The average length of a civil year in the Gregorian calender is different to that of the tropical year.After h

Question

The average length of a civil year in the Gregorian calender is different to that of the tropical year.After how many years will an extra day have accumulated?

Answer 1

According to Wikipedia, the mean tropical year at the beginning of the year 2000 was 365.242190419 days. The Gregorian calendar is an attempt to keep the vernal equinox on or about the same date, so is based on the tropical year at the vernal equinox which is slightly different owing to the eccentricity of the earth's orbit. This tropical year is 365.24237404 days. The Gregorian year is 365.2425 days, which differs from the mean tropical year by 0.000309581 days, which is one day in 3230 years. The Gregorian year differs from the vernal equinox tropical year by 0.00012596 days, which is one day in 7939 years. This last figure is an underestimate because the vernal equinox tropical year is currently lengthening. The Gregorian calendar looks good for a few more millennia without being altered.

Answer 2

The Gregorian calender attempts to keep the first day of spring on March 21 (averaged over a 400 year cycle), by using a fixed set of rules.  At the time it was designed, the idea that the length of the year could change, and that the length of the day could change, were not recognized.

While it is possible to figure todays orbits and precession with a large number of digits, this does not mean that the numbers are accurate for the next 8000 years.  In particular, the rotation of the Earth over that long a period is subject to so much error, that we could lose or gain as much as a (solar) day.  In addition, the point of the vernal equinox could be off from current calculation by as much as 24 hours.

I have seen (and done myself) some calculations that say that the a leap-day "should" be skipped in about 8000 years, but it could be 6500 years, or 12,000 years.

Instead of changing the leap-day rules, it is much more likely that civilization will give up the idea of keeping the first day of spring on March 21.

Answer 3

The civil year is the same as the tropical year.