Notes from Under Sky

The Lunar Dance

Will we ever become tidally locked with the Moon?

Someone wrote:

I heard that the Earth's rotation is slowly slowing down. We have longer days now than during the Roman era. I heard this is due to friction between Earth and whatever.
So when will the Earth stop rotating completely? When it reaches almost that stage, will we have a day that takes as long as a year or more? Will life still exist with one side constantly baked by the sun while the other side completely remains dark? Would you want to live on the bright side or the dark side?

The Earth's rotation is slowing down, due to a tidal interaction with the Moon. Roughly speaking, the Moon raises two high tides on the Earth—one on the side facing the Moon, and one on the other side. If the Moon revolved around the Earth once per day, those high tides would remain in the same place on the Earth. But the Moon does not revolve that fast; instead, it revolves around the Earth about once every 28 days, with respect to the stars.

As a result, the Earth, which does rotate once per day, is rotating "under the tides," so to speak. We who are bound to the Earth by gravity usually think of the high tides coming to us (if we live by the coasts), but it is really we who rotate toward the high tides; they rotate much slower than the Earth.

Because of this disparity in speeds, the tidal bulges in the oceans (and to a lesser extent, the land masses) act as a frictional brake on the Earth's rotation. This brake is not very strong; the Earth's day lengthens by about 1 second every 60,000 years or so. If you lived back in the days of the ancient Greeks, for instance, you would not be able to tell the difference even with a reasonably accurate wristwatch.

However, the differences add up. Because of this increase in the length of the day, astronomical events such as eclipses took place at different times of day and in different locations of the Earth than they would have if the Earth's rotation rate were constant, and the distance between where they "ought" to have been and where they were really recorded tells us how fast the Earth's rotation is slowing down.

By Newton's third law, incidentally, if the tidal bulges are pulling back on the Earth's rotation, the Earth's rotation is pulling forward on the tidal bulges. Those bulges, in consequence, are not directly under the Moon, but are instead slightly ahead of it. They, in turn, pull the Moon forward, pushing it into a slightly higher orbit. This effect, like the slowing of the Earth's rotation, is very small, amounting to (I think) centimeters per year or so.

However, that too adds up and the current consensus is that the Moon orbited much closer to the Earth back in the days when it was young, about 4 billion years ago. Since the strength of the tides varies inversely as the cube of the distance between the Moon and the Earth, a Moon that is, say, 5 times closer creates tides that are 125 times as intense. Imagine the tidal bulges that washed across the land in those days!

As the Earth slows its rotation down, the tidal slowing itself gets smaller and smaller, since the difference between the Earth's rotation and that of the tidal bulges is decreasing. To be sure, the revolution of the Moon also slows down as a result of its receding from the Earth, but that effect is not large enough to counteract the lengthening of the day. If the Earth-Moon system were left alone, the day and month would both lengthen to the point where both lasted about, oh, 40 days or so. At that point, the Earth and Moon would both be tidally locked, the tidal bulges would be in sync with the Earth's rotation, and there would be no further slowdown.

However, the Earth-Moon system is not left alone. In particular, there is the Sun to concern ourselves with. Through a more complex interaction, it would act to bring the Earth and Moon, still tidally locked, back closer together again. I say "would act," because the time scales on which this would happen are in the tens or hundreds of billions of years. Long before that happens, the Sun will become a red giant and possibly swallow the Earth and Moon, making the latter part of this analysis entirely academic (if it wasn't already). The Earth and Moon will probably not come close to getting tidally locked to one another before then.

To answer your other questions, it used to be thought that the Sun would stay at roughly the same temperature for the rest of its lifetime as an ordinary star. It now appears that that won't happen—that the Sun will gradually warm over the next few billion years. Although the increase will be slow from the perspective of the Sun, it will likely be enough to raise the surface temperature of the Earth above the boiling point of water within a billion years or so, and that will be that for life on the surface. We could consider moving elsewhere at that time—assuming, of course, that we're still around to consider it.

See also this article on tidal locking, written some years ago.

Copyright (c) 2004 Brian Tung