The rocking of the moon

I am watching Sagan's "Cosmos" series from decades ago and just learned about a wobble in the moon.

I recall that the reason we always see one side of the moon is that the moon is not round, that it is "heavier enough" on one side that the mutual gravity between the earth and moon keep that heavier side pulled toward the earth. (Mind bender: to the rest of space, the moon is spinning; to us, it doesn't look like it's spinning because it's pointing toward us we make our way around the Sun.)

I recall that humans put some special mirrors on the moon so we could aim lasers at them and measure how long it takes for the laser light to get there, bounce off the mirrors and arrive back home, and thus measure the distance, since we know how fast light travels through space. The principle behind the mirrors is just like your car's reflectors. You've seen your reflection in a store whose corner has a mirror on each wall: as you walk by, you continually see your reflection in that very corner, albeit reversed. The reflectors of a car--and the mirrors on the moon--have three surfaces (one more than the store) so that the image bounces back for up and down motion, too. So, no matter where you are, if you shine a light at that corner mirror, the light bounces straight back to you.

In the Cosmos program, Carl noted how scientists used lasers and those mirrors on the moon to measure our distance from the moon with amazing accuracy ("only in error by about one millionth of a percent"). Picture that the moon's heavy side is facing us, like a bell out in space that always "hangs" directly away from the earth. Scientists measured the distance of the moon from us over quite a long period of time and observed a wobble, back and forth. Some concluded that this was evidence of the moon having been struck long ago by a comet or meteor, making it rock back and forth as it restabilizes toward not wobbling, toward simply facing toward us with no wobble. Cool.