Friday, January 22, 2021

# Explained: Why 2020 is a leap year, and why our great-grandparents skipped one of them

## What is the reasoning behind the rule for leap years, the exceptions to the rule, and the exceptions to the exceptions?

Leap years were introduced because the calendar year was short, but they ended up making the average calendar year longer than the solar year. The difference: a small matter of 11 minutes and 14 seconds.

Saturday is February 29, a date that comes approximately once every four years. Approximately, not exactly, for there are exceptions to the leap year’s cycle of four years.

## Rules and exceptions

Leap years are always multiples of four — 2016, 2020, 2024 — but a year that is a multiple of four is not always a leap year. There are exceptions, such as 1900 and 2100, both multiples of four, yet neither a leap year.

A year ending with 00 is obviously a multiple of four, but is usually not a leap year. These are the exceptions. But again, there are exceptions to such exceptions. For example, 2000 ended with 00 but remained a leap year. As a result, many people alive today — except some who are very young — are likely to spend their lifetimes without skipping a leap year. Our ancestors skipped a leap year in 1900, while our descendants will skip one in 2100.

What is the reasoning behind the rule for leap years, the exceptions to the rule, and the exceptions to the exceptions?

## Why have leap years

Our solar calendar is supposed to reflect one orbit of Earth around the Sun. This helps in anticipating the seasons, maintaining crop cycles, setting school schedules, etc.

Earth takes 365 days and a few hours to orbit the Sun, which is why a year is usually 365 days long. The actual period of the orbit is close to (not exactly) 365 days and 6 hours, which means that the calendar year is about 6 hours shorter than the actual solar year. To compensate, we have leap years.

The leap year was introduced by scholars engaged by Julius Caesar in 46 BC, and made more precise from 12 AD. The reasoning went thus: if the calendar year is 365 days long, it is missing 6 hours. These 6 hours keep adding up, year after year. By the end of 4 years, the calendar years will have missed a total of 24 hours, or one full day. So, why not add an extra day once every four years, the scholars reasoned.

Thus, the Julian calendar had a year that was usually 365 days long, with a 366th day added once every four years. It appeared to make sense. Only, it was never going to work in the long run.

This is because 365 days and 6 hours is an approximation. It is a very small approximation, but even these tiny errors were going to add up one day.

## The errors pile up

To be more precise than earlier, Earth completes one orbit in 365 days, 5 hours, 48 minutes and 46 seconds. However, with three years of 365 days and one leap year of 366 days, the average length of a year in the Julian calendar was 365 days and 6 hours. This was longer, if ever slightly so, than 365 days, 5 hours, 48 minutes and 46 seconds.

In effect, the leap year formula was an overcompensation. Leap years were introduced because the calendar year was short, but they ended up making the average calendar year longer than the solar year. The difference: a small matter of 11 minutes and 14 seconds.

The leap year was introduced by scholars engaged by Julius Caesar in 46 BC, and made more precise from 12 AD. (Thinkstock)

Minute by minute, second by second, the errors piled up, year after year, century after century. In the 16th century, it was calculated that the calendar years until then had accumulated 10 extra days. In 1582, Pope Gregory XIII ordered a drastic compensation by dropping 10 days from the calendar, and October 4 that year was followed by October 15 the very next day.

The need was for further reform, so that the minutes and seconds would not accumulate again in the future. The obvious thing to do was to reduce some leap years —about one leap year every century. And the obvious candidates were the years ending with 00. But if all “00 years” ceased to be leap years, calculations showed, it would result in another over-compensation. Therefore, some “00 years” needed to remain leap years.

Eventually, the reform led to the Gregorian calendar, which we follow today. The formula:

🔴 A year that is a multiple of 4 is a leap year; except:

🔴 A year ending with 00 is not a leap year; except:

🔴 A “00 year” in which 00 is preceded by a multiple of 4 (1600, 2000, 2400 etc) remains a leap year.

That is why 1900 and 2100 are not leap years, but 2000 is one.

## Is that it, finally?

It can never be perfect. We try to clock the Earth’s orbit precisely down to the last second, yet we follow a calendar with a whole number of days. The calendar today is about 26 seconds off from Earth’s orbital period, which adds up to one full day in 3,320 years.

There have been proposals for a future correction — remove a leap year once every 4,000 years, or once every 3,200 years. Years 3200 and 4000, however, are still a long way away. As of 2020, not everyone is bothered.

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