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#.

Thanks to ancient sky-gazing astronomers, who discovered that the polar axis was pointing towards Vega 12,500 years ago, the information provided is extremely pertinent.

This period, which is roughly normal to the ecliptic, is almost half of the Great Year period, which lasts 256 centuries for one full rotation of the polar axis.

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. .
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Answer 2

Although there have been times in Earth's history when the axis of rotation has shifted, it is not possible to predict future changes with certainty based solely on the information provided. The Earth's axis of rotation is influenced by complex factors including gravitational forces from the Sun, Moon, and other celestial bodies, as well as geological processes like plate tectonics. These factors make it difficult to determine whether the Earth will eventually change its axis of rotation to the vertical.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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