Easter calculation
Today is Orthodox Easter. This year, there was a difference of five weeks with the Catholic one. Have you ever wondered why this difference varies from year to year, and sometimes even the two Easter cards coincide? In a nutshell, the answer is:
Easter in all Christian churches is celebrated on the first Sunday after the first full moon after the equinoxes.
And the most interesting, the church considers the days of equinox and full moon according to canonized tables, and not according to real astronomical observations. The Catholic Church tables are fairly accurate and still give the correct results, because in 1582 they switched from the Julian calendar to the more accurate Gregorian. The Orthodox Church has not switched to the Gregorian and still lives on the Julian calendar, which is shifted by 13 days and will continue to shift by 3 days over 400 years. Moreover, the church, in order to determine whether there is a full moon in the sky, does not look at the sky, but looks at canonized tables. They still work normally in the Catholic Church, while in the Orthodox they make a mistake for about 310 years and have already accumulated a fairly large error. That's the whole reason why Easter falls on different days. For a deeper understanding, let's look at all these calendars.
First we give two important astronomical magnitudes:
one tropical year = 365.242189 days (change of seasons)
one lunar month = 29,5305882 days (average distance in days between full moons)
Introduced in 45 BC by Julius Caesar.
one year = 365.25 days = (365 + 1/4) days. Every 4 years there is a leap year in which 366 days, and the remaining days have 365 days. It turns out that the average number of days in a year is 365.25. It is clear that this calendar is not very accurate, because in reality the duration of the year is slightly less. This inaccuracy and gives an error for one day in about 128 years. When Julius Caesar introduced the calendar, he introduced it so that the day of the winter solstice fell on the first of January. But after his death, due to somerash negligence towards accurate calendar maintenance and due to a natural error accumulating by the fourth century, the day of the winter solstice shifted to December 22, and the day of the vernal equinox to March 21. Due to the general confusion in the calendars and in the days of compiling Easter in the year 325, the collection of Christians from different parts of the Earth (the Council of Nicaea) finally fixed the calendar so that March 21 would be the day of the vernal equinox.
Introduced in 1582
As I have already said, the Julian calendar is inaccurate (it accumulates one day of error in 128 years), therefore, closer to the 16th century, it from the Nicene Council has already accumulated an error of approximately 10 days. And it was noticeable: some temples were built so that it was on the day of the vernal equinox that the sun fell into a special place, and by the 16th century it would no longer fall into its proper place. Interestingly, the motivation for changing the calendar was not so much the attachment of agriculture to the calendar, as the desire of the church to accurately calculate the day of Easter. So the new Gregorian calendar:
one year = 365.2425 days = (1 + 1 / 4-3 / 400) days.
This is achieved by throwing out three days every 400 years: an additional rule is introduced for leap years. From now on, those years that are divided into 100, but not divided into 400 are not considered leap years. For example, 1500, 1700, 1800, 1900 are now non-leap years, and 1600, 2000, 2400 are leap years.
What I would like to emphasize:
It is assumed that in 19 years the moon passes exactly 235 full moon (discovered by the ancient Greeks). Despite the fact that the method is quite accurate, it gives an error in one lunar day in about 307 years. And by our time the calendar has accumulated an error for 5-6 days, but anyway, the Orthodox Church uses this one to determine the day of Easter.
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Since the main motivation for the transition to the new calendar was precisely the accuracy of determining the date of Easter, in addition to the solar calendar, it was also necessary to correct the lunar calendar. The Catholics adopted the same Julian lunar calendar as the basis of the new lunar calendar in 1582, but corrected it a little: now, over 2500 years, more or less evenly over the years 8 lunar days are removed. The first deletion was in 1800, the next will be in 2100 (later: 2400, 2700, 3000, 3300, 3600, 4000 - the new 2500-year cycle starts from here and deletions are repeated in 4300, in 4600, ...) But to this time this calendar will already be greatly mistaken. It should be noted that the Gregorian lunar calendar was more accurate and, according to my calculations, gives an average error in one day for about 1000 years. Still interesting, at that time, astronomers did not have very accurate data on the movement of the moon. Now, if they for the 2500 year cycle would have offered 11 deletions, and not 8, then the accuracy of the calendar would increase about 6 times. A calendar would be wrong for one lunar day in about 6,000 years.
Easter in all Christian churches is celebrated on the first Sunday after the first full moon after the equinoxes.
And the most interesting, the church considers the days of equinox and full moon according to canonized tables, and not according to real astronomical observations. The Catholic Church tables are fairly accurate and still give the correct results, because in 1582 they switched from the Julian calendar to the more accurate Gregorian. The Orthodox Church has not switched to the Gregorian and still lives on the Julian calendar, which is shifted by 13 days and will continue to shift by 3 days over 400 years. Moreover, the church, in order to determine whether there is a full moon in the sky, does not look at the sky, but looks at canonized tables. They still work normally in the Catholic Church, while in the Orthodox they make a mistake for about 310 years and have already accumulated a fairly large error. That's the whole reason why Easter falls on different days. For a deeper understanding, let's look at all these calendars.
First we give two important astronomical magnitudes:
one tropical year = 365.242189 days (change of seasons)
one lunar month = 29,5305882 days (average distance in days between full moons)
Julian calendar
Introduced in 45 BC by Julius Caesar.
one year = 365.25 days = (365 + 1/4) days. Every 4 years there is a leap year in which 366 days, and the remaining days have 365 days. It turns out that the average number of days in a year is 365.25. It is clear that this calendar is not very accurate, because in reality the duration of the year is slightly less. This inaccuracy and gives an error for one day in about 128 years. When Julius Caesar introduced the calendar, he introduced it so that the day of the winter solstice fell on the first of January. But after his death, due to some
Gregorian calendar
Introduced in 1582
As I have already said, the Julian calendar is inaccurate (it accumulates one day of error in 128 years), therefore, closer to the 16th century, it from the Nicene Council has already accumulated an error of approximately 10 days. And it was noticeable: some temples were built so that it was on the day of the vernal equinox that the sun fell into a special place, and by the 16th century it would no longer fall into its proper place. Interestingly, the motivation for changing the calendar was not so much the attachment of agriculture to the calendar, as the desire of the church to accurately calculate the day of Easter. So the new Gregorian calendar:
one year = 365.2425 days = (1 + 1 / 4-3 / 400) days.
This is achieved by throwing out three days every 400 years: an additional rule is introduced for leap years. From now on, those years that are divided into 100, but not divided into 400 are not considered leap years. For example, 1500, 1700, 1800, 1900 are now non-leap years, and 1600, 2000, 2400 are leap years.
What I would like to emphasize:
- The accuracy of the calendar immediately increases: now the calendar is mistaken for one day in about 3200 years.
- A lot of people do not even suspect that we all use this calendar in our daily life. (2100 will not be a leap year, and you probably thought it would be).
- Russia switched to a new calendar only with the advent of communism in 1918 (jumped 13 days ahead).
- Interestingly, the distance between the spring equinoxes is slightly different from the tropical year (the change of seasons). This is due to the precession of the earth's axis. Well, it turns out, the Gregorian calendar is much more accurately approximates precisely this value. And the error in the date of determining the spring equinox for 1 day does not accumulate over 3200 years, as in the case of the tropical year, but about 10 thousand years. But it should be noted that this error will greatly increase in 10 thousand years, when the axis of the earth due to the precession of the axis will unfold so much that the distance between the days of the vernal equinox will not be so accurately described by the Gregorian calendar.
Julian lunar calendar
It is assumed that in 19 years the moon passes exactly 235 full moon (discovered by the ancient Greeks). Despite the fact that the method is quite accurate, it gives an error in one lunar day in about 307 years. And by our time the calendar has accumulated an error for 5-6 days, but anyway, the Orthodox Church uses this one to determine the day of Easter.
')
Gregorian lunar calendar
Since the main motivation for the transition to the new calendar was precisely the accuracy of determining the date of Easter, in addition to the solar calendar, it was also necessary to correct the lunar calendar. The Catholics adopted the same Julian lunar calendar as the basis of the new lunar calendar in 1582, but corrected it a little: now, over 2500 years, more or less evenly over the years 8 lunar days are removed. The first deletion was in 1800, the next will be in 2100 (later: 2400, 2700, 3000, 3300, 3600, 4000 - the new 2500-year cycle starts from here and deletions are repeated in 4300, in 4600, ...) But to this time this calendar will already be greatly mistaken. It should be noted that the Gregorian lunar calendar was more accurate and, according to my calculations, gives an average error in one day for about 1000 years. Still interesting, at that time, astronomers did not have very accurate data on the movement of the moon. Now, if they for the 2500 year cycle would have offered 11 deletions, and not 8, then the accuracy of the calendar would increase about 6 times. A calendar would be wrong for one lunar day in about 6,000 years.
Source: https://habr.com/ru/post/393445/
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