Elliptical Precession?

Does anybody know if there is evidence that the axis of earth's orbit (not
it's spin axis) marks out an ellipse on the celestial sphere as it
precesses?

John Schutkeker wrote:

Does anybody know if there is evidence that the axis of earth's orbit (not
it's spin axis) marks out an ellipse on the celestial sphere as it
precesses?

It doesn't. The motion of the ecliptic pole results from torques on
the orbit from the other planets. These torques can be modeled as the
sum of various sinusoidal terms, each with its own amplitude, period,
and phase. Consequently the ecliptic pole follows a nonrepeating path,
never wandering more than a few degrees from the direction of the total
angular momentum of the solar system (the direction perpendicular to
the invariable plane). The largest perturbations are due to Venus and
Jupiter.

-- Bill Owen