Over a huge amount of time, of course, there’s atmospheric drag, such as it is. Or (I don’t have the necessary maths to hand) would Solar tides on the Earth-Moon system steal angular momentum?
Even on long timescales, even at the Moon’s current distance, it’d be insignificant.
You may be right. The major effect of solar tides is slowing the Earth’s rotation, so that could take some energy out of the Moon’s orbit, but that could only slow the Moon’s recession. In order to turn the Moon around, it would have to tidally lock the Earth to the Moon (so the Earth always keeps one face toward the Moon), but the Moon would escape before that point . . . but maybe the parameters they were using at the time showed the Earth locking up before the Moon escaped, and then solar tides brought it back in.
I’m pretty sure that that was, in fact, stated.
OK, maybe I’ve missed something here, but isn’t the logic argument as follows?
First, the earth’s rotation is slowing down. Due to conservation of angular momentum, the moon is moving away (i.e.: longer orbit, slower speed), so the moon’s revolution is slowing down, and for the same reason (as some form of compensation) the moon’s rotation has slowed down to the point where a rotation is ABOUT equal to one revolution (that’s why we see 59% of the surface).
Anyway, if everything is slowing down in this scenario, then how is angular momentum being conserved? I WAG you might argue the moon keeps the same period as its orbit receeds (i.e.: grows larger) but, if this is true, where is the extra energy to account for the increase in speed required to maintain the same period? I would then WAG that the extra energy comes from the moon’s rotation slowing down. But again, this presumes the period must stay the same, but why should it? - Jinx 
Actually, its rotation period exactly equals its revolution period. The reason that we can see 59% of the surface (libration) is that the Moon’s speed in its orbit is not constant because its orbit isn’t a perfect circle.
Now, the Moon’s rotation period equaling its period of revolution is a separate process ocurring at the same time. The Earth raises tides on the Moon, so the Moon always wants to keep its long axis lined up with the Earth. Imagine that the Moon hops into a slightly higher orbit. Its rotation rate is a bit too fast for the new orbit, so its tidal bulge gets a little bit ahead of where it should be, no longer pointed exactly at Earth. Earth’s gravity drags back on the Moon’s tidal bulge. This decreases the Moon’s rotational rate, and also makes the Moon’s orbit larger to conserve angular momentum (see below).
However, since the Moon is already synchronized, this effect is small compared to the effect of the Moon’s tides on Earth (which is really just the Moon trying to slow the Earth down so that Earth’s tidal bulge stays line up with the Moon.)
The Moon’s orbital speed decreases as the size of its orbit increases, and its period increases. Kepler’s Third Law, the Harmonic Law, p^2=a^3, is still in effect.
The angular momentum of an object in orbit is mvr: the mass of the object times its orbital speed times the radius of its orbit. The (average) orbital speed an object, v, is proportional to 1/sqrt(r) (due to Kepler’s 3rd, above). This means that the angular momentum of the orbit is proportional to sqrt(r). Thus, as the Moon’s orbit gets bigger, it’s angular momentum increases.
Yeah, it turns out to be solar tides. On pages 159-160 of the paperback edition of A Choice of Catastrophes, after completing his discussion of the receding moon and concluding with the moon and earth circling each other, “dumbbell-fashion,” every 47 days, Asimov says:
Entirely? No precession, nutation, etc.?
Could the earth fall into “synchronous” rotation with the sun?
Has that already happened with Mercury?
Or is it settling into such motion?
Doesn’t Mercury have days that are longer than its years?
Mercury is a very interesting case. A few decades ago, it was believed that it was locked, but in actuality, it’s in a resonant lock. Mercury’s rotation period is exactly two thirds its orbital period. This works because Mercury’s orbit is particularly eccentric: It has a permanent elongation, and every orbit when it’s closest to the Sun (and therefore, the tidal forces are strongest), the long axis lines up pointing towards or away from the Sun.
If anything, though, Venus is even more interesting. It’s almost locked to the Sun (its rotation period is close to the same as its orbital period), but it’s also got a resonance with the Earth. Whenever Venus passes closest to the Earth in our orbits, it always presents the same face towards us.
Yes, contribute to libration also. My major point was that libration is not caused by a difference between the Moon’s rotational period and revolution period.
Wha?
If it’s rotation period is exactly 2/3 it’s orbital period, then when it makes one orbit, it has rotated through 240 degrees.
Are you saying that because it has such a stretched out orbit, that the 2/3 and 1/3 of an orbit fall exactly at the points of the elongated orbit where its closest.
Here is what I’m visualizing you’re saying in a crude drawing. I highlighted one side of mercury just to indicate it’s orientation. “T2” in the first diagram corresponds to “T2” in the second diagram.
Like the moon to the earth?
That sounds incredible. That point at which we’re closest must “move” every year, say in relation to where the Earth is during our equinoxes.
I mean 540 degrees, or 3 * 180 degrees, so that it is exactly flipped every time it returns to the starting point.
It does move every year. But if we neglect eccentricity (which is relatively small for Venus and Earth), it’s always the same amount of time between closest approaches (this period is called the synodic period of Venus relative to Earth). So the planet can accomplish this by rotating at a constant rate (provided it’s just the right constant rate, which it is). Venus isn’t completely locked to the Sun, though, like the Moon is to the Earth. For the Moon, the two periods aren’t just close to equal, they’re exactly equal, and the Earth doesn’t rise or set (except for a small region at the edges, due to libration). For Venus, this is not quite the case, so the Sun does rise and set over any given point on Venus. Presumably, the Sun was trying to lock Venus, but as Venus’ rotation slowed, it reached the point where it had that resonance with Earth, and decided it liked that better.
And Mercury is, in fact, exactly flipped whenever it reaches the starting point. Don’t think of one side of the planet being “special”, think of it as shaped like a football (it actually is, to a very small extent). When the pointy end of a football is pointing away from the Sun, the other pointy end is pointing towards the Sun, so it doesn’t matter that it’s flipped. Your diagram is a bit misleading, since it seems to show two separate points which are closest to the Sun. If you take care to draw a true ellipse, and put the Sun at one focus, then there will be one unique closest point, at one of the pointy ends of the ellipse.
Oh, OK.
I out-thought myself. I was thinking that if the rotation period was 2/3 it’s orbital period, then it was pointing in a different direction at the same point around the eclipse it traces.
What I overlooked (even though I drew it) was that it points in the exact opposite direction for every one of it’s orbital periods, i.e., it’s always exactly 1.5 days later.
One Moonth
rwj
rwjefferson
Now that was cool! The Man in the Moon is winking at you! 