Gregorian calendar

Our rhythm of life is governed by three natural measures of time which are combined for the calculation of time in calendars:

1) the year (a), the time taken by the earth to travel once round the sun

2) the month (m), the time taken by the moon to travel once round the earth

3) the mean solar day (d), the time taken by the earth to rotate once about itself.

It would be an easy task to establish a calendar if the ratios m/d and a/d were integers. However, they are not, since the tropical year comprises 365.2422 d and the synodical month 29.5306 d, all values being long-term averages. Here the tropical year is the time interval between two successive passages of the sun through the vernal equinox, the beginning of spring on the northern hemisphere. The synodical month (Synode: gathering, conference) is the time interval between two successive new moon events (New moon: moon and sun are located together as viewed from the earth).

Our Gregorian Calendar originated from the ancient Roman Calendar. In 45 B.C., Julius Caesar introduced a new Roman calendar, which included the rule that three years encompassing 365 days were to be followed by a so-called leap year with 366 days. 100 tropical years are thus made up of 36525 days.

The Church was very much interested in Easter being celebrated at a uniform date all over the world and in the date remaining linked to the Jewish Passover holiday. In 325 A.D., the Council of Nicaea recommended that Easter should be celebrated on the first Sunday after the first full moon in spring as had become the tradition of the West-Roman Church. Easter thus became a movable feast between the dates of March 22 and April 25 .

Since the 6^th century so-called eternal calendars had been known which help to determine the date of Easter, with the use a system based on the "Golden Number" and the "Sunday Character". This system makes use of the so-called Metonic cycle (Meton from Athens, about 450 B.C.) which reflects the fact that 19 years encompass on average 235 lunar cycles.

Neither the Metonic cycle nor the Roman leap year rule are exactly correct. As a consequence of the Roman leap-year rule, in the 16^th century the beginning of spring had been shifted by more than ten days towards the beginning of March. A calendar reform was initiated to eliminate and avert this inconvenience. The new calendar was developed by Aloysius Lilius (about 1510 - 1576) and Christophorus Clavius (1537/38 - 1612). It was established by a papal bull of Pope Gregor XIII that Thursday, October 4^th, 1582, should be followed by Friday, October 15^th, 1582. This shifted the date of the vernal equinox to its proper date. Also Caesar's leap-year rule was amended. If the year-date is an integer multiple of 100, the year will not be a leap year, with the exception of those years whose date is a multiple of 400. Following this rule, a century in the Gregorian Calendar encompasses 36524.25 days, which is rather close to its true value.

A refinement of the determination of the Easter date was also included in the papal bull. In the 16^th century, the calculated calendar date of a full moon deviated by three days from its real occurrence. This was corrected by changing the Moon calendar. The texts of Lilius and Clavius contain rather complex prescriptions for a refined calculation of the Easter date.