## Where Does the Leap Year Come From?

How can a year be 365 and a quarter days? Wouldn't that mean that once every four years the Sun would rise at midnight? And rise once every four years at 6PM? We commonly use the word day to describe the time it takes for the Earth to rotate once with respect to the Sun. This is not the same as the time taken for the Earth to rotate once on its axis. In fact the Earth rotates once with respect to the Sun every 24 hours, and once on its axis every 23 hours, 56 minutes and 4.09 seconds, 3 minutes 55.91 seconds, or 3 55.91/60 minutes shorter than a day.In fact the time taken to rotate with respect to the Sun is called a Solar day, and the time taken for the Earth to rotate once on its axis is called a sidereal day.

over a period of

\[\frac{1 \: day}{3 \: 56/60 \: minutes}= \frac{24 \times 60}{3 \: 56/60} = 366.2414\]

days, the Earth will have turned once more on its axis than there are days, so that after 366.2414 days the Earth will have rotated 367.2414 times.We can approximately reconcile this difference between the time the Earth rotates relative to the Sun and the time the Earth takes to rotate on its axis by adding one day every four years to a year. These years where an a day is added are called leap years. 2016, 2020, 2024,... are leap years.