How precise is our tidal lock to the moon?
July 5, 2018 5:02 AM Subscribe
This seems a like a simple question to answer, but I can't find anything online. We're tidally locked to the moon, which means the same side is always facing the earth. But it seems unlikely that it's a perfect lock. If it's imperfect, how long will it be until the opposite side is facing us?
It's not perfect, but it's not rotating. Libration is the slight perceived oscillation of the Moon that means you can see 59% of the surface from Earth.
posted by zamboni at 5:22 AM on July 5, 2018 [15 favorites]
posted by zamboni at 5:22 AM on July 5, 2018 [15 favorites]
Best answer: You question suggests that "perfect lock" means it will always face the same side, and "imperfect lock" means it will eventually show the opposite side. What you are missing here is that tidal lock ≠same side always faces (called synchronous rotation). Synchronous rotation is a specific case where the tidal locking is 1 to 1, that is, a body rotates around its own axis in the same time it orbits another. Tidal locking doesn't require it to be 1 to 1. In the case of the Moon-Earth system, it is 1 to 1, and for purposes of this question, it will forever be. It will never show the other side.
posted by Pig Tail Orchestra at 6:39 AM on July 5, 2018 [2 favorites]
posted by Pig Tail Orchestra at 6:39 AM on July 5, 2018 [2 favorites]
To follow PigTailOrchestra, Mercury is tidally locked to Sol, but in a 3:2 resonance so from Sol's perspective Mercury slowly rotates.
posted by GCU Sweet and Full of Grace at 6:54 AM on July 5, 2018 [2 favorites]
posted by GCU Sweet and Full of Grace at 6:54 AM on July 5, 2018 [2 favorites]
Best answer: Right, tidal locking is not the same as matched rotation, and likewise libration of moon does not mean it’s not perfectly locked.
Tidal locking is a stable state for the planet/satellite system, and if any small forces act on either object, they will return to the locked state unless acted upon by an outside source. When things start out not gravitationally locked, they tend to move ‘downhill’ into the locked state: that’s why so many of the moons in the solar system are locked, or thought to be. If you look in the "timescale" section of the Wikipedia article, it shows how to compute the expected time to lock.
So we know the locking is stable for the two body problem, and it will not ‘drift’ out of lock on any time scale. But we live in a solar system, so all the two-body theory is invalid in the long term, which is why I started with solar system stability.
posted by SaltySalticid at 7:13 AM on July 5, 2018 [1 favorite]
Tidal locking is a stable state for the planet/satellite system, and if any small forces act on either object, they will return to the locked state unless acted upon by an outside source. When things start out not gravitationally locked, they tend to move ‘downhill’ into the locked state: that’s why so many of the moons in the solar system are locked, or thought to be. If you look in the "timescale" section of the Wikipedia article, it shows how to compute the expected time to lock.
So we know the locking is stable for the two body problem, and it will not ‘drift’ out of lock on any time scale. But we live in a solar system, so all the two-body theory is invalid in the long term, which is why I started with solar system stability.
posted by SaltySalticid at 7:13 AM on July 5, 2018 [1 favorite]
I believe tidal locking is a stable equilibrium state. It would take adding energy to the system to force it out of tidal locking. The linked Wikipedia article mentions that the Earth's rotation is slowing down over time, in part because it's giving up momentum to maintain the tidal locking. But the moon stays locked through those changes.
posted by Nelson at 7:15 AM on July 5, 2018 [1 favorite]
posted by Nelson at 7:15 AM on July 5, 2018 [1 favorite]
Best answer: I'll try an analogy before I bow out:
Imagine you toss a marble into a bowl full of honey. It may take a while, but you expect it to eventually settle to the bottom. This is the kind of stability that the tidally locked satellite has. True, if you shake the table a bit, it may move the marble a bit, but it will always settle down to the bottom again. Whether the marble is "perfectly" at the bottom at any given moment in time is a slightly weird question: you generally expect it to stay there, and it's pretty tough to measure if it's a few mircometers away from the true "perfect" bottom of the bowl.
Now imagine you put the bowl in your car and drive around. This is like the Earth and Moon being out in the Solar system. If you ask "how long does the marble stay at the bottom?", the answer is something like "until the car flips over, or the bowl breaks (etc.)". You can't really know when the marble will come out just by studying the marble and bowl (and in fact if you only look at the marble and bowl, you conclude it can never come out!). Also, you can't know when the car will crash until mere moments before it happens. Likewise, all kinds of stuff whizzes around the solar system, and it may well happen that something nudges or kicks the moon out of its locked state, but that is the business of trying to make long-term quantitative predictions on the state of a chaotic system, and we know we can't do that. Hope that helps!
posted by SaltySalticid at 7:42 AM on July 5, 2018 [8 favorites]
Imagine you toss a marble into a bowl full of honey. It may take a while, but you expect it to eventually settle to the bottom. This is the kind of stability that the tidally locked satellite has. True, if you shake the table a bit, it may move the marble a bit, but it will always settle down to the bottom again. Whether the marble is "perfectly" at the bottom at any given moment in time is a slightly weird question: you generally expect it to stay there, and it's pretty tough to measure if it's a few mircometers away from the true "perfect" bottom of the bowl.
Now imagine you put the bowl in your car and drive around. This is like the Earth and Moon being out in the Solar system. If you ask "how long does the marble stay at the bottom?", the answer is something like "until the car flips over, or the bowl breaks (etc.)". You can't really know when the marble will come out just by studying the marble and bowl (and in fact if you only look at the marble and bowl, you conclude it can never come out!). Also, you can't know when the car will crash until mere moments before it happens. Likewise, all kinds of stuff whizzes around the solar system, and it may well happen that something nudges or kicks the moon out of its locked state, but that is the business of trying to make long-term quantitative predictions on the state of a chaotic system, and we know we can't do that. Hope that helps!
posted by SaltySalticid at 7:42 AM on July 5, 2018 [8 favorites]
Best answer: I think this is a harder question than it seems to be at first because the Moon is actually spinning; it spins once for each time it revolves around the Earth, and as a consequence of the fact that its spin rate is the same as its period of revolution, it shows us almost the same face all the time.
The rub comes when we try to look into the future.
Because the Earth and Moon make up a system which is very nearly isolated from external sources of torque, conservation of angular momentum demands that as the Earth's spin slows down from tidal friction exerted by the Moon, the Moon's orbit must get further from the Earth.
And yet, an orbit further from the Earth would have a longer period of revolution, and if the Moon retained the same rate of spin it had when it was closer, it would be out of sync with its orbit, and we would eventually (very slowly) see its entire surface from Earth.
In order to keep this from happening, tidal friction exerted by the Earth on the Moon has to come into play to slow down the Moon's spin as it recedes from the Earth.
However, tidal friction depends on the gravitational field of the Earth being nonuniform across the diameter of the Moon: strongest at the point closest to Earth and weakest farthest away, and as the Moon gets further away, the gravitational field strengths at the nearest and farthest points on the Moon get closer and closer together, while at the same time the average strength of the gravitational field of the Earth declines because of the distance.
In other words, as the Moon moves away from the Earth, Earth's ability to exert tidal friction on the Moon goes down.
Will the effect of tidal friction exerted by the Earth ever lose its grip on the Moon to the extent that the Moon starts to spin faster and faster relative to its orbital period as it moves away?
I'm not sure, but I don't see any easy way to rule it out. As I understand what I've read, it's thought that the Moon will continue to move away from the Earth as Earth's spin slows down until the Moon's orbital period coincides with the length of a single day on the Earth, and at that point the Moon will really be out there -- out where the Earth's gravitational field is pretty weak and quite uniform.
posted by jamjam at 5:00 PM on July 5, 2018
The rub comes when we try to look into the future.
Because the Earth and Moon make up a system which is very nearly isolated from external sources of torque, conservation of angular momentum demands that as the Earth's spin slows down from tidal friction exerted by the Moon, the Moon's orbit must get further from the Earth.
And yet, an orbit further from the Earth would have a longer period of revolution, and if the Moon retained the same rate of spin it had when it was closer, it would be out of sync with its orbit, and we would eventually (very slowly) see its entire surface from Earth.
In order to keep this from happening, tidal friction exerted by the Earth on the Moon has to come into play to slow down the Moon's spin as it recedes from the Earth.
However, tidal friction depends on the gravitational field of the Earth being nonuniform across the diameter of the Moon: strongest at the point closest to Earth and weakest farthest away, and as the Moon gets further away, the gravitational field strengths at the nearest and farthest points on the Moon get closer and closer together, while at the same time the average strength of the gravitational field of the Earth declines because of the distance.
In other words, as the Moon moves away from the Earth, Earth's ability to exert tidal friction on the Moon goes down.
Will the effect of tidal friction exerted by the Earth ever lose its grip on the Moon to the extent that the Moon starts to spin faster and faster relative to its orbital period as it moves away?
I'm not sure, but I don't see any easy way to rule it out. As I understand what I've read, it's thought that the Moon will continue to move away from the Earth as Earth's spin slows down until the Moon's orbital period coincides with the length of a single day on the Earth, and at that point the Moon will really be out there -- out where the Earth's gravitational field is pretty weak and quite uniform.
posted by jamjam at 5:00 PM on July 5, 2018
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The stability of the solar system is generally unknown on the long term, and it’s a classic example of a chaotic n-body gravitational system. So when it comes down to it, we don’t know, and we’re pretty sure we can’t know the long-term fate of solar bodies, other than by waiting and watching.
Which is not to say that we don’t have some good analysis of what’s going on and how stable the tidal lock is on the short term. Here’s a Dynamical history of the Earth-Moon system, and a freely accessible paper on the Tidal Evolution of the Moon from a High-Obliquity High- Angular-Momentum Earth.
Both discuss the evolutionary past of the system and its stability.
posted by SaltySalticid at 5:20 AM on July 5, 2018 [3 favorites]