## Quick reminders about the leap day

I explained the difference between the sidereal day and the solar day in a previous post (one of my popular posts).

A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. The sidereal year differs from the tropical year (the time interval between vernal equinoxes in successive years) due to the precession of the equinoxes. The sidereal year is 365.25636 solar days (20 min 24.5 s longer than the mean tropical year which is 365.242189 solar days)

Most countries use the Gregorian calendar because it was designed to be in sync with the seasons. In other words, the Gregorian calendar tries to keep track of the tropical year which is 365.242189 solar days long (if you round it to 4 decimal digits then it is approximately 365.2422 solar days).

In the Gregorian calendar, every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the year 2000 is. If it is a leap year the month of February will have 29 days.

In the long run, this algorithm produces 365.2425 day year, on average. Compare it to the actual (tropical) year which is  365.2422 days long. This means that after 3,300 years we have to remove 1 day from the Gregorian calendar.

You may see a statement saying that a leap day occurs every 1461 days based on the fact that 365+365+365+366 = 1461.  This assumes that a leap day is occurring every 4 years. Yes, but let’s not forget the exception years: those years that are divisible by 100 but not a multiple of 400.

For the history of the leap day I recommend, Brian Handwerk’s article at National Geographic .