In context of this configuration, velocity and angular momentum pertaining the parabolic path to which our planet is held by its host star (likewise our satellite respective Earth's gravity), the distance or mass of the Sun, Moon and planets is of no consequence whatsoever... Non-withstanding extant primary axial rotation (spin), any object can incur secondary axial rotation: off-set from the former, whereby the Polar axis is perturbed, there simply is no force to counter such.
Accordingly, Mars or any other planet, could exhibit its own particular precession (or not at all) - determined by the relevant criteria of the most recent impact. As such, precession can be altered or re-set to another plane. The introduction of this post [grahamhancock.com] elaborates on the phenomenon of axes of rotation encountered by outward expanding dimensions.
By contrast, your inferred textbook theories & formula [grahamhancock.com] is typical closed system, terrestrial Law - 'downward' gravity in contact with the surface of Earth - eg. the spinning top & the apple tree. Neither of which conform functionally respective 'off-shore', in space...
Therefore, calculation pertaining the duration of precession merely involve direction and momentum transfer - i.o.w. the time of one axial revolution - respective which, Earth's orbit around the Sun has no bearing at all. It's advisable to actually read the threads in this topic and the article links that I provided for your perusal.
Edited 5 time(s). Last edit at 07-Feb-21 09:19 by hendrik dirker.