Re: The Dark Side of the Moon

Yes, the Moon does rotate, yes, its orbital period is equal to its rotational period, and, no, this is not a coincidence. Let me quote from the sci.astro FAQ (with thanks to Laz Marhenke ):

In fact the Moon *does* rotate: It rotates exactly once for every orbit it makes about the Earth. The fact that the Moon is rotating may seem counterintuitive: If it's always facing towards us, how can it be rotating at all? To see how this works, put two coins on a table, a large one to represent the Earth, and a small one to represent the Moon. Choose a particular place on the edge of the "Moon" as a reference point. Now, move the Moon around the Earth in a circle, but be careful to always keep the spot you picked pointed at the Earth (this is analogous to the Moon always keeping the same face pointed at the Earth). You should notice that as you do this, you have to slowly rotate the Moon as it circles the Earth. By the time the Moon coin goes once around the Earth coin, you should have had to rotate the Moon exactly once.

[Another more dramatic example is to stand in a room. Pick one wall to be in the direction of the Sun. Put something (like a basketball) in the middle of the room to represent the Earth. Consider yourself the Moon, and face the Earth. Can you walk around the Earth, always facing the Earth, without turning? Try it!]

This exact equality between the Moon's rotation period and orbital period is sometimes seen as a fantastic coincidence, but, in fact, there is a physical process which slowly changes the rotation period until it matches the orbital period.

When it first formed, the Moon probably did not always show the same face to the Earth. However, the Earth's gravity distorts the Moon, producing tides in it just as the Moon produces tides in the Earth. As the Moon rotated, the slight elongation of its tidal bulge was dragged a bit in the direction of its rotation, providing the Earth with a "handle" to slow down the Moon's rotation. More specifically, the tidal bulge near the Earth is attracted to the Earth more strongly than the bulge away from the Earth. Unless the bulge points toward the Earth, a torque is produced on the Moon.

If we imagine looking down on the Earth-Moon system from the north pole, here's what we'd see with the Moon rotating at the same rate as it goes around the Earth:

  Earth                                         Moon
    __          
   /  \                                        ____           ^
  |    |                                      /    \          |
   \__/                                       \____/       Orbiting
                                                           this way
                                         Tidal bulge *greatly*
                                            exaggerated.

What if the Moon were rotating faster? Then the picture would look like:

  Earth                                         Moon
    __          
   /  \                                         ___           ^
  |    |                                       /   )          |
   \__/                                       (___/        Orbiting
                                                           this way
                                              Rotating
                                          counterclockwise;
                                         Tidal bulge *greatly*
                                            exaggerated.

If it isn't clear why the tidal bulge should move the way the picture shows, think about it this way: Take the Moon in the top picture, with its tidal bulges lined up with the Earth. Now, grab it and rotate it counterclockwise 90 degrees. Its tidal bulge is now lined up the "wrong" way. The Moon will eventually return to a shape with tidal bulges lined up with the Earth, but it won't happen instantly; it will take some time. If, instead of rotating the Moon 90 degrees, you did something less drastic, like rotating it one degree, the tidal bulge would still be slightly misaligned, and it would still take some time to return to its proper place. If the Moon is rotating faster than once per orbit, it's like a constant series of such little adjustments. The tidal bulge is perpetually trying to regain its correct position, but the Moon keeps rotating and pushing it a bit out of the way.

Returning to the second picture above, the Earth's gravitational forces on the Moon look like this:

                                 ___
                    F1    <-----/   )
                    F2 <-------(___/

F2 is larger than F1, because that part of the Moon (the "bottom" half in the drawing, or the half that's "rearward" in the orbit) is a bit closer to the Earth. As a result, the two forces together tend to twist the Moon clockwise, slowing its spin. Over time, the result is that the Moon ends up with one face always facing, or "locked," to the Earth. If you drew this picture for the first case, (where the Moon rotates at the same rate that it orbits, and the tidal bulges are in line with the Earth), the forces would be acting along the same line, and wouldn't produce any twist.

Another way to explain this is to say that the Moon's energy of rotation is dissipated by internal friction as the Moon spins and its tidal bulge doesn't, but I think the detailed force analysis above makes things a little clearer.

This same effect occurs elsewhere in the solar system as well. The vast majority of satellites whose rotation rates have been measured are tidally locked (the jargon for having the same rotation and orbital periods). The few exceptions are satellites whose orbits are very distant from their primaries, so that the tidal forces on them are very small. (There could be, in principle, other exceptions among some of the close-in satellites whose rotation rates haven't been measured, but this is unlikely as tidal forces grow stronger the closer to the planet the satellite is.)