A Leap into the Unknown

Monday  29th February 2016 is a day that shouldn’t really exist! Of course, the Universe doesn’t follow our calendar, so the reason behind its existence is not a physical one. Instead, it is an artefact of the irregular way in which we, as a society, measure the passage of time.

2016 will have one more day than 2015 and 2017, and indeed every other year that isn’t a multiple of four. Everyone knows about these – they’re called ‘leap years’; the name thought to come from the late 14th century, when the days on which fixed dates in the year, e.g. Christmas Day, advanced by two instead of the usual one (i.e. Tuesday to Thursday, ‘leaping’ over Wednesday).

Most people probably also know the reason this happens, which is down to the mismatch between the length of our calendar (365 days), and the length of time it actually takes for the Earth to orbit the Sun (365.25 days). Thus, after every four years have passed, the two calendars will be out of sync by one whole day. Our calendar will be behind, so by adding an extra day to it every four years and making it 366 days long, synchronisation is restored and the problem is solved.

Except it’s not quite as simple as that.

The problem lies in the fact that while it takes approximately 365.25 days for one Earth orbit, that’s not an exact measurement. Here, it gets a little complex, with many different measurements for the length of a year possible, depending on a multitude of variables such as the position of the Moon and its eclipses, or the elapsed time between the Earth’s perihelion, i.e. when it is at its closest point to the sun in its non-circular orbit.

Perhaps the most basic and intuitive measurement is the sidereal year, which is measured with respect to background stars (i.e. one year has passed when the stars are observed to be in the exact same position they were before). However, another measurement, the tropical or ‘solar’ year, is the generally accepted measurement. The tropical year is measured with respect to the change of seasons, i.e. the difference between equinoxes, but due to the irregularity of the Earth’s orbit, this turns out to be about 20 minutes shorter than the sidereal year.

It is not quite as simple as the length of time it takes for the Earth to orbit the Sun (365.25 days)

    “It is not quite as simple as the length of time it takes for the Earth to orbit the Sun (365.25 days)”

The length of a tropical year (as of 2010) is 365.2421891 days, just slightly less than the usually quoted 365.25. This tiny disparity means that adding an extra day every four years in order to account for the extra 0.25 means overshooting by about three days every 400 years. This might seem like too long a period to be worth worrying about, but the current Gregorian calendar was established in 1582, and since then three would-be leap years have been removed to maintain synchronization: the years 1700, 1800 and 1900 (2000 remained a leap year).

A similar idea lies behind the introduction of ‘leap seconds’, in that they too are used to keep things synced up. Instead of matching with the Earth’s orbit around the Sun, however, leap seconds are used to account for the changing rotation of the Earth, which is actually slowing by minuscule fractions of a second every year. This slowing is primarily down to the gravitational pull of the Moon constantly tugging at the Earth in a process known as ‘tidal friction’, but is also due in part to geological activity beneath the planet’s surface. This means Earth days are getting slightly longer all the time, and leap seconds are added whenever necessary to account for this. You may remember the most recent leap second being introduced in June 2015, causing the final minute of that month to be 61 seconds long.

So, the result is that we’ll be getting a whole extra day of 2016; let’s hope it doesn’t rain!

Tom Barratt

Header image by Chris Tse via Flickr
Orbit Image by Image Editor via Flickr

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Editor for the Science Section of University of Nottingham's IMPACT Magazine.

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