A relatively rare event—an extra day in February, the every-four-years February 29^{th}—greets us again this Monday. Why does this happen? As you might expect from my posing the question on this blog, the answer is wrapped up in astronomy.

In fact, our whole calendrical system is based on astronomy. The year is based on the time required for Earth to complete one circuit of the sun. The month is (loosely in a solar calendar, exactly in a lunar calendar) the time between repeating lunar phases, known as the moon’s synodic period. A day is the time of one rotation of Earth on its spin axis. Even a week of seven days is based on the seven naked-eye objects known to the ancients as “planets”: the sun and the moon along with Mercury, Venus, Mars, Jupiter, and Saturn.

But these units of time don’t fit neatly into each other. There are about 12.4 synodic periods of the moon in a year, not exactly 12. We compensate for this with months that are mostly longer than the 29.5 days of one synodic period. And there are 365.2425 days in a year, not 365. Hence a periodic February 29^{th}.

You’ll notice that the “extra” time in a year is pretty close to one fourth of a day. So every four years, we add an extra day to February.

But wait. It isn’t **exactly** one fourth—it’s a little less. After 400 years of adding a day every four years, we would have added a total of about three extra days; we have to compensate somehow. We do so by **not** adding February 29^{th} in three out of four century years. We only have a leap day in century years that are exactly divisible by 400.

Here’s how it works. 1896 was a leap year, as was 1904. But 1900 was not. It is a “century year”, but it is not divisible by 400. The year 2000, however, **was** a leap year.

The effect of this on the time of the northern summer solstice—the exact moment when the sun reaches its northernmost point in the sky—can be seen in the graph. Notice how the trends for the 18^{th}, 19^{th}, and 20^{th} centuries all moved a little lower, corresponding to later dates. The summer solstice reached its latest point in 1903, roughly 3 pm on June 22^{nd}, Greenwich Mean Time (GMT). And note how this trend would have continued if the year 2000 had not been a leap year. 2003’s summer solstice would have been even later than 1903’s; instead, it was around 8 pm on June 21^{st}.

As we moved into the second half of the 20^{th} century, the precision of our clocks improved to the point that the motions of the Earth, its revolution around the sun and its rotation on its axis, were shown to be too variable. Time itself was redefined in terms of the frequency of a particular atomic energy transition. For those who care to know, the official definition of a second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. One minute is 60 times this, and one hour is of course 60 minutes.

Periodically, a leap second is added to keep atomic clock time in sync with what is known as mean solar time. 26 such leap seconds have been added since this began in 1972, the last coming on June 30, 2015.

Do we ever **subtract** a leap second? No, the extra time is necessary because the rotation of the Earth is very slowly but inexorably decreasing. Each day is ever so slightly longer than the day before.

So use the extra time, whether an extra day or an extra second, to good advantage! I plan to have a nice lunch with a new friend on this particular February 29^{th}.