Question

Given the following information, does that mean the Earth will eventually change its axis of rotation to the vertical?

Our Earth rotates at an angle of 23.5 degree to the vertical and its North Pole points to the star Polaris in the celestial sphere currently. Because of precession, it used to point to the star Vega possibly about 12,500 years ago. This means that if we try to find out the effects of precession on our Earth every year the change is negligible. However, at the end of the cycle our Earth is supposed to complete another cycle.

Answer 1

NO, if the angular spacing between Pole Star and Vega as observed from the center of the Earth, is a little `<` than `47^o`.

Explanation:

The information given is very relevant, Thanks to to ancient sky-gazing astronomers for the the information that the polar axis was pointing towards Vega, 12500 years ago.

This period is nearly half Great Year period of 256 centuries for one complete rotation of the polar axis, about normal to the ecliptic.

The inclination `23.4^o` of the axis to the normal remains nearly the same. In other words, the angular spacing of the tilt axis from the normal as observed from the center E of the Earth remains as this angle.

In half period, the shift of the the direction EP, from E to North Pole P, from the reference star Vega to Pole star, indicates that the angular spacing between the two stars has to be near,y `2 X 23.4^o`, as viewed from E. If this is true, then the answer is an affirmative NO

What I could gather is that the bright northern circumpolar star Vega, of the constellation Lyra, has declination `39^o` down, from North Pole star. This is in favor of the answer NO. .