The 7 most bizarre facts about leap day

Once every four years — well, almost every four years — our calendar gifts us with an extra day: February 29th, also known as leap day Most of us who are born on this planet will experience perhaps around 20 such leap days in our lives, most a little less, some a little more, but its importance shouldn’t be underestimated. Leap days, as rare and whimsical as they may seem, actually play a vital role in our role as timekeepers: they keep our annual calendar in line with the seasons, year after year and century after century. Although leap day might have a bizarre historical origin and is accompanied by a series of urban legends that surround it, its very existence is predicated upon scientific, not superstitious, reasons.

Without a leap day, the physics of planet Earth would quickly cause the seasons to move out of phase with our annual calendar, and the equinoxes and solstices would drift around the days, months and seasons. In fact, if we simply added a leap day to our calendars every four years without fail, things wouldn’t line up very well, either, which is precisely what happened for the centuries under which humanity followed the Julian calendar. Only if we properly account for our planet’s axial rotation and revolution around the Sun can we keep our calendar correct, and that’s what leap day is all about. Here are seven of the most bizarre, but still true, scientific facts that everyone should know.

From one day to the next doesn’t correspond to just a 360 degree rotation of the Earth, but enough extra rotation to correspond to the Sun returning to the same position in Earth’s sky. Similarly, the duration of a lunar month isn’t simply the time it takes the Moon to revolve 360 degrees around Earth, but to return to the same position relative to the Sun as seen from Earth.

1.) Our calendar requires them, in part, because a “day” isn’t 24 hours long. Think about how our calendar is structured: we divide the year, the period in which Earth’s seasons repeat, into days, where the Sun rises in the morning, sets in the evening, and then rises again the next day. Now think about our Solar System: the Earth, as one of the planets, rotates about its axis while it revolves around the Sun.

• The definition of a day, if we were to base it on the Solar System, would be the time from sunrise to sunrise (or sunset to sunset, or mid-way between sunset and sunrise).
• The definition of a year, meanwhile, if we were to base it on the Solar System, would be the time it took Earth to return to the same position it began at in its orbit upon completing one full revolution.

Completing one 360° rotation is not the same as one day, as the Earth’s motion through space relative to the Sun means that rotating once on its axis actually leaves you a little bit “behind” where you needed to be.

Even before we understood how the law of gravity worked, we were able to establish that any object in orbit around another obeyed Kepler’s second law: it traced out equal areas in equal amounts of time, indicating that it must move more slowly when it’s farther away and more quickly when it’s closer. At every point in a planet’s orbit, Kepler’s laws dictate at what speed that planet must move.

However, because Earth’s orbit is an ellipse, not a circle, it moves faster in its orbit when it’s closer to the Sun, and slower in its orbit when it’s farther from the Sun. A full 360° rotation always takes the same amount of time: 23 hours, 56 minutes, and 4.09 seconds, but the additional amount you need to rotate, which varies throughout the year, means that each day is usually a few seconds longer or shorter than exactly 24 hours.

This graph shows the equation of time for a specific location on Earth. Where the slope of the graph is positive, days are shortening; where the slope is negative, days are lengthening; where the slope is zero (at the four locations marked), the day is precisely 24 hours. This happens four times per year in a latitude-dependent fashion.

In fact, only four days out of every calendar year have exactly 24 hours. And, if you were wondering: no, leap day isn’t one of them.

The Earth, moving in its orbit around the Sun and spinning on its axis, always defines “noon” and “midnight” in the same fashion: where the Sun’s height above or below the horizon is maximized. This moment in time doesn’t correspond to when Earth has rotated 360 degrees from the prior day, but rather closer to 360.9856 degrees, owing to the added effects of Earth’s motion around the Sun.

2.) A year is not defined by the Earth completing a revolution around the Sun. This is one that trips people up all the time: we commonly think of a calendar year as the time it takes planet Earth to complete a full revolution around the Sun. This is one definition of a year to astronomers — what we call a sidereal (si-DEER-ee-uhl) year — but it’s not the same as what we typically experience as a year: where the seasons recur in a predictable, periodic fashion. Remember, the Earth rotates on its axis as it revolves around the Sun, and due to a variety of gravitational forces, our planet’s axis precesses over time, meaning the axial tilt of about 23.5° doesn’t always point in the same direction, but makes a little circular shape itself on timescales of a little over 20,000 years.

This means that by the time one sidereal year (a complete 360° revolution of Earth around the Sun) has passed, the Earth is now oriented slightly differently with respect to the Sun versus how its axis was pointed the sidereal year prior. Instead of a sidereal year, our calendar needs to be based on the tropical year, which differs from a sidereal year by about 20 minutes, with the tropical year being slightly shorter than a sidereal year. In other words, the day and the year both are not defined simply by a constant celestial motion, but also by changes, as the Earth-Sun distance and the relative Earth-Sun orientation are inconstant.

The presence or absence of a February 29 on the calendar determines with great significance whether the equinox (or solstice) shifts forward or backward in time from the prior year’s equinox (or solstice). 2020 marked the first year since 1896 where the entire United States experienced a March 19 equinox, and 2024 will mark another year with a leap day and the earliest summer solstice since 1796. Leap days occurred every 4 years under the Julian calendar, but the Gregorian calendar revised that to remove some of the leap days (on years ending with “00” but not divisible by 400) to better keep track of time.

3.) There aren’t an even number of days in the year, no matter how you measure it. How many days are there in a year? Some say 365, but this year, it’s 366, right? Not quite. If you were to map out how many “experiential” days there are in a given year, including everything we know about:

• Earth’s rate of rotation,
• Earth’s axial tilt,
• Earth’s orbit around the Sun,
• the precession of Earth’s equinoxes,
• and the gravitational perturbations of all the planets, moons, and other objects in the Solar System,

you’ll find that there are 365.242188931 days in a true calendar year, to the best currently-known precision.

If we said, “There are only 365 days in a year, every year,” then our calendar would start to drift by nearly a quarter of a day each year. If we said, “Okay, every fourth year, we’ll add in a bonus day and call it leap day,” then that would average out to 365.25 days per year, which is better, but still not great. This is, in fact, the basis for the old Julian calendar, which endured for around 1600 years. Unfortunately, by the late 1500s, this became very noticeable, as our calendar had drifted by about 10 days from its original alignment with the solstices and equinoxes, so several days were actually removed from the calendar in one particular year (which varied by country) to bring the calendar back into alignment, signaling a switch to the current Gregorian calendar.

Although a great many countries first adopted the Gregorian calendar in the year 1582, it wasn’t until the 18th century that it was adopted in England, with many countries making the transition even later. As a result, the same date, as recorded in different countries, often corresponds to a different point in time. Whereas the first countries to adopt it in 1582 only needed to remove 10 days from their calendar, Russia, whose calendar was revised in 1918, needed to remove 13 such days.

4.) Our current, Gregorian calendar, complete with its prescription for leap days, isn’t quite perfect either. There’s only one big difference between our current (Gregorian) calendar and the one devised more than 2000 years ago (the Julian calendar) in terms of leap days: which years they occur in. Under the Julian calendar, every year had 365 days unless it was divisible by 4, in which case it had 366 days, including one leap day, which was February 29th. But under the Gregorian calendar, if your year ends in the numbers “00,” as in you’re experiencing the turn of the century, it’s only a leap year if that number is also divisible by 400. In other words, 2000 was a leap year, as was 1600 and as 2400 will be, but 1700, 1800, and 1900 weren’t, and 2100, 2200, and 2300 won’t be, either.

Instead of 365.25 days in a year, which the Julian calendar gave us on average, the Gregorian calendar then gives us 365.2425 days in a year, which is much closer to the actual number of days we experience in a year. In fact, whereas the Julian calendar drifted by about a day with each 150 years that went by, the Gregorian calendar won’t drift by a full day until around 3200 years pass. In fact, if we went one step further than the Gregorian calendar, and excluded every year that’s divisible by 3200 from having a leap day, our calendar, assuming Earth’s orbit doesn’t change in any way over time, wouldn’t be off by a single day until around the year 700,000.

The Moon exerts a tidal force on the Earth, which not only causes our tides, but causes braking of the Earth’s rotation, and a subsequent lengthening of the day. The asymmetrical nature of Earth, compounded by the effects of the Moon’s and Sun’s gravitational pulls, causes the Earth to spin more slowly. To compensate and conserve angular momentum, the Moon must spiral outward. It is for this reason that Earth will no longer have total solar eclipses after another 600 million years, and that the length of each day is getting longer as time progresses.

5.) Earth’s orbit actually is changing, which means our current system of leap days will need to be revised down the road. There’s a fact about Earth that almost nobody appreciates: our rotation rate isn’t quite constant, but is slowing down by a tiny, almost imperceptible amount. Over long periods of time, there’s one factor that’s going to dominate how Earth’s rotation rate changes: the fact that we have a large, massive moon to reckon with. Our moon doesn’t just exert a gravitational pull on the Earth, it pulls ever so slightly more on the part of Earth that’s closer to it than the part that’s in the center, and pulls even less on the part that’s farther away.

This creates a tidal bulge on the Earth, and as the Earth spins and the moon orbits around the Earth, those tidal forces from the moon cause two very small changes that occur together.

• Earth’s rotation rate, ever so slightly, slows down.
• And at the same time, the Moon, ever so slightly, spirals outward, farther and farther away from the Earth.

Earlier, we noted that for the Earth, a full 360° rotation always takes the same amount of time: 23 hours, 56 minutes, and 4.09 seconds. But it turns out that this effect — known as tidal braking — causes Earth’s rotation rate to slow down by about 14 microseconds per year. Over time, that’s really added up; looking back in time thanks to geologic features such as tidal rhythmites, we can determine that the day was:

• about 20 minutes shorter during the Cretaceous,
• a little under 22 hours long about 620 million years ago, in Precambrian times,
• and may have been as little as 6-to-8 hours long some ~4 billion years ago.

This means that, even now, Earth’s day is getting slightly longer. As time marches onward, we’ll need to add fewer and fewer leap days to keep our calendar in sync.

Tidal rhythmites, such as the Touchet formation shown here, can allow us to determine what the rate of Earth’s rotation was in the past. During the emergence of the dinosaurs, our day was closer to 23 hours long, not 24. Back billions of years ago, shortly after the formation of the Moon, a day was closer to a mere 6-to-8 hours, rather than the 24 we possess today.

6.) In about 4 million years, leap days will be unnecessary, and the calendar will contain exactly 365 days for a time. Tidal braking might be almost imperceptible on human timescales, but its effects — very importantly — are cumulative, meaning that they add up over time. (Although they’ve recently been abandoned, the idea of adding “leap seconds” was meant to counter the effects of Earth’s changing rotation, which is also affected by events such as earthquakes.) After another 4 million years have gone by on Earth, the length of one day will have lengthened by about 56 seconds: precisely the amount so that one tropical (calendar) year will require exactly 365.0000 days.

As the 4 million-year mark slowly approaches, we’ll gradually want to start removing leap days from the calendar, having them less and less frequently, in order to keep time with Earth’s orbit around the Sun. Roughly 4 million years in the future, we won’t need leap days any longer, as they’ll be unnecessary and would only pull the calendar out of sync with the seasons. Beyond that, we’ll need to begin skipping days in some sort of “reverse leap day” scenario, and then, over tens of millions of years, we’ll have to begin removing days from the calendar entirely.

When the Moon passes directly between the Earth and the Sun, a solar eclipse occurs. Whether the eclipse is total or annular depends on whether the Moon’s angular diameter appears larger or smaller than the Sun’s as viewed from Earth’s surface. Only when the Moon’s angular diameter appears larger than the Sun’s are total solar eclipses possible, a situation that will no longer be possible about 600-650 million years from now. Eclipses have been predictable phenomena for nearly 3000 years: since the time of the ancient Babylonians.

7.) The long-term changes in leap days coincide with the loss of total solar eclipses. It’s difficult to believe, but the same tidal braking from our moon that causes Earth’s rate of rotation to gradually slow causes the moon to spiral away from the Earth: it’s a consequence of the law of conservation of angular momentum. Both “spinning” and “orbiting” are types of angular momentum, and as the Earth’s spin slows down owing to the moon’s tidal forces, it gets transferred in a fashion that increases the Earth-moon distance.

You know what else depends on the Earth-moon distance? Solar eclipses, and in particular, whether the shadow cast by the moon actually falls on the Earth itself, leading to a total solar eclipse, or whether the shadow cast by the moon ends before it reaches the Earth, which results instead in an annular solar eclipse. Today, about half of our solar eclipses with perfect Sun-moon-Earth alignments are total and about half are annular (along with a few hybrid eclipses, which appear annular along parts of the Earth and appear total along other parts), but this ratio will shift with time. More eclipses will become annular than total with the passage of time, with Earth’s final total solar eclipse coming around 600-650 million years from now.

Along the center-line of an annular eclipse, during the moment of mid-eclipse, the “ring of fire” feature will create a perfectly circular annulus of the portion of the Sun that cannot be eclipsed by the Moon. This photo was taken during the May 2012 annular eclipse, and while only about 50% of all solar eclipses are annular on Earth today, in another 600-650 million years, they all will be, as the Moon continues to spiral away from the Earth due to tidal braking.

The need for leap days should not be underappreciated, as without them, Earth’s seasons would rapidly shift over time, as would the normally reliable dates for the equinoxes and solstices. With our current implementation for leap days, however, those dates never vary by more than a day or two, and remain stable over timescales of millennia. On longer timescales than that, however, we’re going to need to continue to revise our calendar and change our implementation of leap days, as the length of a day is constantly changing with time.

For now, however, this leap year means we simply get an extra day for 2024, and that when 2096 rolls around, we’ll have enjoyed a long streak of every 4th year being a leap year since 1904. However, 1900 wasn’t a leap year and 2100 won’t be either, so to those of you with February 29th birthdays — an estimated 5.5 million of you — enjoy celebrating your special day once every four years until then. After that, you’ll have to wait for eight of them to go by between 2096 and 2104!