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From my basic understating,

Momentum is being transfered from the Earth's rotation to the Moon's orbit by tidal friction. The Earth's rotation slows down and the Moon receedes from the Earth as it moves into a higher orbit. This will continue until the Earth's rotational period is equal to the orbital period of the Moon, i.e the Earth is tidally locked to the Moon.

Assuming I have the above correct - and please correct me if I don't - will there, realistically, be enough time for tidal locking to occur before the sun expands and engulfs the Earth? Or is there another reason the Earth will never be locked towards the Moon?

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2 Answers 2

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As the moon orbits Earth, tidal forces slow down the Earth's rotation by 2 milliseconds per century. Eventually, in tens of billions of years, the Earth and Moon would achieve a double tidal lock, where both are stuck with one side facing the other as they orbit the Earth-Moon barycenter. In 7.5 billion years, the Sun will expand past the Earth's current orbit, but the Earth may drift out further, preventing it from being vaporized.

However, this is beside the point, because in about one billion years, all of Earth's water will have boiled away, meaning that there would be no more ocean tides, and thus the Earth-Moon system will likely never achieve a double tidal lock.

References:

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    $\begingroup$ I know there's large uncertainty in this, but I was surprised to see you list 7.5 billion years (and I presume you quoted your last reference which also states this) for the Sun to expand and possibly swallow the Earth. Almost every other reference to this timescale I've heard has been closer to 5 billion years. I have to wonder where the last reference got its value from. $\endgroup$
    – zephyr
    Commented Oct 20, 2016 at 15:40
  • $\begingroup$ @zephyr The last reference states that the Sun will expand in 5 billion years but not quite to Earth's orbit yet. I'll see if I can get secondary validation for that. $\endgroup$
    – called2voyage ♦
    Commented Oct 20, 2016 at 15:41
  • $\begingroup$ Ah, I think I see the difference. They state "About 7.6 billion years from now, the sun will reach its maximum size as a red giant" which doesn't preclude the commencement of the expansion in 5 billion years. $\endgroup$
    – zephyr
    Commented Oct 20, 2016 at 15:44
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    $\begingroup$ @zephyr One paper says that about 2.55 Gyr from now the sun will reach its maximum $T_{eff}$. 5.42 Gyr from now the sun will be 37 percent larger than today, which still keeps it quite far from Earth's present orbit. 7.59 Gyr from now the sun will reach the tip of its red giant expansion. This seems consistent with the Scientific American article. The paper I linked in this comment also estimates the mass loss of the Sun and finds that the Earth's orbit would expand far out enough to survive, but as a molten planet. $\endgroup$
    – called2voyage ♦
    Commented Oct 20, 2016 at 15:57
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    $\begingroup$ Re Eventually, in tens of billions of years, the Earth and Moon will achieve a double tidal lock ... That's assuming the Earth's rotation rate slows down at the current rate. Bad assumption. This rate is anomalously high compared to rates over the last billion years thanks to two huge north-south barriers to the tides (the Americas and Africa+Eurasia). In about a billion years (see your last reference), the Earth will lose its oceans due to greenhouse warming. As the oceans are responsible for almost all of the tidal deceleration, the Earth will never be tidally locked to the Moon. $\endgroup$
    – David Hammen
    Commented Oct 21, 2016 at 1:28
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I was going to make a few corrections previous answer and comments but I don't seem to have enough rep to add comments. So I may as well answer the question itself.

First, you are right (ignoring the Sun for now) that the Earth will eventually be tidally locked to the Moon, just as the Moon is already locked to the Earth, whence 1 day = 1 month (and a month will be much longer than it is currently).

Before that happens the Sun will get hotter and larger, resulting in the Earth/Moon being swallowed or probably pushed into a higher orbit. By then the tidal effects of the Sun will be much greater which will affect the rotation of the Earth much more than the Moon (exactly how I'm not sure).

A couple of points re previous answer and comments:

  1. It's misleading to say that the Earth will lose its oceans due to greenhouse warming. The ultimate cause is that the Sun is getting hotter.
  2. The oceans are not the only cause of tidal locking, otherwise the Moon (having no oceans) would not have become tidally locked to Earth. Our whole planet has lunar "tides" (resulting in changes in height near the equator of about half a meter) which will continue with or without oceans.

This is my understanding and I am open to being enlightened.

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    $\begingroup$ Sure, the Sun is getting hotter, and that will eventually cause a runaway greenhouse effect. David H isn't suggesting that we'll lose the oceans because of anthropogenic global warming. Yes, there are land (and atmospheric) tides, but they don't transfer anywhere near the same amount of energy & angular momentum as the ocean tides do. So when the oceans are gone, that will severely reduce the rate that the Earth's rotation speed is slowing down and the Moon's mean orbital radius is increasing. $\endgroup$
    – PM 2Ring
    Commented Jul 9, 2022 at 5:29
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    $\begingroup$ Thanks @pm-2ring, I agree entirely with your technical points. I know what David was saying and that he did not mean to suggest anthopogenic global warming. But that it would probably be taken that way by 99% of the population. (And just in case anyone reads this to whom it is not clear: Earth's oceans will evaporate in the distant future due to the warming Sun and the fact that H2O is a potent greenhouse gas, not because of CO2 released by humans.) Also the 1st answer implied that tidal-locking is impossible without oceans (which is not true) it's just the effect is reduced by 92% (est.). $\endgroup$
    – user74292
    Commented Jul 10, 2022 at 5:44
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    $\begingroup$ I like this answer. Everyone needs to know that a world with no water (and therefore no 'tides') doesn't mean that a tidal lock is impossible. Most satellites don't have water, and yet locking happens. Wiki shows time to tidal lock and not a single parameter has anything to do with water specifically. Yes, mu, rigidity, changes with less water, but no planet is perfectly ridged, and if the moon, earth system exists long enough, earth will lock to moon even with no water on the planet. $\endgroup$
    – jpmorris
    Commented Sep 8, 2023 at 21:56

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