Note: In a weird coincidence, I was working on this post when I got word about the similar Saturn video I wrote about earlier. Since Saturn was at opposition last weekend, I wrote that up and posted it first. The article that follows is based on a video by the same animator, and has some of the same themes but covers different ground and dips into the math a bit more as well.
One of the fun things to do with astronomy (and science in general) is to imagine what it would be like if things were different. For example, right now the Moon orbits the Earth at an average distance of about 384,000 kilometers (238,000 miles). Even though that makes it the nearest astronomical object in the Universe, that’s still pretty far—a four-day ride in a space capsule, for example.
But what if it were closer? YouTube user “yeti dynamics” (real name: Nick) is an animator who created a fantastic video showing what it would look like from Earth if the Moon orbited us as the same distance as the International Space Station. The results are pretty amazing! Make it hi-res and fullscreen for the full effect.
Right off the bat, let me give my kudos to the animator! That was very well done, very realistic looking, and—my favorite bit—really cool, so it’s likely to grab people’s attention and get them thinking about the Moon and space.
And given its intent (just showing what it would look like, without any extrapolation on the physics), it’s pretty accurate, too. Indulge me while I dabble in some (fun) math.
When the Moon Hits Your Eye
If the Moon were that close—420 kilometers (260 miles) over the surface of the Earth—it would be more than 100° in size, literally more than half the sky! Right now it’s a mere 0.5° in size, for comparison (which is actually even smaller than you think). It’s neat how it appears to rotate, too, though that’s really just perspective; it’s the same effect that makes it look like features are sinking below the horizon as you orbit. Yeti dynamics also explains that the color of the Moon is from reflected Earthlight: The blue is from the Gulf of Mexico, and the greenish-tan from the United States. It’s dark in the middle because with the Moon blocking the Sun for so much of the Earth, there’s no light to reflect and illuminate the Moon there!
The motion in the video is sped up; at that distance the Moon would orbit the Earth in about 90 minutes or so. It would cross the sky in very roughly five minutes. Note: Nick sent me a note saying that, accidentally, he rendered the Moon upside-down! I'm generally pretty good at spotting these things, but I'm having a hard time picturing that even with a map in front of me. Maybe you can do better: At 35 seconds, Mare Crisium dominates the view near the bottom (and rotates back into view at 45 seconds), then at 1:00, right after the Moon blocks the Sun, the dark crater Plato can be seen to the upper right. Does that help orient you?
All in all, that would be a very impressive sight! Unfortunately, if you saw it, you’d be very, very dead.
The answer is gravity, specifically, tides.
The Pull of the Moon
The force of gravity you feel from an object depends on how massive and how far away it is (measured from its center). The Earth has about 80 times the mass of the Moon, so if you could situate yourself exactly halfway between them, the Earth would pull on you 80 times harder than the Moon. But it’s worse than that; gravity drops as the square of the distance, and the Moon is pretty far away. Right now, the center of the Earth is roughly 6,400 kilometers below you, and the Moon’s center is about 380,000 kilometers above you (actually that can vary depending on where the Moon is in its orbit, but let’s ignore that). Take the ratio and square it, and you see that the Earth pulls on you 3,500 times harder just because it’s closer. Add in the fact that the Earth is more massive, and you’ll find it pulls on you about 300,000 times harder than the Moon!
That’s why you don’t notice the gravity of the Moon. It’s only 0.0003 percent as strong as what you feel from the Earth.
But what if the distance were closer? In the video, the Moon is 420 kilometers (260 miles) from the Earth—in this case, that’s measured from the surface of the Earth to the surface of the Moon. The center of the Moon would then be an extra 1,738 kilometers away (the distance of the Moon’s surface to its center, in other words its radius). So now the center of the Moon is 2,158 kilometers (1,340 miles) away, which is close.
If you redo the gravity calculation, you’d find the force of gravity from the Moon on you is 1/10th that of Earth! When the Moon passed overhead, you’d weigh 10 percent less. I’ll note this depends on your latitude and other factors, but again I’m trying to keep it simple here. You’ll see in a moment why worrying over details isn’t important.
The Tide Waits for No Moon
Weighing a little less every time the Moon goes over you might sound like fun, but then you have to remember about tides. The force of gravity gets weaker with distance. For example, right now the far side of the Earth feels less gravity from the Moon than the side facing it. The difference isn’t much, but it’s enough to stretch the Earth a little bit (it’s actually more complicated than that, of course, but for now that’s close enough). That’s what we call the tidal force. Right now, the Moon’s tides on Earth pull water up and down by roughly a meter or two between high and low tide as the Earth rotates under the Moon every day.
But if we bring the Moon in really close, suddenly one side of the Earth is a lot closer to the Moon than the other: The Earth’s near side is 2,158 kilometers from the Moon’s center, and the far side is nearly 15,000 kilometers away. That’s a huge difference, and the tides felt by the Earth would be amplified enormously—nearly 100,000 times what we experience now! There would be global floods as a tidal wave kilometers high sweeps around the world every 90 minutes (due to the Moon’s closer, faster orbit), scouring clean everything in its path. The Earth itself would also be stretched up and down, so there would be apocalyptic earthquakes, not to mention huge internal heating of the Earth and subsequent volcanism. I’d think that the oceans might even boil away due to the enormous heat released from the Earth’s interior, so at least that spares you the flood … but replaces water with lava. Yay?
In the video, you’re standing in a pastoral park enjoying the view as the Moon passes silently overhead. In reality you’d be drowned, vaporized, and shaken to bits. So, yeah.
And it would be even worse for the Moon. The Earth is more than 80 times more massive than the Moon, and so the tides the Moon feels would be even bigger. In fact, at that distance the Moon would be well inside the Earth’s Roche limit, the distance from the Earth where its tides could break another object apart. In other words, the tides from the Earth would literally rip the Moon to pieces! So we wouldn’t even have a Moon; we’d have a thick debris ring composed of ex-Moon. That would be cool to see, too, except for the whole everyone being dead thing.
I can understand why Nick left that part out. It might distract from what he was trying to show. Animating it might have been something of a chore, too.
As far as even more pedantic scientific nitpickery goes, there are tons of details to consider here—the Earth’s rotation, dependence on latitude, whether the Moon suddenly appeared much closer, or if it spiraled in over a few years—but I’ll leave that as exercise for the ambitious reader. As for me … I think I’ll go listen to some Debussy.