Our calendar is a result of long evolution. The main problem it must contend with is the incommensurability of the basic units, day, month and year: the numbers of days and months in a year are not integers. This makes it rather complicated to develop a calendar that takes correctly into account the alternation of seasons, day and night, and perhaps also the lunar phases.

Our calendar has its origin in the Roman calendar, which, in its earliest form, was based on the phases of the Moon. From around 700 B.C. on, the length of the year has followed the apparent motion of the Sun; thus originated the division of the year into twelve months. One month, however, still had a length roughly equal to the lunar cycle. Hence one year was only 354 days long. To keep the year synchronised with the seasons, a leap month had to be added to every other year.

Eventually the Roman calendar got mixed up. The mess was cleared by Julius Caesar in about 46 B.C., when the Julian calendar was developed upon his orders. The year had 365 days and a leap day was added to every fourth year.

In the Julian calendar, the average length of one year is 365 d 6 h, but the tropical year is 11 min 14 s shorter. After 128 years, the Julian year begins almost one day too late. The difference was already 10 days in 1582, when a calendar reform was carried out by Pope Gregory XIII. In the Gregorian calendar, every fourth year is a leap year, the years divisible by 100 being exceptions. Of these, only the years divisible by 400 are leap years. Thus 1900 was not a leap year, but 2000 was. The Gregorian calendar was adopted slowly, at different times in different countries. The transition period did not end before the 20th century.

Even the Gregorian calendar is not perfect. The differences from the tropical year will accumulate to one day in about 3300 years.

Since years and months of variable length make it difficult to compute time differences, especially astronomers have employed various methods to give each day a running number. The most widely used numbers are the Julian dates. In spite of their name, they are not related to the Julian calendar. The only connection is the length of a Julian century of 36,525 days, a quantity appearing in many formulas involving Julian dates. The Julian day number 0 dawned about 4700 B.C. The day number changes always at 12: 00 UT. For example, the Julian day 2,451,545 began at noon in January 1, 2000. The Julian date can be computed using the formulas given in *Julian Date (p. 41).

Julian dates are uncomfortably big numbers, and therefore modified Julian dates are often used. The zero point can be e.g. January 1, 2000. Sometimes 0.5 is subtracted from the date to make it to coincide with the date corresponding to the UTC. When using such dates, the zero point should always be mentioned.

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