Several Big Sloshes

“I call distraction, Sy. You were going to explain how come the Moon’s drifting away from us but you got us into radians and stuff. What’s that got to do with the Moon flying away by dragging a big wave around the Earth?”

“It’s not dragging a localized bulge of water like you’re thinking, Vinnie, nothing like that wave on Miller’s Planet. For that matter, the Miller’s Planet wave had a sharply‑rising front which also doesn’t look like the textbook tidal bulge.”

“There’s a textbook on this stuff?”

“Many, Al. Heavy-duty people have spent a lot of time on tides. Think about all the military and commercial navies that depend on boats being able to leave port and dock on schedule.”

“And not run aground <heh heh>”

“Well, yes, Vinnie. Anyhow, like a lot of pre‑computer Physics, that work was based on a simplified ideal system — a moon orbiting a smooth planet with a world‑covering ocean. Water’s drawn horizontally towards the sub‑lunar points making an egg‑shaped surface and everything’s neat.”

“Probably nothing like real life.”

“Of course. Here’s a video I built from satellite altimetry data. The grey dot is roughly the point underneath the Moon as that day progressed. The red‑to‑blue height scale’s in meters.. Not as neat as theory, is it?”

“Wow, that’s a mess. Looks like the Moon’s pulling water along the Canada‑Alaska coast okay, and the western Pacific starts to get a dome going. But the water never catches up before the Moon’s gone.”

“Hey, Vinnie, look how the tides just go round and round New Zealand. And what’s that, Hudson Bay, it’s a pinwheel.”

“Yeah, and in between Africa and Madagascar it’s completely out of phase from what it oughta be.”

“What you’re looking at is slosh. Once again, reality overwhelms a pretty theory. Each basin has its own preferred set of oscillations. None of them match up with the Moon. But the other thing — “

“Tiny numbers. Everything’s like less than a couple meters, not not a big bulge at all.”

“Bingo, Vinnie. Against Earth’s 6.4‑million‑meter radius, those small chaotic sloshes don’t make for effective energy transfer driving the Moon away from us. That theory’s toast.”

“So what’s doing it?”

“There’s two theories that I know of, and they’re probably both right. The first one is Earth tides — that bump you think of as traveling around the planet, but the bump is rock instead of water.”

“That can’t be a big effect. Rocks don’t bend.”

“On a planetary scale they’re not as solid as you think, Vinnie. The rock crust is brittle and really thin, less than half a percent of Earth’s radius. It floats on molten outer mantle which has the fluidity of tapioca pudding. When that structure gives under stress the crust layer cracks. The seismologists and GPS techs have measured surface motion all over the world. When they analyze the maps, the lunar component accounts for up to a meter of coordinated vertical daily movement. Figure the whole Earth is continually being squeezed and pulled to that extent and you’ve got a lot of energy being expended every 24 hours.”

“How about the other theory?”

“There’s no direct evidence, so far as I know, but it seems reasonable on physical grounds. We’ve got two gyrations going on here, right? The Moon is on a 29½‑day orbit while the Earth rotates about thirty times faster. But the two motions use different frames. The Earth’s spin axis runs through the geometric center of the planet and tilts 23° from its orbit axis. Meanwhile the whole Earth‑Moon system rotates about its barycenter, their common center of gravity, which stays inside the Earth about ¾ of the way moonward from the Earth’s middle. That rotation is about 5° away from Earth’s orbit’s axis. Imagine a molten blob near the barycenter, happily following the Moon in the Earth-Moon frame, but the rest of the planet is saying, ‘No, no, you’re supposed to be moving hundreds of miles an hour in a different direction!‘ If the blob’s the least bit lighter or heavier than its neighbor blobs, inertial forces expend energy to kick it out of there.”

“So we got two ways to transfer energy steady-like.”

“I think so.”

~~ Rich Olcott