Final answer:
The precession of Earth's axis changes the position of the North Celestial Pole relative to the stars and in our local sky, but does not affect the location of the celestial equator relative to the stars, which remains constant.
Step-by-step explanation:
The phenomenon of the precession of Earth's axis refers to the slow, conical wobbling motion of the planet's rotation axis, much like that observed in a spinning top. This precession, which takes approximately 26,000 years to complete a cycle, affects the orientation of Earth's axis in space, thereby altering the position of the North Celestial Pole and the stars relative to it over time. Consequently, the precession affects the location of the North Celestial Pole relative to the stars (A) as well as its position in your local sky (B) as Earth’s axis changes its orientation. However, the precession does not change the location of the celestial equator relative to the stars (C), since the celestial equator is a projection of Earth's equator onto the celestial sphere and remains aligned with Earth’s orbital plane around the Sun, which doesn’t wobble with the Earth's axis.
Therefore, the correct answer to the student's question is C. The location of the celestial equator relative to the stars is not changed by the precession of Earth's axis.