May 23, 2020 7:00 AM

What’s Up With the Funny-Looking Moons in Onward ?

Yes, I know this is a fantasy movie. That shouldn’t stop us from thinking about the real causes of lunar phases.

two cartoom characters looking at sunset

Let me just say, the Pixar movie Onward was fun. It’s your classic kids go on quest/gain new confidence story, but set in a world with elves and dragons and smartphones—you know, magic stuff like that.

Also, I am aware that it isn’t “real,” which means that they can make up whatever rules for physics they want. But that’s not going to stop me from thinking about real physics.

One of the things you see quite often in the movie are these two moons in the sky. They look cool, but they are also kind of troubling (at least to me). In case you haven’t seen the movie, here is my sketch of the two moons:

I’m assuming these are actual moons showing actual phases—but they are all wrong.

What Causes the Phases of the Moon?

It just so happens we have a real moon in our sky. You should go out and look at it sometimes. If you do, you will notice that its appearance changes over the course of a month. Sometimes it’s a big luminous disc and sometimes it’s just a sliver. But why is that?

You’d be surprised how many people think they know the answer, but actually don’t. Ask them what causes the varying phases of the moon, and here are some of the common (wrong) answers you will hear:

The Earth’s shadow on the moon
The rotation of the Earth
Clouds (the logic here escapes me)

Here’s the real answer: The phases of the moon are indeed caused by a shadow, but it’s essentially the shadow of the moon on itself. When light from the sun hits the moon, it illuminates only half of the moon’s surface, such that one side is bright and one side is dark. You could say the dark side is that way because the moon is blocking the sunlight. It’s sort of like the moon's shadow.

A diagram will help. Here is a view of the Earth and moon along with the light from the sun (not drawn to scale).

Illustration: Rhett Allain

If you were the red dot on the Earth, your view of the moon could be represented by the dashed line. From that angle, you would mostly see the dark side of the moon with just a little sliver of the illuminated part—in other words, a crescent moon. Here what it looks like in real life:

Photograph: Tayfun Coskun/Getty Images

So, as the moon orbits the Earth, the angle that you view it at also changes. This is how all the phases of the moon are produced. Watch this animation (made in Python—here is the code) showing a plain sphere with a single light source illuminating it from different angles.

Video: Rhett Allain

That's pretty much all the phases of the moon. So it has nothing to do with Earth's shadow. Of course, sometimes Earth's shadow does fall onto the moon. But it doesn't happen often, because the sun-Earth-moon orbits aren't exactly in the same plane. When things do line up, we call that Earth shadow a lunar eclipse. It's not a phase of the moon, but something different.

Now go back to the diagram and imagine how our view from that red dot will change as the moon orbits the Earth: When the moon is on the sun side of the Earth, we see only a sliver of light, or no light at all on a “new moon.” When the moon is on the far side of Earth, we look back and see more of the bright side.

So here’s a test: When you see a perfectly round full moon in the sky, where is the moon relative to the Earth? Right, it’s directly behind the Earth (with respect to the sun).

What’s Wrong With the Onward Moons?

Now let's go back to the moons in Onward. Here is a comparison with a realistic moon (on the left):

Illustration: Rhett Allain

There is a clear difference. The Onward moon looks like a circle with a smaller dark circle on top of it—suspiciously like a projected shadow from Earth. You can't make this shape with a sphere that has one dark half and one light half. It's not possible. OK, maybe this Onward moon isn’t actually a sphere. Perhaps there is a giant mountain range that sticks out above the surface such that it catches the sunlight. Of course, both moons would have to have the same strange, curved mountain range.

The funny thing is, this faulty depiction of a crescent moon is pretty common. You can see it in the emblem of Turkey, on the state flag of South Carolina, and many other places. I'm not sure why, but as you can see, it makes no sense when you understand what causes a crescent moon.

So why are the Onward moons like this? I bet the animators just thought it looked cool. It makes you think about ancient times, when this sort of symbol might have been more common. Maybe it also emphasizes the fact that this is not Earth (though the same physics should apply on all planets). But that's fine. I mean, it's just a show.

Dear friends, this will be my last month as a regular contributor for Wired Science. But the physics fun won't stop! Going forward, you'll find my stuff on Twitter, as well as Medium and YouTube. See you on the platforms! —Rhett Allain