Surplus Three Days in 2000 Years

[manesiro]

Surplus Three Days in 2000 Years
We know that Earth takes 365 days 5 hours 48 minutes and 46 seconds in its one revolution round the Sun. Thus one Solar Year consists 365.2422 days. In 10000 years, there will be 3652422 days and in 2000 years there must be 730484.40 days.
Historically, we know that
1. In Julian calendar, every 4th year was a leap year having 366 days. Thus total numbers of days in each century were 36525.
2. In year 1582, 10 days were deleted from the month of October.
3. Year 1600 was a leap year having 366 days.
4. Years 1700,1800 and 1900 were having 365 days each.
5. Year 2000 was a leap year.
Calculating days from first day of first century to 31-12-1500
== 36525*15
=547875
The numbers of days from 1-1-1501 to 31-12-1600 were 36515.
The numbers of days from 1-1-1601 to 31-12-1700 were 36524.
The numbers of days from 1-1-1701 to 31-12-1800 were 36524
The numbers of days from 1-1-1801 to 31-12-1900 were 36524
The numbers of days from 1-1-1901 to 31-12-2000 were 36525
Total numbers of days from 1-1-01 to 31-12-2000 are 730487
Thus we have three days surplus in our history of 2000 years.

[Māori]

Huh?

Should this be in the babbling section?

[Ronald Brak]

Doesn't the Gregorian calendar skip leap years every now and then to keep it accurate, or did you take that into account? (I know very little about the details of the calendar.)

[Gillianren]

If it's a year ending in 00 where the first two digits are divisible by four (1600, 2000, etc.), it's a leap year. If it's not, it's not. Actually, little tiny adjustments (leap seconds) are made to the calendar as required. There are people who are way better at this sort of thing than I--I just study history, not time. Every rearrangement of the calendar since the creation of the Julian calendar (we now use the Gregorian one, as I recall) has been to line up the calendar and the year better.

[Tog]

I played with the numbers a different way, and got 730,485 days. This looks like a variation on the 'where did the $2 go?' puzzle.

My numbers:
Normal year=365
Leap year =366
4 year cycle= 1461 days
25 cycles in a leap century= 36,525
25 cycles in a normal century 36,524
4 century cycle= 146,097
5 cycles to the end of 2000= 730,485 days

According to the Wiki entry on the Gregorian Calendar, 26 June 2006 is day 732,488. Subtracting the days from 1/1/2001 until now, I did get 730,487.

[swansont]

If it's a year ending in 00 where the first two digits are divisible by four (1600, 2000, etc.), it's a leap year. If it's not, it's not. Actually, little tiny adjustments (leap seconds) are made to the calendar as required. There are people who are way better at this sort of thing than I--I just study history, not time. Every rearrangement of the calendar since the creation of the Julian calendar (we now use the Gregorian one, as I recall) has been to line up the calendar and the year better.

Leap seconds are adjustments for the rotation, though, not the orbit. You adjust your clock, not your calendar.

[TriangleMan]

The Wikipedia article on Leap Year notes that the calendar should be out by 1 day every 8000 years.

[antoniseb]

The current length of the tropical year based on the time between vernal equinoxes is 365.24237404 days, and shrinking as the days get longer from tidal friction.

[Gillianren]

Leap seconds are adjustments for the rotation, though, not the orbit. You adjust your clock, not your calendar.

Correct me if I'm wrong, though, but if you adjust the clock, the calendar adjustment follows naturally.

[swansont]

Correct me if I'm wrong, though, but if you adjust the clock, the calendar adjustment follows naturally.

I was thinking that the effect was small, and the accumulated effect wouldn't add up to more than a day. Assuming my back-of-the-envelope calculation is right, in 2000 years you expect about 3 hours of difference.

[ToSeek]

Thread moved from ATM to Astronomy.

[HenrikOlsen]

2. In year 1582, 10 days were deleted from the month of October.

In Italy, Poland, Portugal, and Spain, not everywhere.

The main reason for the discrepancy is that the Gregorian calenday isn't set up to correspond with the Mean Tropical Year (~365.24219 days), but instead with the Vernal Equinox Year(~365.24237404 days), which is the one antoniseb mentioned. use that one and the 3 days aren't lost.

[Damburger]

No matter how many extra days are found, I bet I won't get any extra holiday

[swansont]

No matter how many extra days are found, I bet I won't get any extra holiday

Holiday? Extra days mean you owe three days more work.

[hhEb09'1]

We know that Earth takes 365 days 5 hours 48 minutes and 46 seconds in its one revolution round the Sun. Thus one Solar Year consists 365.2422 days. In 10000 years, there will be 3652422 days and in 2000 years there must be 730484.40 days.

...

Thus we have three days surplus in our history of 2000 years.

True. I pondered this question a few years back. Didn't make sense to me at first either.

Doesn't the Gregorian calendar skip leap years every now and then to keep it accurate, or did you take that into account? (I know very little about the details of the calendar.)

He took it into account.

I played with the numbers a different way, and got 730,485 days. This looks like a variation on the 'where did the $2 go?' puzzle.

manesiro's answer was 730,484.40 days, so that's essentially the same answer. You used the calendar scheme, he used the value that the calendar is supposed to approximate.

The main reason for the discrepancy is that the Gregorian calenday isn't set up to correspond with the Mean Tropical Year (~365.24219 days), but instead with the Vernal Equinox Year(~365.24237404 days), which is the one antoniseb mentioned. use that one and the 3 days aren't lost.

Nope!

2000*365.24219=730484.38
2000*365.24237=730484.74

Both are almost the same--but the last one would round up to Tog_'s, so we'd be missing two days instead of three. (And the .26 difference between the last one and Tog_'s is what goes into making that one whole day difference over 8000 years, that TriangleMan mentioned.)

2. In year 1582, 10 days were deleted from the month of October.

That's the key piece of information.

Over 2000 years, we drop 15 leap days. Over 1582, we'd drop 12--why'd they only drop 10? Because they were only trying to reset the calendar to the time of the Council of Nicaea (325AD), which is when the date of Easter was established.

[swansont]

Over 2000 years, we drop 15 leap days. Over 1582, we'd drop 12--why'd they only drop 10? Because they were only trying to reset the calendar to the time of the Council of Nicaea (325AD), which is when the date of Easter was established.

I think that would explain why June 24 is the midsummer celebration of some culture; it used to coincide with the solstice.

[HenrikOlsen]

And the reason why it's June 24th and not 25th when it's December 25th is due to the roman calendar which numbered the last days of the month from the first day of the next month, and since December is a day longer, the two days are numbered the same.

[manesiro]

I did not know where my previous thread has gone so I started the thread into Fun-N-Game.Excuse me for starting it again in Astronomy when I came to know that previous one has moved in Astronomy.
Days & Dates


Surplus Three Days in 2000 Years
We know that Earth takes 365 days 5 hours 48 minutes and 46 seconds in its one revolution round the Sun. Thus one Solar Year consists 365.2422 days. In 10000 years, there will be 3652422 days and in 2000 years there must be 730484.40 days.
Historically, we know that
1. In Julian calendar, every 4th year was a leap year having 366 days. Thus total numbers of days in each century were 36525.
2. In year 1582, 10 days were deleted from the month of October.
3. Year 1600 was a leap year having 366 days.
4. Years 1700,1800 and 1900 were having 365 days each.
5. Year 2000 was a leap year.
Calculating days from first day of first century to 31-12-1500
== 36525*15
=547875
The numbers of days from 1-1-1501 to 31-12-1600 were 36515.
The numbers of days from 1-1-1601 to 31-12-1700 were 36524.
The numbers of days from 1-1-1701 to 31-12-1800 were 36524
The numbers of days from 1-1-1801 to 31-12-1900 were 36524
The numbers of days from 1-1-1901 to 31-12-2000 were 36525
Total numbers of days from 1-1-01 to 31-12-2000 are 730487


Finding week-day of any date
We know 1st January 2001 fell on Monday. If we divide 730487 by 7, we get 2 as remainder. Thus weekday of 1st month of 1st year of 1st Century (1-1-01) was Saturday.
There were 25 leap years of 366 days in each Century from 1st to 16th. All these centuries from 1st to 15th consisted of 36525 days. The 16th century consisted of 36515 days. There were 24 leap years in 17th, 18th and 19th Centuries. These centuries consisted of 36524 days. Again, 25 leap years in 20th Century as year 2000 was leap year and thus 20th century had 36525 days.
The days will shift by 6 days if previous century consists 36525 days and will shift 5 days if previous century consists of 36524 days as we can see by dividing total number of days of previous century by 7.
Thus
1-1-01 Saturday
1-1-101 Friday
1-1-201 Thursday
1-1-301 Wednesday
1-1-401 Tuesday
1-1-501 Monday
1-1-601 Sunday
1-1-701 Saturday
1-1-801 Friday
1-1-901 Thursday
1-1-1001 Wednesday
1-1-1101 Tuesday
1-1-1201 Monday
1-1-1301 Sunday
1-1-1401 Saturday
1-1-1501 Friday
As we know 16th century was of 36515 days, so the days will shift 3 days and
1-1-1601 Monday
17th, 18th and 19th centuries were of 36524 days and so the days will shift by 5 days and
1-1-1701 Saturday
1-1-1801 Thursday
1-1-1901 Tuesday
The 20th century was of 36525 days; the days will shift again 6 days
1-1-2001 Monday
After finding the day of first day of each century, we can find the day of 1st of any year in that century. (The 16th century has special features and will be described later)
We will take number of years and add to it number of leap years and then divide it by 7 , thus we will know the shift of days from the day of 1st day of that century.
As we know that 1-1-1901 was on Tuesday.
We can know day of 1-1-1991 by adding 22 leap years to 90 years and dividing this figure of 112 by 7.We get 0 as remainder. Thus 1-1-1991 will fall on same day-Tuesday.
After finding day of 1st January of any year, we can find the day of 1st of other months.
1st February +3
1st March +3 if non-leap year
+4 if leap year
1st April +3 to 1st March
1st May +2 to 1st April
1st June +3 to 1st May
1st July +2 to 1st June
1st August +3 to 1st July
1st September +3 to 1st August
1st October +2 to 1st September
1st November +3 to 1st October
1st December +2 to 1st November
The day of 1st of any month is also the day of 8th, 15th, 22nd and 29th of that month. Thus we can find day of any date of any month of any year of any century.
Special case of 16th Century
We know day of 1-1-1501 was Friday.
We can find day of 1-1-1582 by adding 20 leap years to 81 years and dividing by 7 thus we get 3. Thus day of 1-1-1582 will be Monday.
1-2-1582 Thursday
1-3-1582 Thursday
1-4-1582 Sunday
1-5-1582 Tuesday
1-6-1582 Friday
1-7-1582 Sunday
1-8-1582 Wednesday
1-9-1582 Saturday
1-10-1582 Monday
1-11-1582 Monday (because October 1582 had 21 days and so there will be no shift from day of 1st October)
1-12-1582 Wednesday
1-1-1583 Saturday
As number of days in 1582 were 255 (10 days deleted from month of October)
1-1-1584 Sunday
1-1-1585 Tuesday because 1584 was leap year
1-1-1586 Wednesday
1-1-1587 Thursday
1-1-1588 Friday
1-1-1589 Sunday because 1588 was leap year
1-1-1590 Monday
1-1-1591 Tuesday
1-1-1592 Wednesday
1-1-1593 Friday because 1592 was leap year
1-1-1594 Saturday
1-1-1595 Sunday
1-1-1596 Monday
1-1-1597 Wednesday because 1596 was leap year
1-1-1598 Thursday
1-1-1599 Friday
1-1-1600 Saturday
1-1-1601 Monday because 1600 was a leap year
From here, we join the mainstream as described above.
Thus we can find the day of any date of any month of any year of any century.

[Tog]

Saw it the other day in this thread too. Which expanded on this one from last week, where there were several replies.

[ToSeek]

Threads merged.

[bronzeman]

extra 3 vacation days?