sun along the ecliptic, so that both arrive at the vernal equinox simultaneously 1 year later, which is where they started out together. Mean solar time is equal to the local hour angle of the mean sun, (LHAS) + 12h, again starting the mean solar day at midnight. Since mean solar time progresses uniformly, mechanical and electronic clocks can be made to keep this kind of time, which is what we use in everyday life. The greatest difference between apparent and mean solar time, which varies during the year, is +15m.
A tropical year, a year of seasons, is equal to 365.2422 mean solar days. It represents the time it takes the Sun to complete one revolution around the ecliptic with respect to the vernal equinox. The sidereal year, on the other hand, is the period of the Sun's revolution with respect to the stars, and it is equivalent to the period of Earth's orbital revolution. Because of Earth's annual motion around the Sun, a mean solar day is longer than a sidereal day by 3m56s of solar time.
Standard Time
Obviously from the way mean solar time is kept, it is different at places separated by differences in longitude. To get around this inconvenience, the standard time system was introduced in 1884. There are 24 time zones, each theoretically 15o wide, with the zero time zone centered on Greenwich, England, the 0o meridian of longitude, and proceeding east or west of Greenwich. Through the approximate center of each zone runs the standard meridian, whose local mean solar time is the standard time within the zone. In the United States and Canada, the standard meridians are as follows:
Standard Times for the United States and Canada Standard Meridian Time Zone 60o Atlantic standard time (AST) 75o Eastern standard time (EST) 90o Central standard time (CST) 105o Mountain standard time (MST) 120o Pacific standard time (PST) 135o Yukon standard time (YST) 150o Alaska-Hawaii standard time (AHST) These standard time zones are respectively 4h, 5h, 6h, 7h, 8h, 9h, and 10h behind Greenwich mean time (GMT), also known as universal time (UT). Time changes by 1h as the traveler crosses a zone boundary. The zones frequently have irregular boundaries to suit local conditions. Also there are countries that actually span several standard time zones, in which the entire country keeps the same zone time.
The successive time zones run either west or east of Greenwich until they meet halfway around the world at 180o longitude at the international date line, which passes through the center of the 12h zone. The half portion of the zone west of the line is 1d ahead of the other half east of the line even though the standard time is the same in each half. A traveler crossing the date line from Tokyo to San Francisco, for example, gains a day, whereas one traveling in the opposite direction loses a day.
Calendars
The common calendar of ancient peoples was based on the lunar cycle of 29.5d, because changes in the Moon's phase are so readily apparent. Since 12 lunar months cannot be contained in a tropical year a whole number of times, an extra month was added from time to time to bring the seasons back on schedule. Attempts to synchronize the lunar month with the year never proved satisfactory. The Egyptians were the first to base their calendar on a tropical year of 365.25d. Their year consisted of 12 months of 30d each, with 5d extra set aside at the end of the year for celebrations. However, by the time the Julian calendar was adopted on January 1, 45 B.C., it had to be made 445d long in order to bring the seasons back on schedule. The Julian calendar consisted of 365d with every fourth year being 366d.
The true length of the tropical year is 365d5h48m46s, or about 11m14s shorter than 365.25d. Hence, the longer year used in the Julian calendar results in a discrepancy of 3d in 400 y. By 1582 A.D., the accumulated difference amounted to 10d, so the date of the vernal equinox had retreated from March 21, at the time of the Council of Nicaea convened in 325 A.D., to March 11. Accordingly, Pope Gregory XIII called upon the astronomer Clavius to revise the Julian calendar. His solution was to drop 10d from the calendar, so that the day following Thursday, October 4, 1582, thereby became Friday, October 15, 1582. And to avoid future calendar discrepancies, only century years divisible by 400 were leap years, such as 1600 and 2000. This new calendar became known as the Gregorian calendar, and it was readily adopted by Catholic countries. The Lutherans and Protestants finally made the adoption in 1700. When Great Britain and the American colonies changed to the Gregorian calendar in 1752, September 2 had to be followed by September 14, the discrepancy having grown to 12d. Early in this century other countries in Europe and Asia finally adopted the Gregorian calendar or one very close to it. The present Gregorian calendar is accurate to about 1d in 3300 y. However, its accuracy is improved beyond that by interspersing an extra second between days every few years to compensate for a number of irregularities in the celestial clock.