Starts With A Bang

# Throwback Thursday: Measure The Earth’s Axial Tilt This Solstice

How, with a sunny solstice, you can figure out how much our planet is tilted!

“Soon the earth will tilt on its axis and begin to dance to the reggae beat to the accompaniment of earthquake. And who can resist the dance of the earthquake, mon?” –Peter Tosh

Every year, there are two special days where every place on Earth receives the same amount of sunlight — 12 hours — split evenly between night and day: the equinoxes! If the Sun were a perfect point, instead of a disk taking up about half-a-degree on the sky, this split would be exact, and perfectly identical everywhere on our world. As it is, it’s still pretty close.

Like all known objects that revolve around another due to gravity, the Earth rotates along its journey around the Sun. But on those two days of the equinox (from the Latin, meaning “equal nights”), the Earth’s axis-of-rotation makes a 90° angle to the imaginary line connecting the Earth to the Sun.

As a result, every place on Earth spends exactly half the day basking in the sunlight and half the day out of view of the Sun, enjoying the night.

As the Sun rises during the equinox and ascends through the sky, rising towards its zenith, something unremarkable but very interesting happens right as it reaches its highest point above the horizon. You don’t normally think about it, but that highest point — astronomical noon — marks something very significant.

At that very moment, the angle the Sun makes with your location on Earth exactly determines what your latitude is!

Let’s go over why this is. On the equinox, the Sun will pass directly overhead to an observer on the equator. But to someone at any other latitude, because the Earth is curved, the Sun will never quite reach that maximally perfect overhead perspective.

If you’re exactly at the equator — like point A, above — then at its highest point in the sky, perfectly vertical objects will cast no shadow. But at any other latitude, no matter how close you make your measurement to the Sun’s maximum ascent in the sky, you will always see a shadow. (And right at the poles, in fact, you’ll see an infinite shadow, which is what you get when you’re perfectly perpendicular to the Sun’s rays.)

When an object casts its shortest shadow during an equinox, however, that’s when things get really interesting. Because that’s when you can learn what your latitude is.

You can figure out what your latitude is for yourself by taking a stick that’s exactly perpendicular to level ground, measuring its length, measuring the minimum length of its shadow, and just doing a little bit of geometry from there.

The angle you measure when the Sun reaches its highest point on the day of the equinox — in degrees — defines for you what your latitude is at any location on Earth.

And the same technique, applied during the equinox on any round world, would give you your latitude at that location. That, of course, is during the two equinoxes. But this Sunday, the solstice arrives!

The two solstices are maximally different from the two equinoxes. On the equinox, the angle the Sun makes with the Earth is perpendicular to the Earth’s axis of rotation, but on the solstices, that angle is at its maximum difference from 90°.

“How different is it,” you ask?

It’s different by the amount that your planet is tilted by. In other words, that difference tells you, exactly, what the tilt of the Earth is!

So if you already know your latitude — which at this point, if you didn’t determine it on the last equinox, you can look up — you can figure out the tilt of the Earth on its axis. If you want to do it during this year’s June 21st (or, in the winter, on the December 21st) solstice, here’s what you do.

Start with level ground, and make sure it’s as close to level as humanly possible. Take a straight object that’s as close to perpendicular to that level ground as you can make it; even someone who’s not great at it but who’s careful can usually get it within just a degree or two. Make sure you measure its length accurately, from the ground to its very top. And as the Sun reaches its highest point in the sky — not at “high noon,” mind you, but at its astronomical zenith — measure the length of the shadow that it casts.

(You want to find the zenith angle, below right, and not the sun angle, below left.)

Those two measurements will allow you, because you have a right triangle, to figure out what the angle is between the vertical stick and the angle of the Sun. Mathematically, take the inverse tangent of the length of the shadow divided by the length of the stick, and you’ll get an angle in degrees.

Now, take your latitude, which you can look up on google if you like, and do the following for a June (December) solstice:

• If you live North of the Tropic of Cancer (South of the Tropic of Capricorn), subtract your measurement from your latitude; that’s the tilt of the Earth!
• If you live South of the Equator (North of the Equator), subtract your latitude from your measurement; that’s the tilt of the Earth!
• Or, if you live between the Equator and the Tropic of Cancer (between the Equator and the Tropic of Capricorn), add your latitude and your measurement together; that’s the tilt of the Earth.

And that’s how you, yourself, can measure what the tilt of the Earth on its axis is! If someone tells you “the poles have shifted,” as some conspiracy theory sites may tell you periodically, this is a simple, straightforward and easy experiment you can perform to test it for yourself!

Travel the Universe with astrophysicist Ethan Siegel. Subscribers will get the newsletter every Saturday. All aboard!

That’s one of the coolest things you can measure on the Solstice, and you don’t even need any astronomical equipment to do it. You could even do this, by following these same steps, on any planet. So long as you knew what your latitude was, you could measure the tilt of any world.

So enjoy the solstice this Sunday, and to those of you who try it, I’d love to know how close you come to the “accepted” modern value of 23.44°. If our axial tilt ever does change, you can be the first to truly know!

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