MAKING GREGORIAN CALENDAR “TROPICAL YEAR COMPLIANT”

                      

When Gregorian calendar was introduced in 1582 we may have thought it would not be necessary to reformat it. Do you know even the Gregorian calendar is not synchronized with the tropical year? The present Gregorian year consists of 365.2425 days while it has been found that the tropical year was of 365.24219 days in 1900.

Not only it was 365.24219 days long in 1900, in 2013 it was asserted that it may keep on changing as mentioned in the following piece of information picked up from the site https://en.wikipedia.org/wiki/Tropical_year.

“According to Blackburn and Holford-Strevens (who used Newcomb’s value for the tropical year), if the tropical year remained at its 1900 value of 365.24219878125 days, the Gregorian calendar would be 3 days, 17 min, 33 seconds behind the Sun after 10,000 years. Aggravating this error, the length of the tropical year (measured in Terrestrial Time) is decreasing at a rate of approximately 0.53 second per century. Also, the mean solar day is getting longer at a rate of about 1.5 milliseconds per century. These effects will cause the calendar to be nearly a day behind in 3200. The number of solar days in a ‘tropical millennium’ is decreasing by about 0.06 per millennium (neglecting the oscillatory changes in the real length of the tropical year).”

So obviously we would have to keep on modifying the Gregorian calendar to take care of such changes.

The site mentions that we may have to reform the Gregorian calendar by omitting the leap day in 3200, keeping 3600 and 4000 as leap years, and thereafter making all centennial years common except 4500, 5000, 5500, 6000, 6500 and so on to make it tropical year compliant.

The problem stems from the fact that even though Sun takes 365 days, 5 hours, 48 minutes, 45 seconds to complete its journey from the day it crosses the celestial equator from north to south to the day when it crosses the equator again, it would make the calendar very unwieldy if we made the calendar year 365 days, 5 hours, 48 minutes, 45 seconds long. So the calendar year has to have a round number of days – 365 or 366 days, only much the same way as a day can’t be of 23 hours 56 minutes and 4.1 seconds since earth revolves around its axis in only. So we have opted to have a day of 24 hours only instead of 23 hours 56 minutes and 4.1 seconds.

But we have to ensure that our calendar may be tropical year compliant only despite having such constraints. We have to ensure that spring equinoxes occurred on same dates year after year despite such constraints. However, Julius Caesar took up the task of making the calendar tropical year compliant.

He noticed that Roman calendar was a mess because every alternate year used to be of thirteen months instead of twelve months. While the twelve-month years used to be of 355 days the thirteen-month years used to be of 377 or 378 days as follows, at that time.

1st year  …   of 355 days

2nd year  …   of 377 days

3rd year  …   of 355 days

4th year  …   of 378 days

5th year  …   of 355 days

6th year  …   of 378 days

7th year  …   of 355 days

8th year  …   of 378 days

So it gave an average calendar year of 366.25 days over a period of eight years.

Julius Caesar tried to overcome this vagary by making each year 365 days long but by making every fourth year a leap year, a year of 366 days instead of 365 days.

So it gave a calendar year of 365.25 days on an average instead of 366.25 days.

Though Julius Caesar cleared the mess by introducing the Julian calendar – so named after his name – in 45 B.C.E to a good extent, it was noticed that over a time it introduced an error of 1 day every 128 years, that is, 0.00781 day a year. So it became difficult to calculate the correct date of Easter because every 128 years the tropical year shifted one day backwards with respect to the calendar.

So it was felt that it should be replaced by something more compliant than it. Gregory Pope XIII re-tuned the average year to have become a 365.2425 day year instead of 365.25 day year in 1582 by making three leap years – the leap years that were multiples of 100 non-leap years but not 400. He made a provision of 97 leap years (instead of 100 leap years) and 303 non-leap years (instead of 300 non-leap years) over 4 centuries.

The calendar introduced by him came to be known as “Gregorian calendar”.

Since it was felt that 21 March was the proper day for vernal equinox (because 21 March was the date for vernal equinox during the Council of Nicaea in C.E. 325), he calibrated the Gregorian calendar to make that day vernal equinox by dropping 10 days, as vernal equinox had moved (1582-325)/128 days – approximately 10 days backwards by 1582.

But by using the latest techniques of calculating the tropical year (solar year) – the average time the earth takes to make one round of the Sun, it was found that even the Gregorian calendar is not “tropical year compliant” since the earth took 365.24219 days to make one round of the Sun during the year 1900 – not 365.2425 days.

Even though on the face of it, Gregorian year is found to be only 0.00031 day (26.784 seconds) longer than 365.24219 days it was realized that even this small difference would add up to massive 3 days 2 hours 24 minutes over 10000 years due to which the tropical year would begin 3 days 2 hours 24 minutes ahead of 1st January after 10000 years.

So it was felt that if we want to continue with the Gregorian Concept we may have to make some changes in it by making some more leap-years non-leap years to align it with the actual length of the tropical year from time to time.

Though apparently just any calendar may be good enough for us to record the past events of our life and plan further activities of our life in advance but if we change the format of the calendar in between, we would have to keep a track of the changes done in the calendars from time to time also. Unless we keep a track of the changes we would not be able to recalculate the old dates on which various events of historic importance that may have occurred in the past if we keep on making changes too frequently.

If we make any change in our calendar it becomes difficult to perceive when the past events may have occurred unless either a date converter is provided along with it or the dates of their occurrence are changed on the pattern of the new calendar the same way as the historians had re-dated the past events by extending the Julian calendar backward naming the extended calendar “Julian Proleptic Calendar”, according to the Julian year.

Do you think

(i) We should keep on changing the format of the calendar so frequently?

(ii) Would such changes not create problems of re-dating all past events?

(iii) Can’t we have a calendar which could be more resilient?

I don’t know what steps may be taken to synchronize the Gregorian calendar with the tropical year by whom but according to me it would be better if thought of synchronizing the Gregorian calendar and the tropical year in one of the following ways.

THE POSSIBLE WAYS OF BRIDGING THE GAP BETWEEN THE CALENDAR YEAR AND THE ACTUAL YEAR

(i) By making the years divisible by 1000 but not by 2000 also non-leap years, that is, by declaring the years 3000, 5000 and 7000 also non-leap years. By doing so, the  Gregorian calendar would have 365.242 days long per year instead of 365.24 days long as follows, over a cycle of 2000 years.

Average number of days per calendar year  = (365 x 1516 + 366 x 484) / 2000 = (553340 + 177144 )/ 2000 = 365.242 days.

So the gap would narrow down by 0.00014 day per year every 2000 years.

(ii) By truncating the second to  1. 242 / 1.24219 times its present size. It would instantly make the calendar year 365.24219 days long instead of 365.24 days long permanently.

Since, it will be too cumbersome to omit the leap day in 3200, keep 3600 and 4000 as leap years, and thereafter making all centennial years common except 4500, 5000, 5500, 6000, 6500 and so on to make it tropical year compliant, I have edited the https://en.wikipedia.org/wiki/Tropical_year on Jan 8, 2018 by adding following text at the end of the article.  

Actually it would be enough to declare that the years divisible by 1000 but not by 2000, such as 3000, 5000, 7000 and 9000 would be also non-leap years. It would make the Gregorian calendar which is at present 365.24 days long, 365.242 days long over a cycle of 2000 years, as follows.

Average number of days per calendar year = {365 x 1516 + 366 x 484} / 2000 = (553340 + 177144 ) / 2000 = 365.242 days.

Alternatively, we can make the Gregorian calendar tropical year compliant yet by making a second 365.24/365.24219 times its present size also. It would instantly make the Gregorian calendar completely tropical year compliant. Once we redefine the second in this manner, we would not have to make any changes in the leap year pattern of Gregorian calendar ever until the tropical year itself may change.

 

 

 

 

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