This age-old question has been answered by various calendar systems since the beginning of history. Ancient civilizations made logical use of the length of the day, lunar month, and solar year in these systems. But, the desire to know when a particular date falls over the years is foiled by the fact that the length of a day, or lunar month, is not an integer number of units to the length of a solar year. Solar year is the time it takes the Earth to return to the same spot on its orbit -- about 365.2422 mean solar days.
The problem was compounded in ancient times by the fact that it would take many generations of observation to determine the length of the year with great precision. Also, computational techniques, such as decimal notation, were not available. Eventually, some societies did learn the length of the solar year to good precision and had to decide what to do with the fractional day at the end of the year. The simple solution would be to have the 366th day, after the start of the year, as a shared day between two years, but I know of no system that adapted this method. It seems that day sharing was universally considered inconvenient. This is fortunate since, in our modern computer age, it avoids having a Y2K-type catastrophe at the end of each year.
What if the fractional day at the end of the year was ignored and a year of 365 days was instituted? After the first 365-day year it would take ¼ of the first day, of the next year, for the Earth to reach its yearly starting position. After four years of this it would take the whole first day, of the fifth year, to reach this point. In 40 years it would take the first ten days, of the 41st year, to reach the start point. To observers on the ground this meant that the seasons of the year were starting 10 days later every 40 years. In 120 years the accumulated error would be 30 days -- about a lunar month. The four seasons found in the Temperate Zone would completely shift over, into alien months, in 360 years. In this system, the proper time to plant crops or celebrate holidays would require re-computation every few years. This would not be a big problem today, but in the ancient world only a few persons in the entire kingdom would have the knowledge, or time, to carry out the computation. Even with these faults, the Egyptians used this system. They employed 12-months of 30-days and 5 extra days after the last month to create their 365-day calendar.
The Romans, under Julius Caesar, thought they had the season-drifting problem solved by inserting an extra day in their 365-day calendar, every four years. But the system was not perfect because the 0.2422 fractional day, at the end of the year, is about 11.25 minutes short of the 0.25 day the Romans had calculated. So, the leap year corrections were putting the calendar eleven minutes ahead every four years. This was still a big improvement over the Egyptian system because the date of various holidays and seasonal events would remain fixed over many generations. It would take 128 years of accumulated 11.25 minute error for the calendar seasons to be permanently a day ahead of the actual seasons. In 400 years the error would be 3.12 days. Yet, when a system is in use by many people it becomes unpopular to change it. So after 16-centuries of use, the Julian calendar had moved the calendar seasons 12-days ahead of their observed arrival.
The modern Gregorian calendar was introduced by Pope Gregory XIII, in 1582 AD, to replace the Julian calendar. This system is largely the Julian calendar with two changes. Firstly the leap year rule was changed so that centurial years (for instance: 1600, 1700, and 1800) must be evenly divisible by 400 to be leap years. In a 400-year period 3 leap days would be lost compared to the Julian calendar. Recall that the Julian calendar would gain 3.12 days in this time period. This difference limits the gain in 400 years to 0.12 days for the Gregorian calendar: it will take 3300 years to gain a permanent day. (This is such an achievement that I wonder why there were no world-wide festivities to mark the 400th anniversary of the calendar in 1982?)
Secondly, ten days were dropped so that the seasons would occur as they did in 325 AD. This was probably done because the First Council of Nicaea had set the rules for determining the date of Easter in that year. Where the Pope had sway, the day after October 4th 1582 (Julian) was October 15th 1582 (Gregorian). Other countries held on to the Julian calendar much longer and had to drop a few more days when they switched. England and the American colonies converted in 1752, Japan adopted this Western calendar in 1873, Russia had to wait until the government changed in 1918, and Turkey held out until the 1926-28 period when reformers took power. A recently published book: Mapping Time: The Calendar and its History by E. G. Richards gives a global survey of calendars from the prehistoric to modern. While not must reading for the average amateur, if you see it in a library or bookstore, peruse chapter 19 for a fascinating look at the multi-century struggle to reform the Julian calendar into the Gregorian calendar.
Civil calendars are unsatisfactory for carrying out date calculations (calendrics) and comparing astronomical data gathered under different calendars. The Julian day count is a common astronomical calendar that facilitates comparison and manipulation of dates. It is a continuous count of dates since January 1, 4713 BC; this start date was chosen to encompass all dates within recorded history.
Date Formulas Usage Example
The typical amateur astronomer may not have a great need to translate between Julian and Gregorian dates. On the other hand, it is very useful for dating old documents such as used in genealogy research. Here is an example of converting a Julian birthday to Gregorian, by way of Julian day count:
This is George Washington's birthday. But for an historian or genealogist there is a peculiar twist to this result. In the period that Washington lived, the English New Year was on the Feast of the Annunciation on March 25. So, for the first twenty years of his life Washington's date of birthday was 1731. Calendar reform that adopted the Gregorian calendar in 1752 shifted the start of the year to January and his birthday to 1732.
Since the formulas presented here can't take into account all machinations to the Julian/Gregorian calendar switch prior to the modern age, research is advised before taking a calculated result as historical fact.
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