The Europeans (barring Greeks) had a somewhat crude calendar before the Romans came into contact with the egyptians after the conquest of Egypt by Julius Caesar in 44 B.c. Julius Caesar, on the advice of the Egyptian astronomer Sosigenues introduced the leap year system by making the lenght of a normal year, as 365 days and adding an additional day, every fourth year. At the same time, the lengths of the months were fixed at their present duration. The whole system came to be known as the Julian calendar or the Roman calendar. It is divided into 12 months. We already know the names of the months and the number of days in each month. The month names July and August are in honour of Julias Caesar and his successor Augustus. Julius Caesar wanted to start the New Year on the winter solstice day, but people preferred to commence it on January 1st, 45 B.C. as a new moon was due on that day. That is why January 1st is the New year day in this calendar which is also the Christian calendar, on which the Christian festivals are based.
The Julian year of 365.25 days was longer than the tropical year (you should have read about it in Equinoxes) of 365.2422 days by 0.0078 days, so that the winter solstice which fell on December 21st in 323 A.D. fell back by 10 days 1582 A.D., that is, it occured on December 11th in that year. So, the year was losing connection with the seasons. In 1582 A.D. A Pope Gregory introduced a new reformed calendar in which century years which were not divisible by 400 were not to be counted as leap years (that is, years 1700, 1800,1900 are not leap years even though they are all divisible by 4; year 2000 A.D. is a leap year). In consequence, the number of elap years in 400 years was reduced form 100 to 97.
Therefore, the number of days in 400 years = 365*400+97.
Average tropical year = (365*400+97)/400) = 365.2425 days
which is very close to the actual value of the tropical year which is 365.2422 days. The error would amount to one day in 3300 years. To nullify the shifting back of the winter solstice, the day succeeding October 4th, 1582, Thursday was considered as October 15th, 1582, Friday, that is, 10 days were cut off from that year. This reformed version of the Roman calendar has come to be known as the Gregorian Calendar.
Some countries of Europe like Great Britain did not adopt the Gregorian reformation of the calendar immediately. In Great Britain it was officially introduced in 1752 A.D. As the error by that time amounted to 11 days, September of 1752 was deprived of these 11 days and September 3rd, 1752 was designated as the September 14 th, 1752.
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We have already discussed the concept of Ahargana, which expresses any instant of observation as so many days and fraction of a day from a choosen epoch. In modern astronomy, the epoch chosen is 12 noon GMT, on January 1st, of the year 4713 B.C. The Julian date of any day is the number of days which have elapsed since the epoch.
EXAMPLE:
Find the Julian date corresponding to January 3rd, 1991, 6 p.m. GMT.
First let us find the Julian date corresponding to January 1st, 1991, 12 noon GMT.
Number of years elapsed from the epoch of January 1st, 4713 B.C. to January 1st, 1 B.C. = 4712.
Number of years elapsed from January 1st, 1B.C. to January 1st 1991 = 1991.
(Remember that the year 1 B.C is followed by the year 1 A.D.)
Total number of years elapsed from the epoch to January 1st, 1991 = 4712+1991 = 6703.
Now 1 B.C. (which is actually 0 A.D.) and 4713 B.C. (which is 4712 A.D.) are leap years. Also, before the year 1991, the last leap year was 1988.
Number of leap years (if the Julian calendar had been followed throughout) = (4712/4)+1+(1988/4) = 1676.
But the Gregorian system was used from 1582 A.D. onwards. Hence, the years 1700, 1800 and 1900 were not leap years. Also 10 days were dropped in 1582 due to the reformation brought about by Gregory.
Hence the Julian date of January 1sr, 1991, 12 noon GMT
=6703 * 365 + 1676 - 3 - 10
=2448258 days.
The Julian date of January 3rd, 1991, 6 p.m.
=2448258 + 2 + .25
=2448260.25 days.