How humanity’s most enduring calendar failed us all

Galileo died on January 8, 1642, and on Christmas Day of that same year, Isaac Newton was born. Back in 1616, two extremely famous playwrights (among their other literary endeavors), Miguel de Cervantes and William Shakespeare, died just one day apart: April 22 for Cervantes, and April 23 for Shakespeare. And the famed Plymouth Rock, a granite slab in honor of the first solid ground that the Pilgrims stepped on upon disembarking from the Mayflower, is presently inscribed with “1620” in honor of the year that legendary step was taken: December 26, 1620.

But, upon closer inspection, none of these facts are true. While physicists often refer to Christmas Day as “Newtonmas” in honor of Isaac Newton’s birth, that’s only true because England, unlike the rest of the world, hadn’t yet switched over to the Gregorian calendar; Newton’s actual birthday was January 4, 1643 according to our modern timekeeping practices. Cervantes and Shakespeare actually died 11 full days apart, not just one, as their countries were on different calendars at the time. And the Plymouth Rock landing actually occurred on January 5 of 1621 according to our modern calendar, not “1620” as written.

The reason for all of this historical confusion? A flawed calendar that dates all the way back to Julius Caesar. Here’s the science behind how humanity’s most enduring calendar, the Julian calendar, failed us all.

This image shows a clever one-page calendar view for the current year (which is also a leap year): 2024. Note that the monthly patterns differ from how they behave in a non-leap year, displaying a new pattern unique to leap years, corresponding to the fact that February has 29 days instead of 28.

Imagine that you weren’t here on planet Earth, but rather were in an unusual position: millions of miles up above the Sun’s north pole, looking down on the Solar System. As you observed the Earth, the third planet from the Sun, orbiting around it, you’d easily be able to measure how much time it took for that planet to complete a full 360° revolution around the Sun. That’s one way to measure a year, and to astronomers, that’s known as a sidereal (sy-DEER-ee-al) year, which, unsurprisingly, takes a little bit over 365 “days,” where a day is defined by the amount of time it takes Earth to spin 360° about its axis.

Unfortunately, that simple definition doesn’t quite match up with how we experience the year here on Earth. To any inhabitant of planet Earth, it isn’t a 360° revolution that determines the year, but rather the recurrence of the seasons: the conditions that a terrestrial observer on Earth experiences. That lines up with what astronomers call the tropical year, which recurs from:

• spring equinox to spring equinox,
• summer solstice to summer solstice,
• autumnal equinox to autumnal equinox,
• or winter solstice to winter solstice.

Basically, if you took a look at Earth’s axis and said, “this is how it’s oriented, with respect to the Sun, right at this moment,” a single tropical year would mark the very next time that the Earth’s axis returned to that exact same orientation.

Just 800 years ago, perihelion and the winter solstice aligned. Due to the precession of Earth’s orbit, they are slowly drifting apart, completing a full cycle every 21,000 years. Over time, the Earth drifts slightly farther from the Sun, the precession period increases, and the eccentricity varies as well. The most accurate measure of the “year,” as experienced by Earthlings, is to go from either equinox-to-equinox or solstice-to-solstice, but this does not correspond to a single 360 degree revolution of Earth around the Sun.

If you wanted to construct a calendar that kept time accurately over long periods of time, you’d have to ask yourself the right question: how long, precisely, is the tropical year, and what calendar system would lead to a definition of a “year” that matched up to a tropical year over long periods of time?

The length of the tropical year has been measured to extraordinary precision, and is known accurately to a fraction-of-a-second. In terms of the amount of time it takes to make up one Tropical Year today, it’s precisely 365.24219 days. In more conventional terms, that’s 365 days, 5 hours, 48 minutes, and 45 seconds.

This, quite notably, is about 20 minutes and 24.5 seconds shorter than a sidereal year, as the Earth’s equinoxes (i.e., the orientation of our axial tilt) very slowly precesses with respect to the Earth’s orbit around the Sun. On timescales in excess of 20,000 years, Earth’s axial orientation shifts in a circular pattern, which causes where our celestial “north” and “south” poles are to change over time. While today, Polaris marks the North Star (to within 1°), the pole stars in both hemispheres have changed significantly, and periodically, over time. 5000 years ago, when the Egyptian pyramids were being constructed, the star Thuban, in the constellation of Draco, was the northern hemisphere’s pole star instead.

Today, in the year 2024, Polaris makes an excellent “North star,” as it’s located within about 1 degree of the celestial north pole. As Earth’s axis precesses, the presence and properties of a pole star change; 5000 years ago, the star Thuban in the constellation of Draco was an excellent pole star for humanity. This precession plays an important role in determining the true number of days in an actual calendar year, but plays practically no role in the total amount of heat that Earth receives from the Sun.

However, these details — and these levels of precision — are relatively new assets to human knowledge. Thousands of years ago, it was known that the lunar calendar (based on the number of full moons in a year) didn’t line up with the solar calendar (our proxy, before we knew about the structure of the Solar System, for the tropical year), and so most calendrical systems typically consisted of 12 full moons, or lunar “months,” with an occasional 13th “intercalary” month inserted into the year to keep the lunar and solar calendars aligned.

The problem with this system, back in the era of the Roman Republic, was actually political: abuses of power led people with political aims to either grant or deny the insertion of an intercalary month dependent on who was in power. In the year 46 B.C.E., then-consul Julius Caesar proposed a reform: let the calendar be governed by the Sun, i.e., a solar calendar, to free it from the concerns of human tampering. The result, taking place on January 1, 45 B.C.E., was the adoption of the Julian calendar, which assigned 365 and ¼ days to the year: with 365 days to most years and an extra “leap day” to every fourth year. This approximation wasn’t a Roman invention, but had been known to the Egyptians for more than 1000 years already back in Caesar’s time.

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.

For approximately the next 1600 years, a large portion of the world, including nearly all of what we know as the “western world,” adopted the Julian calendar (or a nearly-identical variant of it) in an effort to keep time in a uniform fashion. However, by the middle of the second millennium of the Common Era, it had become notable that the way Earth experienced the year — governed by solstices and equinoxes — had drifted considerably with respect to their initial calendar dates within the Julian calendar.

• The winter solstice, originally occurring on the 25th of December in the Julian calendar, was now occurring in the first half of the month.
• The spring equinox, originally occurring in late March, was now occurring in the first half of March: on March 10th, in fact.
• The summer solstice had also shifted from the second half of June to the first half of June,
• and the autumnal equinox, originally in late September, was now happening in the first half of September.

The culprit was the very small mismatch between the 365.25 days assigned to the “average” year by the Julian calendar, versus the actual length of the tropical year on Earth of 365.24219 days. This difference, although small, really adds up over timescales of more than 1000 years.

The Earth, moving in its orbit around the Sun and spinning on its axis, appears to make a closed, unchanging, elliptical orbit. The amount of daylight at any location on Earth depends on both the latitude of the observer and the tilt of Earth’s axis relative to the Sun.

That tiny difference might only correspond to an average 10.8 minutes per year, but after some 1600 years had passed, that had accumulated to put the Julian calendar and the actual tropical year out of sync by around 12 full days. Either humanity was going to have to get used to a “drifting” calendar, where the seasons grew more and more out of sync with the calendar from their initial placement, or a new type of calendar system would have to be adopted, with some sort of “shift” imposed to put the calendar and the actual experiential year back into their original, intended configuration.

The next great leap in refining humanity’s calendar came in the 16th century: with the invention and promulgation of the Gregorian calendar. Pope Gregory XIII, in 1582, put forth a new calendar which swiftly overtook the Julian calendar in many parts of the world. In order to better align our calendar with the actual tropical year, the way we insert “leap days” was changed. Instead of occurring every 4 years, as in the Julian calendar, leap days would only be inserted every 4 years except for years that ended in “00,” marking a turn-of-the-century. Only if those years were divisible by 400 would they get a leap day; the year 2000 did, but 1900 didn’t and 2100 won’t.

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.

That reform marked a huge improvement: instead of the 365.25 days-per-year that the Julian calendar brought, on average, the Gregorian calendar delivered a more accurate 365.2425 days-per-year, averaged over the centuries. Compared to the actual length of a tropical year, 365.24219 days, the Gregorian calendar is only off by about 27 seconds per year. This means, whereas the Julian calendar was pulled out-of-sync from the tropical year by one day roughly every 128 years, it would take some 3200 years for the Gregorian calendar to drift out-of-sync from the tropical year by even one day.

(Remarkably, if we added one small additional modification — that the years 3200, 6400, 9600, and all other years divisible by exactly “3200” wouldn’t get leap days — it would then take somewhere around 700,000 years for this new calendar to drift a single day out-of-sync with the tropical year.)

But in 1582, when Pope Gregory XIII put out his calendrical reform, there was another issue to deal with: the fact that the “old” calendar and the actual solar/tropical year were already misaligned by a significant amount. Although it was controversial, the decree was that, since “leap days” had been incorrectly added to 12 calendar years by this point under the Julian calendar:

• 100,
• 200,
• 300,
• 500,
• 600,
• 700,
• 900,
• 1000,
• 1100,
• 1300,
• 1400,
• and 1500,

the “fix” would be to remove some of them.

Starting in 1582, the Gregorian calendar began to displace the less-accurate Julian calendar all across the world. In order to accommodate this change and account for the mismatch induced by Julian calendar drift, dates needed to be removed from the calendar to allow humanity to “catch up” to the Earth. In 1752, the UK and its territories (including the now-USA) made the switch, having a September with 11 days missing in that particular year.

For many countries across the world (particularly in western Europe), including modern-day Italy, Spain, Poland, and Portugal, the resolution was that the “old” Julian calendar would continue to be used until October 4, 1582 (which was a Thursday), and then the next day (which would still be assigned as a “Friday”), would fall under the “new” Gregorian calendar system, but would be October 15, 1582. In other words, the 10 days from October 5, 1582 to October 14, 1582, never existed; they were omitted in order to allow the calendar year and the actual seasons to sync back up again. (Historically, these dates were chosen for religious reasons: they were the days that had the fewest feasts of saints to them.)

This “new” system of the Gregorian calendar quickly gained worldwide acceptance and came into use. Later in 1582, France and the Netherlands adopted the new calendrical system. In 1583, Austria, Switzerland, and Germany joined them. But many countries, particularly countries with large non-Catholic populations, resisted adopting the new system despite its superiority as a calendar.

The protestant parts of Germany, the Netherlands, and Switzerland, along with all of Denmark, Norway, and Iceland, didn’t adopt the Gregorian calendar until 1700. England (and its colonies, such as the modern-day USA) didn’t follow suit until 1752. Sweden and Finland adopted the Gregorian calendar in 1753, Japan in 1873, Egypt in 1875, and Russia adopted it in 1918. (Which is why the “October revolution” is so named, despite beginning on November 7, 1917, under the Gregorian calendar.) Greece became the final European country to make the change, back in 1923.

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.

The countries that switched later on, in order to get back into sync with the rest of the world, had to remove more than 10 days from their calendar, dependent on the number of Julian leap days that were inserted where the Gregorian calendar had none.

• In the United Kingdom and its then-colonies, because the year 1700 had passed, 11 days needed to be removed: September 3-13 of 1752.
• In Egypt and Japan, the year 1800 had also passed, and so 12 days had to be removed from their calendars when they switched.
• In Russia, because the year 1900 had passed prior to their adoption, 13 days had to be removed, and February 1-13, 1918 never existed there.

And for the places in the world (including a number of Orthodox churches and other religious calendars) that still use the Julian calendar for anything, the Julian dates remain 13 days out-of-sync with the modern (Gregorian) ones, but will drift to becoming 14 days out-of-sync as February 28 transitions to March 1 in 2100, as that will be a leap day on the Julian but not Gregorian calendars.

If we use modern, Gregorian dates for all parts of the world equally, we discover that many of the “facts” we learned about history didn’t occur when we were taught. Cervantes and Shakespeare actually died 11 days apart, not 1. Isaac Newton wasn’t born on Christmas in 1642 (the year Galileo died) but rather on January 4 of 1643. And the Plymouth Rock landing took place on January 5, 1621, rather than in 1620.

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.

Today, given the structure of the Solar System and our knowledge of gravity, it turns out there’s even more to the story than just picking a single calendar scheme that best matches up with the actual tropical year. Over time, because the Earth has a large moon and spins on its axis, there are tidal, frictional forces at play between the Sun-Earth-Moon system, which causes Earth’s rotation to slow, its day to lengthen, and also for the Moon to spiral out away from the Earth over time. The difference from one year to the next might be small — compared to precisely one year ago today, our planet takes an extra 14 microseconds to complete a full rotation — but those tiny differences inevitably add up over time.

While there are 365.24219 Earth days in a tropical year right now, that number is changing over time as Earth’s rotation continues to slow. In another 4 million years, we’ll have to remove leap years entirely, as a “longer” day will mean there will be precisely 365.0000 Earth days in a tropical year. Beyond that point, we’ll have to introduce negative leap days to keep our calendar in sync with the seasons. Some 21 million years from now, that number will drop to 364.0000 Earth days in a tropical year, and around 200 million years from now, Earth’s rotational period will lengthen so severely that it will overtake Mars for being the planet with the third-longest rotational period in the Solar System.

The Julian calendar held sway for some 1600 years, and while the Gregorian calendar is an improvement, it won’t be good forever. If we can survive, as a species, for thousands of years to come, we may want to consider a calendar that evolves along with our planet. It’s the only way to keep the tropical year and our way of marking time in sync, even as the physical properties of the Solar System change with time.