In an online book
Geodätische Astronomie: Grundlagen und Konzepte
by Albert Schödlbauer I saw a picture of precession and nutation of Earth's axis.
In German but I suppose it is understandable.
The precession is: $$ 360 ^\circ / (25.728 \text{ years}) = 50.2 '' \text{ per year} $$
In the book the autor states that the true rotation axis moves along a small cone wrt the average rotation axis.
This is the small elliptical cone with axes a/b in the picture.
Then he goes on and states that the true axis moves along the great precesion cone with an angular velocity of $$ 50.2'' \cdot \sin{(23.5)} = 20.1'' \text{ per year}.$$
Can someone explain why this is so, I don't get it by myself.
In another book the same is stated in the following way.
The earth's rotation vector is inclined $23.5^\circ$ to the pole of it's orbital plane, the ecliptic. The period of the resulting precession is about $26,000$ years, corresponding to a motion of the rotation vector of $20$ arcsec per year [$2\pi \sin{(23.5^\circ) / 26,000}$ radians per year].
Why ??
While: The line of intersection of the ecliptic and celestial equator precesses at a rate of $50$ arcsecs per year