<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by kingdavid</i>
<br />if a day is exactly 365.2564 days and every 4 years we compensate by adding a day, then that leaves 0.0064 days every year not acounted for:
331 years since gregorian calendar
0.0064 days missed every year:
331*0.0064=2.1184 days behind now? is this true?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Jim's answer was pretty good, but you might not have understood it.
First, let's fix up your calculation. 365.2564 is the length of the sidereal year. Although that is the type of "year" closest to the true time for the Earth to make one complete revolution around the Sun, it is not the "year" used in calendar making, which is known as the tropical year, 365.2422 days. That is the interval at which the seasons repeat, which has more practical value to Earth inhabitants. The two types of "year" differ because the Earth's spin axis is precessing while the Earth orbits. The tropical year is the interval between times when the Earth's spin axis has its maximum tilt toward the Sun.
With ordinary leap years, the calendar year is 365.25 days long. This is too long (comapred with 365.2422 days) by 0.0078 days per year. In a 400-year interval, this accumulates to 3.12 days too long.
The way the calendar corrects for this is by an exception rule for leap years. This exception rule states that century years (divisible exactly by 100) will not be leap years unless they are also exactly divisible by 400. Following this rule, the following years that would normally be leap years are in fact not leap years: 1500, 1700, 1800, 1900, 2100, 2200, 2300, 2500, ... The following century years remain leap years, as would normally be the case anyway: 1200, 1600, 2000, 2400, 2800, ...
As you see, this system shortens the calendar by three days every 400 years. And that brings it pretty close to the actual length of the tropical year. The remaining error of 0.12 days per 400 years will not cause an error of one day until about 5000 A.D. But it isn't worth making a rule to cover that case, partly because we will probably be free of Earth-time dependence by then, but more practically because Earth's rotational spin varies in unpredictable ways that could accumulate to a few days in that amount of time, messing up any system we set up now.
From a short-term perspective, the year 2000 was a normal leap year with nothing special happening. But from a longer-term perspective, the year 2000 was the rare century year that stays a leap year. That only happens for one day every 400 years. -|Tom|-
P.S. The following single lines of program code compute a continuous day count G or the day number within the year H, allowing for the variable length of each month, leap years, and exception century years. Y = 4-digit year, M = month number, D = day of month. These work for all dates A.D. Calculations must be done in integer arithmetic: throw away any remainder from divisions. The 7-digit constant at the end can be dropped unless you wish to synchronize your day counts with the official Julian Day Number system.
G=367*Y-7*(Y+(M+9)/12)/4-3*((Y+(M-9)/7)/100+1)/4+275*M/9+D+1721029
H=G-(367*Y-7*Y/4-3*((Y-1)/100+1)/4+1721059)
