## The Wobbling of the Earth and Other Curiosities

#### December 26, 1999

Okay, now for some answers to my various subsidiary puzzles!
```>In the theory of rigid rotating bodies, the wobbling of a
>body in the absence of external forces is called "precession".
>But in astronomy, the "precession" of the earth refers to a
>*different* effect!

>So: who knows what this other effect is?
```
Answer: The precession of the earth is the slow turning of the earth's axis of rotation due to the gravitational torques of the sun and moon.
```>Also: who knows what "nutation" means in the theory of spinning tops?
```
Answer: it's the rapid small wobble of the top's axis which one sometimes sees superimposed on the slower precession of this axis. This doesn't happen in the absence of external forces (gravity in this case).

For details, see Felix Klein and Arnold Sommerfeld's 4-volume masterpiece, "Theorie des Kreisels", meaning "The Theory of Tops". Or if that's too weighty, try Klein's slender "The Mathematical Theory of the Top".

```>And who knows what it means in astrononmy, when applied to the motion
>of the earth?
```
Answer: The nutation of the earth consists of various smaller and more rapid wobblings due to the gravitational torques of the sun and moon, superimposed on the slower precession of the axis.
```>And finally, just for the sake of a well-rounded education: what's
>the period of the precession of the earth?  What's the period of
>the nutation of the earth?
```
Answer: The period of the precession is 26,000 years. This is easy to guess if you remember that Christ was born in the age of Pisces and right now we're getting close to the age of Aquarius. That means it takes about 2000 years for the earth's axis to turn by one sign of the zodiac. Since there are 12 signs in the zodiac, this means the period of precession is close to 24,000 years.

The nutation consists of various components, but the largest has an amplitude of only 17 seconds and a period of 18.6 years. For a bit more on this stuff, read on....