A blog by Dave Zvenyach

Leap Years

The science of time is just absolutely bonkers.


2020 is a Leap Year. As a practical matter, that means that – for those who observe the Gregorian calendar – we have 29 days this month, not 28. The reason we have a leap year is to correct for the fact that the year is slightly longer than the 365 days we normally have in a year. In the musical Rent, the question is posed: “how do you measure a year?” The proposed measure (525,600 minutes) is wrong if you are measuring a tropical year. As it turns out, answering the question is much much more complicated than it seems.

First, it's worth asking what we typically mean by a year? If you thought that it's the time that it takes for the Earth to complete a single revolution around the sun, you'd be wrong. That's a Sidereal year, and is not what society uses to measure a year. Instead, we use the Tropical year, which measures the time between seasons (more on that in a bit).

Second, it's worth considering how we measure a tropical year? Here's where things get bonkers.

In the old days, back when astronomers hypothesized that Earth was at the center of the universe, the way that you'd measure a tropical year would be to use an armillary to measure the time between equinoxes at a given location. And that's what Hipparchus did in the second century BCE. According to the history of the tropical year, Hipparchus calculated that the tropical year was “equal to 365.25 days minus 1/300 of a day-and-night.”

Eventually, astronomers start to question things, and start to look more deeply at the numbers. Copernicus comes along with heliocentrism, and even tries to redefine the year to be more like the sidereal year (that doesn't happen), and gets more accurate. For the next few centuries, Kepler and others start measuring things using new tables and methods of observation. They get even better, but they're all in agreement that it's still a bit of a work in progress.

Then, modern day astronomers redefine the tropical year to be time interval needed for the mean tropical longitude of the Sun to increase by 360 days. Don't worry if you don't understand that. But there's a twist here, which is that because the Earth's rotation is slowing down, the length of the tropical year length is decreasing. It gets wilder. As the authors note in The history of the tropical year, eventually the tropical year won't be more than 365 days. It will actually be exactly 365 days, and we won't need leap years. In fact, eventually we'll maybe need to lose a day.

But that's not even the wildest thing…. although it's still on my to-read list, there's a book called Time: From Earth Rotation to Atomic Physics, that alludes to (among other things) the possible redefinition of the second.

In other words, expect everything we know to be true about time to be basically wrong. Amazingly, with regard to leap seconds, we have a few years before we'll know for sure. As the authors explain: “By 2023, a more precise time scale, a redefinition of the second, and applications requiring more precision and accuracy may lead to a redefinition of timescales.”

Happy leap year, everyone! Let's enjoy them while they last.