Science In Real Life

It’s that time of the month here at Science In Real Life – no, the blog is not going to bloat and cramp for the next few days. It’s time to talk about Earth’s moon, the reason we have months in the first place. The moon has been an important influence on human culture ever since there was such a thing as human culture. We’re all so accustomed to seeing it hang there in the night sky that we sometimes take it for granted. In fact, there is some non-obvious science up there along with the man in the moon and all that green cheese.

First, the moon does not orbit the Earth. No, really. I promise, it doesn’t. Neither does the Earth orbit the moon. Instead, they both orbit a common center of gravity known in fancy jargon as the barycenter (from the Greek word meaning ‘weight center’, although now that sounds more like a place where Weight Watchers would set up shop). So where’s this barycenter? First, we pretend the Earth and the moon both have all of their mass located at a single infinitesimal point at their  respective centers. We can do this because both of them are as near to perfectly spherical as makes no odds. Now draw a line between the two points. The barycenter must be somewhere along that line. But where?

What we do is think of it as a game of interplanetary tug of war. If the Earth and moon had equal mass, the barycenter would be at the halfway point. But the Earth has more mass, so it pulls the center of mass closer to it. By invoking precise ratios of Earth’s mass to the moon’s mass, we can calculate that the Earth and the moon both orbit a common point about 1700 kilometers below the Earth’s surface. If you were in a hollowed out chamber at that exact point … well, nothing unusual would happen, except you might regret not bringing a magazine or something.

You might have thought that you’d float, weightless. Well, there are points like that in the Earth-Moon system (and indeed in any system of two bodies orbiting each other). They are called Lagrange points because they were first discovered by Leonhard Euler. What can I say, science is funny about names. Seriously, though, it was Joseph-Louis Lagrange who, with his brilliant re-formulation of Newtonian mechanics, made a proper understanding of Lagrange points possible. They are, simply, points where a small object can remain stationary relative to two large orbiting bodies because gravity and centrifugal force cancel out (see the previous essay for a proper discussion of centrifugal force).

For a system like the Earth and its moon, or like the Sun and the Earth+moon together, there are five Lagrange points, arranged as can be seen in this diagram:

Points L4 and L5 have the fascinating property of being completely stable: situate an object there and, like an incumbent local politician, no matter how you push it out of place the forces conspire to bring it back again. The other three are only stable against pushes in certain directions, but this has proven useful enough for NASA to send many probes to the Earth-Sun L1 position.

But now back to Earth’s moon. We’ve covered some of the details of the orbital mechanics, but how did the moon get there in the first place? In comparison to the other moons present in our solar system, Earth’s moon is, to put it bluntly, weird. It’s abnormally large relative to its planet, for one thing, and its very presence is almost unique among the inner planets. Mars has two dinky moons, Phobos and Deimos, but those are about as important as a fur-lined parka in the Bahamas. So what gives?

Frankly, we don’t know for sure. The leading theory is that early on in the formation of the solar system, another planet about the size of Mars basically rear-ended the Earth in a collision that makes Boston traffic look like bumper cars. This collision would have to have been colossal, and that has resulted in this hypothesis having the delightful name of the Big Whack. It would literally have torn both planets apart. That Mars-sized body, named Theia, would have been almost totally disintegrated, but the idea is that the forward momentum of the debris (from both Earth and Theia) would have been enough to settle into an orbit around the Earth. Still molten hot, its own gravity then coalesced it into our beloved moon. There are still some unresolved difficulties with this theory, mainly having to do with geological composition, but for now it’s the best answer we’ve got.

So remember: when the moon hits your eye like a big pizza pie, that’s-a painful …