### Will the Earth ever be tidally locked to the Moon?

• 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?

• 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:

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.

@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.

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.

@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.

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.

@DavidHammen - astounding.