Regarding the Gregorian Calendar

[a1call]

This thread is being started as a reply to Hornblower and in order to not off track the original thread:


http://cosmoquest.org/forum/showthre...21#post2044221

You appear to have some inaccurate information about the dates and times of the equinox, and in any case I am unable to understand your line of thought.

The dates of the Gregorian calendar were set by Pope Gregory’s astronomers and took effect in February of 1582. The next spring equinox occurred at approximately 2:50 AM March 21 local time in Rome, according to my best estimate by extrapolating back from recent published times. That was midway between leap years, so the long term average time of the equinox was restored to March 21, as the Pope wished. Of course it fluctuates over the short term and it fell in the afternoon of March 20 in 1584, the first leap year after the decree.

The March equinox this year was at 5:14 AM on March 20, Universal Time (UT), which would be the local standard time in London. That made it the evening of March 19 from the central USA west to the International Date Line. Since this is a leap year that is about the earliest the equinox time comes in the 4-year cycle. The time in a leap year comes about 18 hours earlier over the course of a century, so it is clear that the date in UT for leap years has been March 20 for the past century. That 18hr/century shift is what makes the Gregorian correction of omitting three leap years every four centuries necessary.

The Gregorian calendar is based on the following rules:


*- If the year is divisible by 4 then it is a leap year
*- However if the year is divisible by 100 then it is not a leap year
*- However if the year is divisible by 1000 then it is a leap year


This gives the Gregorian year the average length:


365 + 1/4 - 1/100 + 1/1000 = 365.241 days


The actual length of the year (duration between spring equinoxes) is:


365 d 5 h 49 m 30 s = 365 + 5/24 + 49/(60x24) + 30/(60x60x24)= 365.243 days


The error in Gregorian calendar is about 0.002 days per year which means it will miss by one day in about
1/0.002 = 500 years (585 years without rounding)


But there is another issue with the Gregorian calendar. As I mentioned before it is applied globally using the international dateline (despite the name, not based on any international treaties ). This is based on a static longitude. If the dateline was advanced by 5 h 49 m 30 s, then the syncing would keep globally. But as is because the dateline is not synced to the tropical year it can result in dates which don't match the tropical year periods.

[Celestial Mechanic]

The leap year rule is:

*- If the year is divisible by 4 then it is a leap year
*- However if the year is divisible by 100 then it is not a leap year
*- However if the year is divisible by 400 then it is a leap year.

{Emphasis mine}

This results in an average year length of 365.2425 days. If I recall correctly, the tropical year is about 365.2422 days, so the Gregorian calendar is off by one day in about 3300 years.

I am not sure why you are concerned about the international date line. The Gregorian calendar was designed to keep the March equinox near March 21, not precisely on it relative to Rome or any other municipality on Earth.

[a1call]

The leap year rule is:

*- If the year is divisible by 4 then it is a leap year
*- However if the year is divisible by 100 then it is not a leap year
*- However if the year is divisible by 400 then it is a leap year.

{Emphasis mine}

This results in an average year length of 365.2425 days. If I recall correctly, the tropical year is about 365.2422 days, so the Gregorian calendar is off by one day in about 3300 years.

I am not sure why you are concerned about the international date line. The Gregorian calendar was designed to keep the March equinox near March 21, not precisely on it relative to Rome or any other municipality on Earth.

Thank you for the rule correction. I was going by memory.

The tropical year length that I used is from wikipedia with a link to it in the original thread. The difference I calculate with your correction is a day in 4800 years (corrections are welcome and appreciated).

I will try to clarify the issue with the IDL the best that I can

The period of a year (Spring equinox to Spring equinox) is not divisible by a whole day.

Consider the longitude at which it was midnight at the moment of equinox 2012.

Let us for the sake of argument set this longitude as the dateline.

Let us set the calendar date to 21st of March through out the word at the moment of equinox.

Let us keep the dateline constant.

The moment of equinox 2013 will be about 5:50 am at the dateline.

At the moment of the equinox, points to left of the dateline and upto about a quarter of the globe will be dated March 20th while the rest of the globe will be dated March 21st. While a year ago the whole word was dated March *21st.

However, the Synchronicity to the tropical year would be maintained if the dateline is rotated 5:50 per year and the whole globe would be on March 21st.*

If the dateline is advanced every year by the excess of a year's period over 365 days the Synchronicity would be maintained for thousands of years and it would always be March 21st at the moment of the equinox throughout the world.

[antoniseb]

The rule for the Gregorian Calendar was created in the 1570s and applied in 1582. At that time the length of the day was shorter than it is now. We will need to modify the rule before your calculated 4800 years from now if there is still a goal to sync the Vernal Equinox with March 21st at that time.

[Hornblower]

Thank you for the rule correction. I was going by memory.

The tropical year length that I used is from wikipedia with a link to it in the original thread. The difference I calculate with your correction is a day in 4800 years (corrections are welcome and appreciated).

I will try to clarify the issue with the IDL the best that I can

The period of a year (Spring equinox to Spring equinox) is not divisible by a whole day.

Consider the longitude at which it was midnight at the moment of equinox 2012.

Let us for the sake of argument set this longitude as the dateline.

Let us set the calendar date to 21st of March through out the word at the moment of equinox.

Let us keep the dateline constant.

The moment of equinox 2013 will be about 5:50 am at the dateline.

At the moment of the equinox, points to left of the dateline and upto about a quarter of the globe will be dated March 20th while the rest of the globe will be dated March 21st. While a year ago the whole word was dated March *21st.

However, the Synchronicity to the tropical year would be maintained if the dateline is rotated 5:50 per year and the whole globe would be on March 21st.*

If the dateline is advanced every year by the excess of a year's period over 365 days the Synchronicity would be maintained for thousands of years and it would always be March 21st at the moment of the equinox throughout the world.

Any nation can choose, by law, to jigger its basis for date keeping so that the moment of the March equinox always will occur on the 21st as officially reckoned within its borders. As far as I can tell, none of Planet Earth's soverign nations have any compelling need or desire to do this. It is much simpler for commercial and diplomatic purposes to stick to standard time zones and a fixed International Date Line.

It is not unheard of for a nation to make itself an exception to the standard system. Not too long ago, Samoa, just east of the International Date Line, chose to disregard it and reset their date reckoning to be better in sync with their trading partners in nearby New Zealand and not-so-faraway Australia.

[a1call]

Any nation can choose, by law, to jigger its basis for date keeping so that the moment of the March equinox always will occur on the 21st as officially reckoned within its borders. As far as I can tell, none of Planet Earth's soverign nations have any compelling need or desire to do this. It is much simpler for commercial and diplomatic purposes to stick to standard time zones and a fixed International Date Line.

It is not unheard of for a nation to make itself an exception to the standard system. Not too long ago, Samoa, just east of the International Date Line, chose to disregard it and reset their date reckoning to be better in sync with their trading partners in nearby New Zealand and not-so-faraway Australia.

The reason for the use of the IDL is not the issue. I am not suggesting it should be abondoned. The point of this thread is to explain why/how a static dateline will create a conflict with the local calculation of in another locale.