## The Wobbling of the Earth and Other Curiosities

#### December 17, 1999

```Jim Heckman wrote:

>John Baez wrote:

>> Okay, here comes the puzzle.  The earth is not spinning
>> exactly around the first principal axis.  It's a bit off,
>> so it wobbles.  Estimate the period of this wobble!

>Well... On dimensional grounds alone, it seems like it would almost
>*have* to be ~( I1 / (I1-I2) ) times the period of the earth's rotation...
>(I'm *guessing* that the wobble period -> infinity rather than -> 0 as
>earth -> spherical.)
```
Are you also guessing that the wobble period doesn't depend on the wobble tilt, or something like that? And is there some reason you're guessing this?
```
>Well... Again dimensionally, inertia is (mass * distance^2). I'm pretty sure
>earth's radius is ~6700 kilometers and I *think* the polar vs. equatorial
>flattening is ~50 kilometers, so
>
>( I1 / (I1-I2) ) ~ ( 6700^2 / (6700^2 - (6700-50)^2) ) ~ 70
>
>so... ~70 days?
```
I'd prefer not to comment on this until I get a few more takers - I don't want to spoil the fun.