According to the rules for setting up the civil calender, the years 1600 and 2000 are divisible by 400 and?

Question

according to the rules for setting up the civil calender, the years 1600 and 2000 are divisible by 400 and hence are leap years ,what would the average length of a civil year be (averaged over 400 years) if they were not leap years?help please!

Answer 1

The Gregorian calendar attempts to keep the vernal equinox on or close to March 21; hence it follows the vernal equinox year. The average length of this calendar's year is 365.2425 mean solar days (which can be thought of as 97 out of 400 years being leap years) whereas the vernal equinox year is 365.2424 days.

The Gregorian solar calendar is an arithmetical calendar. It counts days as the basic unit of time, grouping them into years of 365 or 366 days. The solar calendar repeats completely every 146,097 days, which fill 400 years, and which also happens to be 20,871 seven-day weeks. Of these 400 years, 303 (the "common years") have 365 days, and 97 (the leap years) have 366 days. This gives an average year length of exactly 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds.

The Gregorian solar calendar is an arithmetical calendar. It counts days as the basic unit of time, grouping them into years of 365 or 366 days. The solar calendar repeats completely every 146,097 days, which fill 400 years, and which also happens to be 20,871 seven-day weeks. Of these 400 years, 303 (the "common years") have 365 days, and 97 (the leap years) have 366 days. This gives an average year length of exactly 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds.

The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 mean solar days long, which has an error of about one day per 3300 years with respect to the mean tropical year, which in 2000 had a length of 365.24219 days (each day consisting of 86,400 SI seconds) but less than half this error with respect to the vernal equinox year of 365.24237 days. By either criterion, the Gregorian calendar is substantially more accurate than the one day in 128 years error of the Julian calendar (average year 365.25 days).

In the 19th century, Sir John Herschel proposed a modification to the Gregorian calendar with 969 leap days per 4000 years, instead of 970 leap days that the Gregorian calendar would insert over the same period. This would reduce the average year to 365.24225 days. Herschel's proposal would make the year 4000 common instead of leap. While this modification has often been proposed since, it has never been officially adopted.

On timescales of thousands of years, the Gregorian calendar falls behind the seasons because the slowing down of the Earth's rotation makes each day slightly longer over time (see tidal acceleration, leap second, and precession) while the year maintains a more uniform duration. Borkowski reviewed mathematical models in the literature, and found the results generally fall between a model by McCarthy and Babcock, and another by Stephenson and Morrison. If so, in the year 4000, the calendar will fall behind by at least 0.8, but less than 1.1 days. In the year 12,000 the calendar would fall behind at least 8, but less than 12 days.

Answer 2

How many days in 400 years?

How many years in 400 years?

Divide.

Answer 3

The Julian calendar has a leap year every four years, hence 100 leap years in 400 years and an average year of 365.25 days. The Gregorian calendar modified this by leaving out three leap years in every 400 years, hence 97 leap years in 400 with an average year being 365.2425 days. If century years divisible by 400 were not leap years, this would reduce the number of leap years to 96 in 400 and the average year would be 365.24 days