Why do we have leap day? Simply put, because the time it takes the earth to orbit the sun is not an integer multiple of the 24 hour solar day. There are a number of ways to measure the time to revolve, depending upon what you choose as the reference point. For example, astronomical years include the siderial year, the solar (or tropical) year, and the anomalistic year (see here), with the differences due to precession (and to a lesser degree, nutation).

Our current Gregorian Calendar is set up to approximate the solar year. We know that the solar day is a fraction of a day more than 365 days. This fraction accumulates over multiple years, eventually adding up to a full day. Adding one day every four years corresponds to a year of 365.25 days (the Julian year). However, this is actually a little longer than the solar year, by about a day a century. Thus, if you omit the leap day once a century (on the ‘century years’ such as 1800, 1900, and such), you become closer with a year of 365.24 days. However, this in turn proves a little too short. Thus, our current calender “adds back” a leap day every 400 years, thus making those ‘century years’ divisible by 400, such as the year 2000, leap years. Thus, the modern Gregorian calendar corresponds to an average year length of 365.2425 solar days, which will remain accurate to the average solar year for several millenia to come.

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Tags: Astronomy, calendars, Gregorian calendar, leap day

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