Re: Can a sphere have more than one axis of rotation?

As far as calculating axies of rotation involving different torques and angles, I have little knowledge.

About the earth's axis - it always stays paralell to the same plane. It therefore does not precess in relation to the plane. Consider that when the earth is on one side of the sun, the north pole points away from it (at 23.5 degrees), while when the earth is on the exact opposite side of the sun, (1/2 year later) the north pole points toward the sun. (at 23.5 degrees.) Thus the axis of rotation of the earth always points in the same direction!

Additional comments:

Earth rotates once about its central axis (a line between the North and South geographic poles) once every 23 hours, 56 minutes. In addition of course, it revolves (orbits) all the way around the sun every 365 days or so. The direction in which the Earth's poles point is NOT perpendicular to it's orbit - in other words, it's equator is NOT on the "ecliptic plane" formed by its orbit around the sun. Now as the earth revolves around the sun in its orbit, the direction in which the North and South poles are facing does NOT change relative to the background stars. That's why the North Star is still the North Star all year round, whether its Winter or Summer. And thanks to all of this, we have seasons in temperate zones!

However, the North and South poles are NOT constant: they do in fact change, but very, VERY slowly. This change is called "precession of Earth's poles", or just precession. To imagine this, think of a top that is spinning on its axis: as it slows down, the top begins to "droop" - it's axis of rotation drops from "straight up", and begins to spin around more slowly than the top itself. This is analogous to the precessing of the Earth's poles. The Earth's poles are actually doing a full precession (North pole spinning away from the "North Star" in the sky, then returning back to its area) once every 26,000 YEARS!

Finally, Earth's poles do NOT precess in a perfect circle against the background stars: like a top spinning down, the earth's precession is gradually "wobbling" itself, becoming more elliptical rather than circular. This is called "nutation" - yet another motion of earth! And in fact there are even variations in nutation over 100s of thousands of years!!

As a final answer to the mathematical question, though, neither precession, nutation, nor their variations over time would be additive with earth's rotation. First of all, the time scales are hugely different: 1 sidereal day versus 26,000 or moreyears. Second (and more mathematically speaking), precession is a motion OF the axis of rotation, NOT a rotation of the earth ABOUT an axis. (I.e., no point on a precessing sphere has a motion which will trace out a great circle around that sphere - which isn't true of rotation.)

Hope this helps! Lew Gramer