Tidal Locking

The recent years have brought us lots of news about new exoplanets. A lot of the discoveries are credited to NASA’s hard working space telescope Kepler. The way Kepler works means that the first new planet candidates were primarily orbiting really close to their parent stars. You have probably seen lines like “the planet XYZ is orbiting so close to it’s host star ZYX that it is tidally locked and always turns the same side towards the star” in the news about the discovered stars. What’s this tidal locking thing then? How come a planet that orbits freely around a star has its rotation synchronized to the planet’s motion around the sun?

Turns out we don’t need to look at other solar systems to find other examples of tidal locking. The rotation of our very own moon is tidally locked, showing the same side towards us all the time. Mercury, the innermost planet in our solar system is also tidally locked to sun, but it exhibits a more complex 3:2 ratio (so it rotates three times around itself for every two orbits around the sun) because of the eccentricity of Mercury’s orbit.

But back to the issue here: how does all of this happen and what’s the connection with tidal locking and tides (they are indeed related)? To understand what happens, we need a little bit of physics:

Let’s go back in history to a time when the moon was still rotating around its axis so that an observer on earth, if there would have been one, would have seen all the sides of moon would he have stared long enough. To keep things simple, let’s assume that the moon orbits the earth on a circular orbit and that the only force in effect is earth’s gravity pulling the moon towards earth. We know that the gravitational force is proportional to the product of the masses interacting and inversely proportional to the square of distance between them.

tidal_forcesThe second part is actually important here: if we think of the moon as two halves of a sphere, cut along a plane perpendicular to the earth’s gravitational pull, we can see that earth actually pulls the different halves with a little bit different force. The farther half of the moon is – well – farther away and thus feels a slightly smaller force. This unevenness causes the moon to deform from an ideal sphere and get elongated along an axis pointing towards earth.

Now that the moon is spinning, the bulge is actually not pointing straight towards earth. The moon rotates all the time and since it’s actually made of rock, it resists the deformation. This makes the bulge shift a bit to the side where the moon is rotating.

Now that the moon is shaped like an american football and it does not point straight to earth, the interesting part happens: The bulge closer to the earth feels a bigger gravitational pull than the bulge on the other side of the moon. Since the forces are not aligned along the axis that points towards earth, the net torque isn’t zero. This makes the gravitational pull of earth actually slow down the rotation of the moon until the bulge is aligned with the gravitational pull, ie. the orbiting body is tidally locked.

This actually happens to the earth too: same mechanism causes earth to deform and tides in oceans. The bulges created by moon’s gravity are not exactly in sync with the moon either, so the moon slows down our rotation. This loss of angular momentum is transferred to the moon which lifts its orbit and makes it get farther away from us. At current pace, the moon’s orbital radius grows by 38mm per year and our day gets 15 microseconds longer each year because of the slowing down.

All of this because of a force between two bodies in the emptiness of space.


2 thoughts on “Tidal Locking

  1. I’d guess that might happen eventually with moon, although the tidal effect gets weaker all the time as the moon get further away. As a wild guess I’d say that the moon is probably not big enough to slow down earth’s rotation sufficiently at least before the sun dies. I’d also guess that sun is not close enough to exert a noticeable torque on us. Wikipedia tells that the sun’s and the moon’s tidal effects are of roughly the same magnitude, but since sun is so much further away, the gradient of the gravitational force is really small (eg. the force does not change noticeably).

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