# Same side of the Moon always faces the Earth: The Moon's recession rate.

The Perfect Master gives the recession rate of the Moon as 4 inches per month. Either Cecil is remembering a figure from his childhood (and he is much, much older than I thought) or this has been a minor clerical error.

The recession rate of the Moon is 3.8 centimeters (approximately 1/2 inches) per year. (Cite.) Also, despite the fact that its orbit is getting bigger, the Moon will orbit the Earth until the Sun becomes a red giant. (After that, it’s all a bit academic.)

The rate Cecil gives for the increase in the length of the day (1 second ever 100,000 years) is correct.

A link to the column in question: Why does the same side of the moon always face the earth?

Yargh! Dangit! I kept telling myself, " . . . and don’t for get the link!" and I kept the article open in another tab just so I would be able to copy the link, and then I went and forgot the link. Thanks, QED.

I’m sure you meant 3.8 cm = 1.5 inches.

When I was a kid, my parents bought us youngums a set of Time-Life natural science books. One book (entitled “The Universe”) spoke of a time when the moon would continue receding from the earth until at some point the orbit would start decaying and eventually the moon so close to the earth that it would break up into little pieces (Roche limit?) and the earth would become a ringed planet.

1. Why would the orbit begin to decay?

2. When was this supposed to happen and how long would the breakup take? (I would have to assume it could only occur before the Red Giant stage since it’s generally understand that the inner solar system will be mostly engulfed duing the Sun’s obesity phase).

3. Assuming that the earth is still a thriving ecology of some sorts, what effect would it have on the lunar tides? Just before, during, and after the moon’s breakup? Is it worth hanging on a Florida beach during the event? Assuming we still launch space craft into orbit, what’s the highest altitude they could reach before moon dust, particles, cobbles becomes a distinct hazard while in orbit?

4. Assuming we become a ringed planet, would there be a permanent equatorial tidal bulge? If so, how high would it be?

There’s no reason the orbit would begin to decay. Either the book you read was wrong, or you’re misremembering it. It is true that if the Moon somehow managed to get too close to the Earth (within the Roche limit) it would break apart. Shortly before it reached this point, the tides would be enormous (about a hundred thousand times greater than currently, by my estimate), since the Roche limit is much closer than the Moon’s current position, and tidal forces have a strong dependance on distance. There will also be a good deal of matter that would get rained down to Earth following the breakup, which would most certainly not be good for any life that happened to be on the surface. The rings, once formed, would probably be continuous, and extend all the way down to the upper edges of the Earth’s atmosphere. The only reason that Saturn’s rings have gaps is because it also has a number of sizable moons, whose orbits influence the orbits of the ring particles in various ways (one of the influences, incidentally, is to keep the rings stable, without which they would have only lasted a few million years). And it’s safe to say that if this happened, the Earth would have a permanent equatorial bulge, since it already has such a bulge, and I see no reason to suppose it would go away.

I don’t think it’s at all safe to say that. The crust is extremely thin compared its diameter, and the mantle on which it floats is fairly fluid, or at least, plastic. Once the tidal force of the Moon has been removed, I see no reason why the tidal bulge wouldn’t settle. You’d still have the polar flattening due to the Earth’s rotation, but that’s not what the OP was talking about.

[bad word deleted]! I had 1 1/2 . . . somehow deleted the 1.

Now, I shall continue as if I have some shred of credibility left . . .

I think you must be confusing two different things. The Moon’s orbit is going to get bigger and bigger. It will never decay. Ignoring the Sun and its evolution, the Moon would move away for a few billion years, and evenutally it will be far enough away that it will drift out of the Earth’s influence and go on its own orbit around the Sun. There’s no reason for the Moon’s orbit to decay. I think you’re conflating this with a hypthetical scenario where something gets close enough to Earth to be torn about by tides, or a hypothesis for the formation of Saturn’s rings.

The Earth’s Roche limit for an object with the Moon’s density is only 1.5 Earth radii!
The Moon’s radius is .27 Earth radii, so it would have to be pretty darn close. Also, the Roche limit isn’t a magical line, where as soon as you cross the line, the object instantly breaks up. Depending on how fast it was coming in, the Moon might crash into the Earth while remaining, to some degree, intact.

Long before the Moon reached that point, the tides it raised would be tremendous. You’d want to vacate Florida and seek higher ground well before the Moon broke up, I think.

Yes, I think so. If you put a moon’s worth of mass in a dense ring around the Earth, it should increase the Earths’ oblateness, putting a bulge at the equator and flattening the poles. Again, assuming that we have the whole mass of the Moon, that close to Earth, it would still be creating tides (though not what we’re used to.)

As a practical matter, a very dense ring will not last long, especially if it’s only .5 Earth radii above the surface! Rings are thought to spread out quickly, and the innermost edge would be lost to the atmosphere. Also There will be a lot of collisions between ring particles which will grind them down to dust, and the dust is lost rapidly due to Poynting-Robertson drag, so you’d lose most of your ring in a few thousand to ten thousand years. All that dust spiraling in and hitting the upper atomsphere would be awful pretty, though. I shudder to think of the environmental ramifications, though! (This is mostly vague speculation on my part, but I actually work on planetary rings IRL, so it’s at least informed vague speculation. Take it with a healthy grain of salt.)

If you’d like some points of comparision, Saturn’s Roche lobe for an icy moon is around 2 Saturn radii, and Saturn’s rings have a total mass of only 1/2 the mass of the Moon—spread out over an area of 44,000,000,000 square kilometers. (Imagine a piece of tissue paper covering a soccer field.)

[On preview, I see that Chronos got in ahead of me, but I spent a lot of time on the post, and it contains some detail he didn’t include, so I’ll submit it anyway.]

The Moon’s orbit decaying rings a bell with me, too. This was around 1960, from a library book whose title I can’t remember. It wasn’t a Time-Life book as far as I can remember but may have been about the same size. Of course, I haven’t seen that claim since.

But we’re not talking about removing the Moon. Its mass would still be there—closer to the Earth, in fact—but made into a ring. What I believe he meant by “permanent” was that the bulge would be stationary, rather than traveling around as it does now due to the Earth’s rotation under the Moon.

I remember that book, too. I don’t recall whether it was Time/Life (actually, wouldn’t it have been plain Life in that era?) but I seem to recall it being more or less in that house style.

I believe it also gave the now exploded “birth from the Pacific” theory and the “magma-bubble scar” theory of crater origin.

Hell, at 2 moon radii away we could FEEL the tides :eek:. Or at least set world record long jumps!

1. After reading through the responses (especially John W. Kennedy), I now recall that it was “Life” rather than “Time-Life”, and the book in question was published in the early 60’s. The-earth-and-how-it-becomes-a-ringed-planet was an illustrated side bar within the book. As a kid, I thought this was really cool science and wondering what it would look like to have rings in the sky–day or night. So I pretty certain of this detail.

2. Podkayne’s observation was correct. I assumed the equatorial bulge would be permanent relatively speaking.

Come to think of it, would the rings form over the equator or would they form at the current elliptic of the moon (what is it–5 degrees or so?) Or would be transitioning from the elliptic to the equator?)

1. Watching the moon landings as a kid, I remember there were three main arguments being pitched for the moon’s origin. 1) captured, 2) rising from the Pacific, and 3) forming in the same dust cloud. I never heard of the 4) collision theory (mars sized object collides with earth at an offset angle. Blob of matter is ejected from which coalesces into the moon) until reading about it in Scientific American 10 or 15 years ago. So far, 4) seems to be the strongest candidate for lunar origins.

Why would the moon drift away? From what little I know of celestrial mechanics, a higher orbit means energy is being inputted into the system. Where is that energy coming from?

Any chance the moon would end up in a Lagranging (?) orbit between the earth and sun?

If the moon is flying away from the parents nest, what about the rest of the planets? Are they punching out? Your answer implies that this is the case (excluding extra-solar events like a star passing by within a few light days or weeks of the solar system).

The “daughter”, “sister”, and “pick-up” theories all have major problems.[ul]
[li]The “daughter” theory (Pacific Ocean) never had a believable mechanism, and was completely wrecked when plate tectonics made it clear that the Pacific is a temporary phenomenon much younger than the Moon.[/li][li]The “sister” theory fell apart when it became clear that the Moon has no iron core, as the Earth does.[/li][li]The “pick-up” theory, on the other hand, failed when space probes showed that the mineralogical variety within the Solar System is tremendous, but the Moon is mineralogically almost identical (as these things go) to the Earth, apart from the aforesaid lack of an iron core.[/li][/ul]
The collision theory, developed in the 1970s, but first widely presented in the 1980’s, took up the challenge by asking the question, “How did what is apparently a large part of the Earth, without the core, get blasted into space to form the Moon?” The answer that works appears to be: “A collision with a Mars-sized object at an early period.” Most of it went into making the Earth bigger, but part of it splashed, and eventually became a ring that accreted into the Moon.

[QUOTE=user_hostile]

Come to think of it, would the rings form over the equator or would they form at the current elliptic of the moon (what is it–5 degrees or so?) Or would be transitioning from the elliptic to the equator?)

The rings would start out tilted, but very quickly they’d turn into a thick ring over the equator, then settle into a thinner ring in the equatorial plane.

The Moon raises a tidal bulge on the Earth, but the Earth spins faster than the Moon orbits. Thus the gravity of the bulge pulls the Moon ahead, while the Moon’s gravity pulls back on the bulge. This adds energy to the Moon’s orbit by subtracting it from the Earth’s rotational energy, increasing the length of the day, as Cecil mentioned.

Do you mean, will the Moon end up at the Earth-Sun Lagrange point? Actually, the Moon would likely pass through that point when it left Earth orbit, but it’s an unstable equilibrium, so it’d just slide on through.

I’m not sure if I understand your question . . . Solar tides do have a tendency to push the planets into higher orbits, but planetary orbits are much larger and take a longer time to change, and there are other effects (such as gravitational interactions with other planets) that have a larger effect. The timescale for planets to leave the Solar System is enormous.

(Podkayne)

Several years ago (I think it was in the 20th Century), a Scientific American talk about the fate of the universe if it continued to expand forever. The time scale was something like 10^100 to 10^110 years before it reached a point where a point of equilibrium is reached. So yeah, we’re talking long term. But now that you mention it, I hadn’t even given any thought that the perturbing effects of other planets would have a far more significant effect.

Unstable equilibrium sounds like an oxymoron. But I’m assuming that a Lagrange point is like a ball sitting on a tiny dimple on an other wise flat desk-- even a tiny push will knock it out and start it rolling. In the case of the moon, can I assume that even if it magically were placed into L sweet spot, outside forces (tidal and other planetary interactions) would bump the moon out of the dimple?

By the way, much thanks to all of you who responded to my questions. I’ve enjoyed this little excursion into “What if?”

It depends on the point. The L1, L2, and L3 points (between the Sun and Earth, beyond the Earth, and on the opposite side of the Sun from the Earth) are unstable (sometimes called “metastable”), like a pencil perfectly balanced on the point. In nature, you won’t find anything in the L1, L2, or L3 points, though it is possible to keep objects in them artificially; some research satellites have been placed in L1 and L2, because it takes far less rocket power to keep something parked in a metastable position than to keep it in a completely unstable one.

But the L4 and L5 points (60 degrees ahead of the Earth and 60 degrees behind) are truly stable. If the Moon were to end up in one of them, it would stay there, unless it is too large. (The three objects in a Lagrange situation must be very large, large, and small, in certain proportions.) However, I gather from what else has been said that the probable future course of the Moon won’t take it to them…

The “Trojan” asteroids are (by definition) in the L4 and L5 points with respect to the Sun and Jupiter, and there are dust clouds in the L4 and L5 points with respect to the Earth and Moon.

And don’t forget the Sun blowing off its outer layers to form a planetary nebula, chance interactions with other stars, etc.

Actually the way to think about it is that you have a curvy desk. (Bad for writing; good for celestial mechanics analogies!) Most places that you put a ball on the desk, it’ll roll around. (Assume it’s a frictionless desk, so things will keep rolling forever.) As JWK says, the L4 and L5 Lagrange points are stable; they are subtle depressions in the desk. If you put a ball near the L4 or L5 point, even if it’s moving around a little, it’ll orbit around those points happily. That’s a stable equilibrium. The L1, L2, and L3 points are saddle points. They’re an equilibrium in the sense that a ball perched right at the middle of a saddle will stay there, but only if you put it exactly at the middle, perfectly still, and never bump it at all. If the ball gets any kind of a nudge, it’ll roll away down one side or the other. Like JWK says, it’s like a pencil balanced precisely on its point.

The Moon would leave the Earth by slipping through the Lagrange point between the Earth and Sun, or the Lagrage point behind the Earth. (The numbering of L1, L2, and L3 varies from author to author, so I’ll just be descriptive!) It could eventually wander into the L4 or L5 point and be a Trojan, but that’s not guaranteed.

I recall reading the whole “the moon will move away from earth, then move back towards earth and shatter, forming a ringed planet, but practically that would never happen because the sun would have turned red-giant long before then” point in Isaac Asimov’s A Choice of Catastrophes. I’ll have to look again to get specific details.

Weird! I cannot imagine what mechanism they could be invoking to bring the Moon back in.