A leap of faith

The Setting of the Sun Over the Pacific Ocean as seen from the International Space Station.
Credit: © NASA
The Setting of the Sun Over the Pacific Ocean as seen from the International Space Station.
A leap of faith

Civil timekeeping is founded on astronomical cycles: Our year is based on the time it takes Earth to orbit the Sun, and our days are based on the period of Earth’s rotation on its axis. But these cycles don’t relate to each other exactly, which leads to divergences...

Not as simple as it sounds

Our 24-hour solar day is defined as the period between successive sunrises, so in a calendar year we expect to count 365 sunrises, which should take 8 760 hours. But using a chronometer to accurately measure the time it takes for Earth to orbit the Sun, we find it actually takes 5 hours, 48 minutes and 46 seconds longer—nearly one quarter of a solar day. This means that every four years, our 365-day calendar comes up short by one day; so rather than add an extra quarter-page to calendars each year, we skip four years and add a 29th day to February, hence the term “leap year”. Sounds easy enough.

This implementation dates back to the time of Julius Caesar who, following the advice of the astronomer Sosigenes of Alexandria, organised the Roman Republican calendar to ensure that dates remained in sync with the seasons.

But adding a day every four years is a bit too much, and after 100 years our calendar winds up being a day too long. The solution is elegant… we omit adding leap days to century years, so 1700, 1800, and 1900 were not leap years. But even then, our calendar still gets out of sync and winds up one day short every 400 years. So contrary to the previous rule, whenever the century year is divisible by four hundred, a leap day is added: For example, 1600, 2000, and 2400 are leap years.

Close enough

Even with all these rules in place the calendar is still off, but by just one day in 8 000 years… all because the period of Earth’s orbit around the Sun isn’t evenly divisible by the period of a solar day. But one day in 8 000 years represents an error of just 0.0001%... and that’s close enough for civil timekeeping purposes!

Greater accuracy based on the period of Earth’s orbit and rotation is futile, due to gravitational anomalies. Earth’s rotation varies randomly by a few milliseconds per day; and the day is getting longer by 0.001 seconds per century. Besides, 8 000 years from now I’m quite sure we won’t be flipping calendar pages, or checking our watches. We’ll have something more… futuristic?

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1 Comment(s)
Jack's picture

Hi Louie!

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