There are not exactly 365 days in a year. The actual length of a year is 365.2422 days, just close enough to 365.25 days to cause a mathematical muddle when coming up with a calendar.

Finding a simple way to keep the calendar coordinated with the cosmos was a major astronomical effort. Ancient Egyptians thousands of years ago were the first to use a year of 365 days, but their calendar had no leap year.

This error caused the seasons to drift slowly forward with respect to the calendar and took 1,460 years to return to where it started. All they needed to have done was add a day every four years. So simple, yet so difficult!

Two thousand years later, the Romans developed a calendar with leap years.

Their calendar consisted of alternating 29- and 30-day months to roughly correspond with the moon cycle. This made 354 days, but they added an extra day to make the number odd, which they considered more astrologically favorable, so their year had 355 days.

To keep in sync with the cosmos, they inserted an extra month every second year, consisting of 22 and 23 days alternately, so that each four years constituted 1,465 days, and the average length of the year was 366-1/4 days.

That one extra day added 24 days in as many years, so for every third eight-year period they added only three 22-day months instead of four. This finally brought the average length of the year to 365-1/4 days, which was close but not close enough.

A problem was that priests had the power to add or subtract days as needed when the calendar differed from the celestial motions. Bribes and corruption quickly caused abuses of this power. Priests would add days to prolong or shorten political terms, or to manipulate election dates. The calendar fell into chaos, and by the time of Julius Caesar it was off by more than 60 days.

Caesar abolished the system in 45 B.C. and decreed that every fourth year should have 366 days, the other years each having 365.

Again a good system, but over time the system lost oversight. Sometimes a leap year was added in the third year instead of the fourth, or in times of crisis leap days were left out entirely because they were considered unlucky.

Even administered correctly, the Julian calendar was not precise. Every 128 years, the seasons shifted one day earlier with respect to the calendar. By 1582, the calendar had accumulated more than 10 extra days.

Pope Gregory I decreed that March 21 was the proper day for the vernal equinox, because that was the date established during the First Ecumenical Council in 325 and was the basis for the determination of Easter.

Church mathematicians calculated a more accurate calendar borne of necessity. The Julian calendar had Easter sometimes falling before the equinox, which cannot happen according to church doctrine. The Gregorian calendar dropped 10 days from the Julian calendar to bring the calendar back into sync with the heavens.

The Gregorian calendar is about as accurate as we can get it for 2,500 years, but we will still need to add a day every now and then since Earth’s orbit varies a few nanoseconds per year. The first one will happen around the year 4082.

Richard Brill is a professor of science at Honolulu Community College. His column runs of the first and third Friday of the month. Email questions and comments to brill@hawaii.edu.