Why Is There a Leap Year?

The Earth's imperfect path around the sun leads to an extra day every four years. Dot Physics blogger Rhett Allain explains how leap years work -- and why there should be more of them.

Really, the question should be: why aren't there even more leap years? Let me start with the basics.

A Year

What is a year? To a child, this may be defined as the "the time I must wait until the next Christmas." Perhaps a better definition would be:

Year: The time it takes the Earth to make one complete orbit around the Sun with respect to the background stars.

The "with respect to the background stars" is a pretty important part. Really, how do you know when you get all the way around the Sun? You have to have some reference point. The nice thing about using the stars as a reference is that they are super far away. They are so far away that their angular position doesn't really change too quickly.

Drawings.key

The Earth's orbit isn't completely circular - I tried to represent that non-circularness in the diagram (diagram not to scale and batteries not included). Oh, and this is technically called the sidereal year.

But wait. There is more. There is also the tropical year. This is the time it takes for the Earth to go from one summer solstice to the next (or you could use the winter solstice). The solstice is the day (and time) that the Sun is directly above the Earth's equator that the Sun is at the farthest point above or below the Earth's equator. Or, you could use the spring or fall equinox. The equinox is the day that the Sun is directly above the Earth's equator. No, this doesn't happen every day. Since the Earth's rotational axis is tilted, the Sun is directly over the equator just twice a year.

Drawings.key 1

Again, this diagram is not to scale. Also, in this above diagram, the Sun is over the equator. What you don't see is that the axis is still tilted - just in and out of the screen.

Why would this tropical year be different than the solar year? Here is the deal. This measurement of the year depends on the direction of the Earth's rotational axis, which unfortunately is not actually constant. The axis of the Earth rotates around, just like a spinning top on a table as it slows. This is called precession. So, the tropical year is a little bit shorter than the sidereal year. Enough about years (except to say that there are other ways to define the year, I just included the two important ones).

A Day

How do we define a day? There are two common definitions. First, the solar day. This is the time it takes for the Sun to move in the sky from its highest position (noon) and back to its highest position. You know, noon to noon. Makes sense, doesn't it? Oh, and in case you weren't paying attention, the Sun mostly like is not straight over head at noon (unless you are at the equator on the solstice).

The problem with the solar day is that it doesn't really tell you how fast the Earth spins. Why? Because the solar day depends on both the rotation rate of the Earth AND the orbit of the Earth around the Sun. The Earth does both of these things at the same time. Here is a diagram of the motion of the Earth around the Sun.

Drawings.key 2

Here the red dotted line represents the angular position of the Earth. You can see for the sidereal day, the Earth has gone through one complete rotation (with respect to the background stars). During this time, the Earth has also moved in its orbital motion around the Sun. So, if you started a clock when the Sun was at the first position, it would take longer than a sidereal day for the Sun to get back into the same position in order to compensate for the orbital motion of the Earth.

Calendars and Leap Year

In terms of how we keep track of time, it is easiest to go by the solar day and the tropical year. Here is the key point: the solar day and the tropical year aren't locked in anyway. So, if we call a solar day 24 hours, then how many of these days fit into a year? The answer: not an even number. The simple approximation is to say that there are 365.25 days in a year (although this is also wrong). But the 0.25 days means that after 4 years, we need to add a day to the year so that we still have the summer solstice around June 21.

Wait. Did I say "around"? Yes, I did. Since the Earth's orbit is not circular, the orbital speed of the Earth is not constant. This means that the actual time and day that the Sun is right over the Earth's equator changes a little bit. But if you never added this day every four years, in 100 years, the solstice wouldn't even be in the same month.

The Answer

Ok, just to be clear. If you define a second based on something non-astronomical, you can get real measurements for these things. The common way to define a second is based on atomic transitions for particular materials (you know - like an atomic clock). With this definition, a sidereal year is something like 365.256363 solar days. This is why just having a Leap Year isn't enough to keep the days in the proper season each year.

Ok. So that is it. Happy Leap Year. Oh, I am sure there will be many other blogs posting about leap year. For example, here is a nice video that explains Leap Years.

Now you have it all. Words and a video.

Homepage photo: NASA/Wikimedia