# Homework Help: Earth's Euler angles - nutation?

1. Mar 6, 2006

### Ahmes

Hi,
I would like to see the resemblance between planet Earth and a spherical top. I draw here the x-convention Euler angles as I know them: 24 hours to complete one complete one revolution around it's own z' axes. And the 23.5° Earth axes revolves around the "sun's z axes" - the line perpendicular to the plane where the Earth orbit's the sun.

So where is the nutation? does the 23.5° ever change?
Thanks.
http://img214.imageshack.us/img214/5059/earthorbit3nb.png [Broken]

Last edited by a moderator: May 2, 2017
2. Mar 6, 2006

### Andrew Mason

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Apparently it does. While the precession rate is very slow (a period of 26000 years) the nutation (which puts ripples in the cone prescribed by the axis as it precesses) has a variable period but predominantly about 18.6 years. See: http://en.wikipedia.org/wiki/Nutation

AM

Last edited by a moderator: May 2, 2017
3. Mar 7, 2006

### BobG

There's at least two significant bodies causing the Earth's axis to change. The Sun causes precession and the angle between the Earth's axis and the ecliptic plane does change very slowly over time. The Moon's orbital plane is about 5 degrees off of the ecliptic plane, so it's angle relative to the equator varies between around 18.4 to 28.4 degrees. The Moon's orbit around the Earth causes a jitter in the Earth's rotation axis that follows an 18.6 year cycle. (Actually, you also need to toss in the effect of the other planets, as well, if you want a precise calculation of the motion of the Earth's axis, but the planets obviously have much less effect than the Moon and Sun).

If you have access to an Astronomical Almanac, Section B describes how to calculate both precession and nutation. The International Earth Rotation Service's website (http://www.iers.org/) also has the 1976 Precession Theory and 1980 Nutation Theory (which are easy to use), plus the newer, more detailed IAU 2000A model. The IERS is updating their website to present a more professional appearance, so the site map is probably the easiest way to find info until they finish construction.