I made a massive mistake

Contributed by
Aug 18, 2006

OK, one more thing about planets and such. In my original article, I screwed up my math (that's what you get for writing in a hurry under deadline pressure when your server has crashed and you think it's hacked and you'll be out hundreds of bucks to fix it and also have to use backups from two weeks ago because you forgot to do them more recently and haven't written a script to do it automatically, but that's no excuse).

I said that the barycenter of the Earth-Moon system is about 1700 kilometers underneath the Earth's surface, which is correct. Since the Moon is moving away from the Earth by 4 centimeters a year, I said that the barycenter will then be above the Earth's surface in about 40 million years (1700 km/4 cm/yr).

Bzzzzt. I was wrong. The barycenter moves outward from the center of the Earth more slowly than the Moon does, by the ratio of masses of the Moon and the Earth. So for every kilometer the Moon moves out, the barycenter moves out 1/81 of that or so. I redid the math, and I get that the barycenter will reach the Earth's surface when the Moon is about 524,000 kilometers away. At 4cm/yr, that's more like 3 billion years from now. That's a long time, so I guess we don't have to worry so much about the Moon having to be called a planet any time soon.

I should also note, as a few people in the comments and via email have pointed out, the Moon's recession changes with time. Its current rate of 4 cm/yr is likely to be higher than normal due to some complicated physics with how the Moon and Earth interact (and the speed of the ocean tides and shape of the continents). So in the future the recession rate will likely be lower than 4 cm, meaning the Moon will be a moon for even longer than 3 billion years.

So there you go. I sometimes have to debunk myself. Anyway, I corrected my original entry and linked it to here for all to see my off-centered correction.

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