why do we have a leap year every 4th year, but not on the 100th, 200th and 300th year, but on 400th year...?

Question

what is the actual phenomenon behind this gergorian calendar system?

Answer 1

Copying substantial portions of Wikipedia articles is an odious practice.

Here's how I explain the leap year rule to students. First some history. The ancients knew that the year is very nearly 365 1/4 days. Julius Caesar introduced the Julian calendar in 44 or 45 BCE, and by the year 8 CE, the practice of having a leap year every four years was established in the western world.

We now know that the actual length of the solar year is 365 days, 5 hours, 48 minutes, and 45 seconds. This means that the Julian year is 11 minutes, 15 seconds too long, and this error of 675 seconds per year accumulates over time.

At the Council of Nicea (325 CE), scholar-theologians determined that Christ rose from the dead (Easter) on the first Sunday after the first full moon after the vernal equinox (first day of spring). But with the accumulating error in the Julian calendar, Easter was getting earlier and earlier in the calendar. By the 16th century, the situation was becoming intolerable. The calendar error of 675 seconds per year had amounted to 10 days in the 1250 years between 325 and 1582 when Pope Gregory fixed the calendar.

To see why the Gregorian system works, the arithmetic is easy.

(675 sec/yr x 400 yrs) / (3600 sec/hr x 24 hrs/day) = 25/8 days, or 3 1/8 days, or 3 days, 3 hours, almost exactly.

By using 97 leap years every 400 years, the calendar is correct to 3 hours per 400 years, or 27 seconds per year. Since the Julian calendar was off by 675 seconds per year, the Gregorian calendar eliminates 96% of that error.

A good way to eliminate 3 leap year days every 400 years is to eliminate the century years not divisible by 400, and that's what they did.

As shown above, the Gregorian calendar is off by 3 hours (one-eighth of a day) every 400 years. This error accumulates to one day every 3200 years (400 divided by 1/8), so the calendar must be adjusted by a day every 32 centuries.

That, however, will not be our problem, since we won't be around to worry about it.

Answer 2

Hi Sudhakar!

Leap years do not precisely recalibrate the solstice to the calendar. One leap year in a four year cycle corrects for exactly six hours per year, but the actual solar year is only 5 hours 49 minutes longer than the calendar year. These 11 or 12 extra minutes a year begin to pile up. In a hundred years, the solstice was happening almost 19 hours too early, and over 400 years the discrepancy reached 3.12 days.

To correct this, in 1582 Pope Gregory XIII decreed that three leap days must be taken out of the cycle every four hundred years. In the Gregorian calendar, years divisible by 100 but not by 400 (such as 1900 and 2100) are not leap years.

(The Pope also ruled that, to make up for the error since the time of Caesar, ten days had to be dropped from the calendar. By the 1500s, the winter solstices were happening about December 11 and spring was arriving around March 11. The change took effect in October 1582. The day after October 4, 1582 became October 15.)

The Gregorian reform is still not precise. Over many centuries, the 3 left-over hours every four hundred years will start to add up. As long ago as the time of astronomer John Herschel in the early 1800s, it was realized that the Gregorian calendar with its 400-year rule will add one leap year too many to the calendar every 4000 years, 970 instead of the number which is closer to accurate, 969.

In 3000 years the solstice will be running one day late. To correct this, it will eventually be necessary to make a further modification and drop a leap year. One way to modify the rule would be to make millennial years divisible by 4000 not leap years. (Currently, millennial years that are divisible by 2000 are leap years, such as the years 2000 and 4000.)

An alternative is the way chosen by the Orthodox Church when it adopted the Gregorian calendar. Under the Orthodox rule, century years which, when divided by 900 yield a remainder that is either 200 or 600, are leap years. In other words, the Gregorian rule of two leap years in eight century years becomes two leap years in nine century years. In both versions, the years 1900, 2100, 2200, 2300, 2500, 2600 and 2700 are not leap years, but 2000 and 2400 are. The year 2800 is a leap year under the Gregorian calendar, but not in the Orthodox. Conversely, 2900 will be an Orthodox leap year.

The Orthodox rule has been adopted in Russia and likely will be picked up by the rest of the world in centuries to come. Although less elegant than the 4000-year rule, it has the advantage of making the calendar correction more gradual than an abrupt jolt after letting the discrepancies pile up for 4000 years.

Answer 3

Hello, I have read that this is because there are 365.242375 days in the year. Since it is very difficult to have a day at the end of each year that is only 0.242375 days long, (this would be a little under 6 hours), we have instead invented the calendar gymnastics that you have mentioned. Making most years last only 365.0000 days and adding in a leap year with 366.0000 days makes a good first approximation, but this strategy will still accumulate error over the centuries. Pope Gregory realized this and he and his scholars invented the current scheme. I have read that his scheme will not get out of synch for some 8-10,000 years or so, so it is a good one for our purposes.
Now when Humanity colonizes Mars, there will need to be a different strategy for those living there....

Answer 4

According to the Gregorian Calender, there are roughly 97 leap years every 400 years. This is achieved by having 24 leap years every century, and 25 every fourth century. As a result we do not have leap years in the 100th, 200th and 300th year, but have one on the 400th year.

Answer 5

Why end there, shall we've one each 12 and performance 31 days in February... significant reason is because we stick with the Gregorian calendar, and that is the way the almighty Pope Gregory the XIII mandatory it. Calendars are very annoying to regulate. We used the Julian calendar for over 1500 years, in spite of information for plenty of that element that it had change into very innaccurate. yet Gregory's advisors did the mathematics and said that there are about 365 a million/4 days a three hundred and sixty 5 days. So basic journey says to operate the further day each 4 years, once that the relax will develop into an finished variety (for this reason, an finished day).

Answer 6

Because the earth does not take EXACTLY 365.25 days to orbit the sun (that would be too convenient - lol)

So tweaking by a day every 4 years might solve 95% of the time lost, however over many 4 year periods, this 5% will add up. So every 4 centuries and 4 millenia etc. It was worked out that it would have to be changed by a certain amount.

The leap-year and indeed leap-century are done so as to tweek the clocks bit by bit to keep it as accurate as possible in the grand scheme of things.

Answer 7

Because the year isn't 365.25 days long as leap year every 4 would imply. It's closer to 365.2422. That works out to being about 3 days off every 400 years. On the advice of Luigi Livio, Pope Gregory decreed that the best correction to the inaccuracy would be to skip leap year day 3 times every 400 years. Works out pretty well.

Answer 8

The fact that the time it takes the Earth to go around the Sun is not divided evenly into times that the Earth rotates to have the same side face the Sun. So yes there is a natural cause for what seems like a weird system.

Answer 9

Our calendar system is an approximation of the actual amount of time it takes for the earth to revolve around the sun in its orbit.

See the link below for much more detail.

Answer 10

to make the calendar work out right. A year is a bit more than 365 days, so that bit of time must be worked out.