Why do we have leap years?

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📓 The short answer

Leap years exist because a full orbit around the Sun takes 365.242189 days, so we add extra days to keep our calendar aligned with the seasons. The Gregorian calendar uses specific leap year rules to stay closely synced with the solar year, skipping three leap years every 400 years for better accuracy.

📚 The long answer

It takes 365 days for the Earth to travel around the Sun, right?

Wrong. It actually takes 365.242189 days for a full orbit, or about 5 hours, 48 minutes, and 56 seconds longer than the common, Gregorian calendar year.

If we didn't account for this extra 1/4ish of a day, our calendar would be way off after a while. Over 700 years, this discrepancy would add ~169 days, eventually shifting Northern Hemisphere summers into December.

graphic showing the difference in length between the solar year, the common year, and the leap year — Not to scale.

Adding an extra day in years divisible by four (e.g. 2024) helps compensate for the roughly 1/4-day difference between the common year (no leap year) and the solar year (actual orbit). But simply adding an extra day every four years is not precise enough...

Why are three leap years skipped every 400 years?

If we held to a "have a leap year every four years" protocol, we'd still end up pretty out of sync with the solar year after a while.

That's because adding a day every four years makes the average length of a year 365.25 days, which is ~11 minutes and 15 seconds longer than the true solar year. So after four years, we'd have an extra ~45 minutes, and after 129 years, we'd be off by ~1 day. That's closer to the solar year than no leap years at all but still not close enough.

When the Gregorian calendar was introduced in 1582, it got closer to solving this problem by instituting three rules for leap years:

Leap years occur in years divisible by four (e.g. 2028).
Leap years are skipped in years divisible by 100 (e.g. 1900).
But leap years do occur if they are divisible by 100 and 400 (e.g. 2000).

That means that every 400 years, three leap years are skipped. So from 2000-2400, leap years will be skipped on 2100, 2200, and 2300.

The date of the northern summer solstice between 1750 and 2250. The graph shows the date (in GMT) of the northern summer solstice (the moment the sun reaches it northernmost position in the sky, or the beginning of summer in the northern hemisphere) through the years. As the summer solstice occurs on the same astronomical date each year (although changes may occur on much larger time scales), the graph basically shows the difference between real, astronomical time and the Gregorian calendar. Each year, the Gregorian calendar is approximately 0.24 days faster than the astronomical calendar, which is corrected by a leap day once every four years. This 4-year cycle is clearly visible in the graph. To compensate for the largest part of the remainder of the difference, there is no leap year in 1800, 1900, 2100, 2200, as can be clearly seen in the graph, too. Note that the summer solstice in 1800 and in 2200 are not on equal dates; this shows that the leap year compensation as described before is not perfect and more complicated schemes are necessary to keep the Gregorian calendar synchronized over even longer time scales. However, the Gregorian calendar was actually intended to synchronize with the vernal equinox, not the summer solstice, which is not exactly the same thing over the medium term... — Each dot represents the date of the northern summer solstice (in GMT) from 1750 to 2250. You can see the 4-year pattern created by leap years, where the calendar catches up a bit by adding an extra day. But the overall trend still drifts downward: the Gregorian calendar runs about ~0.24 days too fast each year.

"Gregoriancalendarleap solstice" by BasZoetekouw is licensed under CC BY 3.0.

It isn't a perfect solution though. Following these rules over 400 years will make the average year length 365.2425 days, a tiny bit longer but pretty darn close to the true solar year of 365.242189 days. It'll take thousands of years for us to need more calendar tinkering.

🧠 Bonus brain points

Do other calendars have leap years?

Yes, but they don't operate on the same Gregorian system. The Chinese calendar runs on the lunar cycle, so each month is 29 or 30 days. Every 2-3 lunar years, a leap month is added to keep up with the Gregorian calendar. The Hebrew calendar also runs on the lunar cycle and includes a leap month.

The Hindu calendar is lunisolar calendar, tracking both the Earth's orbit around the Sun and the Moon's orbit around the Earth. Both leap months and days are added to correct for any misalignment.

Many other calendars have also included leap days and months to adjust against the solar year cycle.

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Caitlin

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🌐 Wikipedia article of the week

Athletics at the 1904 Summer Olympics – Men's marathon

"The men's marathon at the 1904 Summer Olympics in St. Louis, United States, took place on August 30 of that year, over a distance of 24 miles 1500 yards (40 km).

The race was run during the hottest part of the day on dusty country roads with minimal water supply; while 32 athletes coming from seven nations...competed, only 14 managed to complete the race, which was a bizarre affair due to poor organization and officiating.

While Frederick Lorz was greeted as the apparent winner, he was later disqualified as he had hitched a ride in a car for part of the race. The actual winner, Thomas Hicks, was near collapse and hallucinating by the end of the race, a side effect of being administered brandy, raw eggs, and strychnine by his trainers. The fourth-place finisher, Andarín Carvajal, took a nap during the race after eating spoiled apples."

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💡 Today You Should Know

Why do we have leap years?

Why do we have leap years?

📓 The short answer

📚 The long answer

Why are three leap years skipped every 400 years?