One Giant Leap

February 29 has come around again.  It’s Leap Year Day.  Why do we insert this day into the calendar every four years?  Why do we subject a small but significant number of people to only one quarter of the number of actual birthdays as the rest of us?  This extra day represents our species’ attempt to keep our calendar "in sync" with the yearly motion of our home world around our star, the Sun. 

As an astronomer, to me the story of the leap year day is fascinating.  The current best astronomical definition of a year is what we call the tropical year which, in the year 2000, had the value of 365.2421897 days.  (The tropical year is defined as the time between successive northward crossings of the equator by the sun, around the time of the autumnal equinox near 21 March).  Notice the fractional bit is not quite 0.25 days.

It has been known since ancient times that the Earth year was approximately 365 and a quarter days.  In Ancient Rome, Julius Caesar instituted the Julian Calendar consisting of three years of 365 days with every fourth year being a leap year of 366 days.  This gave the calendar an average year length of 365.25 days.  But this also differs from the true astronomical value and falls behind the motion of the Earth by one whole day approximately every 128 years. 

By the 16th century this drift had stretched to 10 days and was becoming intolerable, especially for the Church which needed to calculate the date for Easter.  So, Pope Gregory XIII stepped in and appointed the German mathematician Christopher Clavius and the Calabrian astronomer and physician Aloysius Lilius to fix the calendar.  Their first step was to nothave a leap year every 100 years.  This reduced the average calendar year by 1/100 = 0.01 days from 365.25 to 365.24 which is much closer to the actual value.  However, this was still not quite right, and the error would amount to one whole day every 457 years.  So, their final step was to restore the leap year day every 400 years.  This would add 1/400 = 0.0025 days to 365.24 days, making a new average year length of 365.2425 which is very close to the astronomical value of 365.2421897 days.

At that point, Pope Gregory XIII said “make it so” or something like that, and thus the Gregorian Calendar, which we use to this day, was introduced. Under this system, the century years 1700, 1800 and 1900 were not leap years, but 1600 and 2000 were leap years.  The year 2100 will not be a leap year.  The Gregorian Calendar has 97 Leap Year days every 146,097 days.

But what to do about the 10-day drift in the old Julian Calendar?  Clavius recommended to the Pope that the correction be applied in one go, and Gregory agreed.  So, in Rome, the last day of the Julian Calendar, Thursday, 4 October 1582 was followed by the first day of the Gregorian Calendar, Friday, 15 October 1582.  Yep, ten days were wiped from the calendar that year.  Interestingly, the Gregorian Calendar was not adopted across Europe at the same time, with different countries introducing the new calendar at various times over the next few centuries.  Imagine the chaos that caused between countries.

But how good is this new calendar which deviates from the astronomical value by only 0.0003103 days per year?  This tiny error will now take almost 3,223 years to accumulate one whole day.  It looks like Clavius and Lilius have done what, in technical terms, we astronomers would call a “Pretty Good Job”.  (For their efforts, both Clavius and Lilius have had craters named after them on the Moon).

So, is the issue of year length and calendar synchronization finally solved by Pope Gregory’s clever use of knowing when to insert February 29?  Well, it’s not that simple.  In reality, the tropical year is not fixed but is changing ever so slightly.  Furthermore, due to tidal friction and other forces, the day length is changing by the tiniest amount each year also, so it’s quite difficult to institute a change to the calendar beyond the year 3200 AD (which should NOT be a leap year - can someone please send a memo to the future?)

Since the invention of atomic clocks in the mid-20th century, we have been able to measure time with great precision, and this has allowed astronomers to add leap seconds to our clocks to manage the drift more precisely.  Since 1972 a total of 27 leap seconds have been added individually, usually on either June 30 or December 31, (creating a leap minute of 61 seconds), but the practice will be discontinued beyond 2035, as scientists have agreed to let the drift accumulate for a while.

What does all this mean?  From the perspective of 29 February 2024, I think it is safe to leave these future corrections to our distant descendants.  Our planet’s clocks and calendars appear to be in good hands.  In the meantime, I hope we all enjoy Leap Year Day, and I wish a very happy birthday to a very exclusive group of individuals - the Leaplings.  There may even be a Year 10 leapling at the college who is celebrating their fourth leap birthday this year.  

And finally, just out of interest, a Martian tropical year is 668.5921 Martian days.  Would anyone like to develop a calendar with appropriate leap years for Mars?  Now there's a great numeracy exercise.

Dr Len Halprin

VCE Physics

(Title image attribution:  Free-use licence from Vecteezy,  https://www.vecteezy.com/free-videos/earth)