Leap years, equinoxes and dates: A very short history of the calendar

To make a calendar, it’s necessary to define a “year”. That sounds easy enough – we all know that it takes about 365 days for the Earth to make one complete revolution about the sun. But what does that really mean? And where should we begin counting the days? It turns out that making a useful calendar isn't as simple as it seems.

One of the earliest known attempts to define a year happened long before we knew that the Earth really does circle the sun. About 6000 years ago, Egyptian astronomers realised that when the bright star Sirius rose just before sunrise, the Nile would soon flood the water-starved fields – and they discovered that there were 365 days between one of these beneficent dawn conjunctions of Earth, sun and star, and the next.

Measuring the time between two star conjunctions like this gives what astronomers call a “sidereal” or star-based year. So the 365-day year has a very long history, and many ancient peoples used it.

Today, we’re more likely to speak of 365¼ days, but even this more accurate measurement has a long history. For example, in 238 BCE the Egyptian ruler Ptolemy III initiated a 366-day year every fourth year, to average out that extra quarter of a day. It was a great idea, but the “leap” year didn’t really catch on until 46 BCE, when Julius Caesar added it to his own calendar reforms.

The story doesn’t end there, though, because Caesar’s “Julian” calendar – the prototype of our modern one – used a second way of defining a year, called the seasonal or “tropical” year. This is the time between two successive spring equinoxes.

Equinoxes happen when the sun appears to be “on” the equator as it “travels” around the Earth. They’re a good basis for a calendar, because they signal the change of seasons, when the sun appears to cross the equator from north to south at the southern spring equinox, and then from south back to north six months later.

But there’s a problem: the equinoxes are coming a tad earlier each year, so the sidereal and seasonal years aren't quite the same.

This phenomenon is called the “precession of the equinoxes”, and amazingly, it was discovered nearly 2200 years ago. Hipparchus of Nicaea compared ancient astronomical records and noticed that the background stars all appeared to be slowly moving in the same direction.

Picturing the universe as a “celestial sphere”, with the Earth at the centre and all the stars fixed to the surface, he made the inspired deduction that this drift in the position of the stars corresponded to a small rotation of the celestial sphere’s north-south axis.

Today, of course – post Copernicus, Kepler, and Newton – we say it’s the Earth’s axis (not the celestial sphere’s) that's pivoting about its centre, causing the illusion that the stars are drifting around us.

This means that the Earth is not only spinning about its axis each day, but the axis itself is slowly rotating, like that of a top. So the direction of north is changing – and this means that the points defining the equinoxes are also changing.

As the world turns

It takes about 72 years for the Earth’s axis to rotate through one degree – so it takes nearly 26,000 years to make one 360-degree circular turn. It’s a very slow spin!

For a number of years, however, scientists have been aware that additional factors are perturbing the axis’s precession, changing the direction of “north” and “south” in unexpected ways. These factors include gravitational changes on Earth due to melting polar ice sheets and changing amounts of continental groundwater.

So the universe is not a clockwork machine – the Earth’s axis wobbles a bit as it rotates, and astronomers have to take an average value for the length of the seasonal year. Today, this value is 365.2422 days – 0.0078 days less than the 365.25 days in the Julian calendar. Not enough to worry about, you’d think. Still, after about 128 years, this difference amounted to a whole day (because 1/0.0078 = 128.21). By the 16th century, it had become critical.

Many uneducated folk were terrified at having their days “stolen” from them, and suspected all sorts of evil intent by the pope and his “conjuring” mathematicians. 

One of the calendar’s key roles in that non-secular age was to pinpoint the date of Easter Sunday – the first Sunday after the first full moon after the northern spring equinox. Today, the March equinox usually occurs sometime on the 20th or 21st. In fact, 21 March had been the official Christian date of the northern spring equinox since 325 CE. Some 1255 years later, however, the seasons had moved ahead of the Julian calendar by about 10 days (1255 divided by 128.21 is approximately 10).

In other words, by 1580 the actual spring equinox occurred around 11 March by the Julian calendar, while the official equinox was 10 days later.

Pope Gregory XIII had already commissioned his best mathematicians and astronomers to construct a new calendar. But when it was finally finished it caused considerable popular outrage, because it meant that 10 days appeared to be “lost” from people’s lives before the new calendar could begin. The pope decreed that on the day after 4 October, 1582, the calendar would read not 5 October, but 15 October.

Many uneducated folk were terrified at having their days “stolen” from them, and suspected all sorts of evil intent by the pope and his “conjuring” mathematicians. But this 10-day jump brought the date of the actual northern spring equinox back to around the official date of 21 March.

In response to Gregory’s initiative, Queen Elizabeth I consulted with her best astronomers, who approved the new “Gregorian” calendar. It had a 365-day year plus leap years, but the 366-day years no longer occurred every four years; rather, leap years were those whose date was divisible by four (as in the Julian calendar) except for century years (1600, 1700, and so on), which must be divisible by 400 to qualify as a leap year.

It sounds convoluted, but with an average calendar year of 365.2425 days, it will take 3000 years for the Gregorian calendar to run ahead of the seasons by just one day. (The difference between 365.2425 days and the seasonal year of 365.2422 days is just 0.0003 days, and 1/0.0003 = 3000.)

Public outcry stayed Elizabeth’s hand – an outcry due more to Protestant prejudice than to superstition. Protestant regions on the Continent also rejected the change, so that although the pope prevailed in most Catholic countries within a few years, most of the Protestant jurisdictions took a century or more to accept the Gregorian calendar. It wasn't adopted in Britain until 1752.

Today, it is virtually universally accepted for everyday secular use. Some critics would like to simplify it, but still, it’s a marvellous invention. And, along with the earlier calendars, it’s a fascinating part of the extraordinary history of astronomy.