Celestial sphere modeling – centers and apparent motions Which statements correctly describe common idealizations and apparent motions used in basic astronomy for surveying?

Introduction / Context:
The celestial sphere is a powerful abstraction for performing astronomical computations needed in surveying (e.g., azimuth and time). Different contexts adopt different centers and rely on the fixed-star approximation to simplify analyses.

Given Data / Assumptions:

• Celestial sphere can be modeled as topocentric (observer-centered) or geocentric (Earth-centered).
• Over short times, stars maintain fixed relative positions.
• Earth's rotation causes apparent diurnal motion.

Concept / Approach:
Both topocentric and geocentric models are used. The topocentric model is convenient for instrument pointing and local horizons; the geocentric model is useful for global coordinate systems. Regardless of the center, the sky exhibits apparent east-to-west rotation around the celestial poles due to Earth's west-to-east spin.

Step-by-Step Solution:
Acknowledge both choices of center are legitimate abstractions.Adopt fixed-star approximation for short-term surveying tasks.Recognize apparent diurnal motion east→west around the pole.Therefore all statements are correct.

Verification / Alternative check:
Instrument manuals and astronomy texts routinely switch between topocentric pointing and geocentric coordinates without contradiction.

Why Other Options Are Wrong:
Since each statement is true within standard practice, any single alternative would be incomplete.

Common Pitfalls:
Confusing apparent motion with actual stellar motion; the diurnal motion is Earth's rotation, not stars revolving around Earth.

Final Answer:
All the above