The calendar

Why 365 days? If the year always had 365 days and (for example) March 21 was the day that earth passed the vernal equinox, then after 10 years

(since 10×5 hr 48 min = 58 hr = 2${\frac{1}{2}}$ days),

March 21 would occur 2${\frac{1}{2}}$ days before the earth got to the vernal equinox;

after 500 years, March 21 would occur 125 days before; and by then, March 21 would be in late autumn. So we have inserted an extra day every 4 years to offset the imbalance. A calendar with this extra day every four years (leap year) is called a Julian calendar. Since the year is actually only 5 hr 48 min longer than 365 days, we need slightly less than one day to make up the difference every four years ( 4×5 hr 48 min = 23 hr 12 min, not 24 hours).

If we were to continue with the extra day (24 hrs.) every 4 years, we would eventually get out of step again.

(23 hr 12 min. ×100years = 2300 hr 1200 min = 2320 hr = 2320/24 days = 96${\frac{2}{3}}$ days in 4 years.)

So if we had 100 leap years in 400 years we'd get ahead of the seasons by about 3${\frac{2}{3}}$ days every 400 years.In order to keep the schedule of the calendar, we must omit a leap year about once every 400 years. That is currently done in a century year that is not evenly divisible by 4. This omits 3 days that would otherwise be there in the Julian calendar. Therefore, the following years are not leap years: 1700, 1800, 1900, 2100, etc. The year 2000 was a leap year. This revision identifies the Gregorian calendar. By controlling the leap year in this fashion, we are able to keep the calendar in line with the seasons. It would be even closer to the actual seasons if we had one more leap year every 1200 years.