Happy Vernal Equinox!

Spring is just around the corner for most of the northern hemisphere, and with that comes the promise of long and gloriously toasty summer days. If the chill of winter is still in the air where you live, you might be wondering how much longer it’ll be until those longer days arrive.

So, how many extra minutes of sunshine are we gaining each day? And, now that I’ve mentioned it, why does the number of daylight hours change throughout the year in the first place? What exactly does that change look like? And what does all of this have to do with the sine and cosine trigonometric functions we’ve been learning about?

Stay tuned because those are exactly the questions we’ll be talking about today!

How Many More Minutes of Daylight Tomorrow?

The sun was up and shining for 12 hours 10 minutes and 11 seconds today where I live in Los Angeles. Yesterday, the sun took 12 hours 8 minutes and 3 seconds to cross the sky. Which, if you do the math, means that today gave us 2 minutes and 8 seconds of additional sunshine. And, barring an astronomically unlikely solar catastrophy, tomorrow will give us 12 hours 12 minutes and 19 seconds of sunshine—2 minutes and 8 seconds more than today.

Hooray!

Today gave us 2 minutes and 8 seconds of additional sunshine.

The even better news is that for the next week or so, the minutes of sunshine will continue increasing by 2 minutes and 8 seconds per day. And for the week or so after that, it will continue increasing at the slightly slower pace of about 2 minutes and 7 seconds per day. In fact, this time period around the vernal or spring equinox—and actually peaking at the equinox—is the time of year when the number of daylight hours is growing the fastest.

But, you might be wondering, why is that? And for that matter, why does the number of daylight hours change at all throughout the year? To answer that, we need to talk about a bit of basic Solar System astronomy.

How does 23.5 degrees change everything?

Picture Earth and all of its inhabitants happily spinning like a top around its axis once per day. Now picture that happily spinning top slowly traveling around the Sun once per year. With a bit of thought (and perhaps a model made with a flashlight and ball), you should be able to convince yourself that if the axis around which the Earth spins is perfectly lined up with the axis around which it revolves around the Sun, then every location on the planet will always experience 12 hours of day and 12 hours of night—every day, all year long.

Unless you’ve actually been living in a cave (and thus not able to see the comings and goings of day and night), you’ll recognize that this doesn’t sound like the Solar System we live in at all—from which we can draw the conclusion that these two axes must not actually be aligned. Which is, in fact, true—we know that the axis about which the Earth spins is tilted about 23.5 degrees with respect to the axis around which it revolves around the Sun.

What does that do? In short, a lot.

Why do daylight hours change?

More specifically, for our purposes here the most important byproduct of Earth’s tilted axis is the fact that the number of hours of daylight changes throughout the year—and exactly how it changes depends on the latitude at which you live. If you think about it (or take a look at that flashlight and ball model you played around with earlier), you’ll see that the top half of the Earth is tilted towards the Sun for half the year and away from it for the other half.

Parts of the planet tilted towards the Sun receive more than 12 hours of sunshine per day, parts pointed away from it receive less. As the Earth travels around the Sun throughout the year, the degree to which a part of the planet is tilted towards or away from the Sun changes. And with that change comes a change in the number of daylight hours that part of the Earth receives.

Parts of the planet tilted towards the Sun receive more than 12 hours of sunshine per day.

As a location goes from winter into summer, the rate of change in the number of daylight hours peaks at the spring equinox—which is why the number of daylight hours is increasing at a maximum rate right now in the northern hemisphere. After the spring equinox, the rate at which daylight increases tapers off until halting at the summer solstice. At that point the number of daylight hours gradually begins to decrease, picking up steam until reaching a peak at the autumnal equinox and then gradually decreasing until once again halting at the winter solstice.

At which point the cycle begins anew.

Daylight hours, sine, and cosine: What’s the connection?

As this periodic nature might lead you to guess, the number of daylight hours and the rate at which that number of hours changes turns out to be closely related to the sine and cosine trigonometric functions we’ve been talking about lately. In fact, if you make a plot of the number of daylight hours throughout the year, you’ll see that it looks almost exactly like a sine function.

Why is that? And what does the graph of a sine function actually look like in the first place? Unfortunately, we’re all out of time for today. So the answer to those questions is going to have to wait until next time.