As Earth’s rotation slows, how long will it be before the rules for deciding on leap years have to be revised?
Chris Daniel
Glan Conwy, UK
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Leap years are needed because it takes Earth about 6 hours, or a quarter of a day, more than 365 days to complete one orbit round the sun. An extra day in the calendar every four years allows Earth time to catch up with where it should be. If this weren’t done, the seasons would gradually get earlier in the year.
Over a period of 400 years, a total of 96.88 days need to be added to the calendar. The nearest whole number to this is 97. To achieve this, a leap year is omitted if the year is divisible by 100 but not by 400 – hence the years 1800 and 1900 weren’t leap years, but 2000 was.
However, even this pattern won’t be accurate enough over a longer period, and in the year 3600, the extra day may have to be omitted again to keep the planet and the calendar aligned.
Earth’s daily rotation on its axis is slowing at a rate of nearly two-thousandths of a second every century. This means that while Earth’s orbit around the sun will still take the same length of time, each day will gradually become longer than 24 hours.
At the end of each year of these longer days, there will be a decreasing fraction of a day remaining for Earth to complete its orbit round the sun, so it will take more time to accumulate the need for a leap year. The first leap year to disappear completely would be the regular one at the end of a century divisible by four, as only 96 leap years would be required every 400 years instead of 97. This would happen in 29,000 years, when Earth’s day will be half a second longer than it is now.
Our calendar years are too long by 0.0003109 days, so, after 3216 years, five months and a few days, we will be one day ahead
Hillary Shaw
Newport, Shropshire, UK
Earth’s days are getting longer by 1.8 milliseconds per century. But a leap year change will first be necessary because of another issue: the Gregorian calendar year is 365.2425 days, while an actual year is 365.2421891 days long.
This slight mismatch means our calendar years are too long by 0.0003109 days, so, after 3216 years, five months and a few days, we will be one day ahead – what we would call 2 January in the year 5240 should in fact be 1 January. We could then institute an amendment to the Gregorian calendar, namely: “If the year is divisible by 3200, have an extra leap day.” So, in such years, we would have a 30 February. Call this the Anthropocene calendar.
Lengthening days should, in theory, save us from the aberration of 30 February – except this effect is rather too small. By the year 9600, our day will be just 0.11 seconds longer. From our current 86,400 seconds in a day, a lengthening of the day by 1.8 milliseconds extra per century means we will only lose one day of our annual calendar in 51.84 million years. So this 3200-year extra leap day rule would need to remain in force until our days had lengthened by 1/3200th of a day, which will take 16,200 years.
The good news is we will only ever need five “February 30ths” before we can revert from the Anthropocene calendar to the Gregorian one in 19,200. By 12,900,000, we will have lost a whole quarter day in the year, now just 365 days long, and can have a very simple calendar where every February has just 28 days in it. In 70 million years, there will be just 364 days in the year (and every February will have just 27 days).
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