Isaac Newton, and others since his day, have shown that the Earth's precession is caused by the gravity of the Moon and Sun acting on the oblateness of the Earth. Since it can be calculated so accurately I have to believe it is true. The obliquity, or angle between the plane of the Earth's orbit and the axis, is about 23 degrees but varies between 22.1 and 24.5 degrees, in-phase with the precession circuit. Is this sometimes called nutation? Some say the obliquity change is caused by the Moon's orbit varying between 18 and 29 degrees to the plane of the equator with a period of 18.6 years. How could this change the obliquity with a period of 26,000 years? Who calculated it? Why should it be in phase with the precession? Is there any known connection between the precession and orbit cycles?
Thank you for your question. The motion of the Earth's axis of rotation is very complex and is affected by several perturbations.
The most important, as you said, is the precession. Due to the action of the gravity of the Moon and the Sun acting on the oblateness of the Earth, the terrestrial spin axis describe circles of an average value of 23 degrees and 27 arcminutes around the normal of the ecliptical plane (the orbital plane of the Earth). As you said, the value of the obliquity also changes with time. The period for a complete rotation of the spin axis is 26,000 years.
On top of this motion, there are some irregularities. The plane of the orbit of the Moon is also precessing, with a period of 18.6 years. This causes the celestial poles to describe ellipses, with a semimajor axis of 18.42" and a semiminor axis of 13.72". What that means is that the motion of the celestial poles around the normal to the ecliptic is not a perfect circle, but is a perturbed motion given by the sum of the precession motion plus the motion on the nutation ellipse. (You can try to visualize this motion by imagining an ellipse whose center is one point on the circle of precession. The celestial pole would rotate around the ellipse with the 18.6 year period, while the ellipse itself is rotating around the normal to the ecliptic plane with the 26,000 year period. This description is analogous to the ancient epicycle theory of Ptolemaeus.)
I should mention that the other planets also have an effect on the plane of Earth's orbit, causing the vernal point to move by 0.114 arcseconds per year.
Finally, the precession cycle was first noticed by the Greek astronomer Hipparchus, in the 2nd century B.C.
I hope that answers your questions.
This page was last updated on July 18, 2015.