Atmospheric refraction corrections: which statements correctly describe how refraction corrections vary with the altitude of a celestial body?

Introduction / Context:
Atmospheric refraction bends incoming light, shifting the apparent altitude of celestial bodies. Accurate astronomical observations require altitude-dependent refraction corrections.

Given Data / Assumptions:

• Standard atmosphere; observations near horizon are most affected.
• Altitude measured from the sensible/visible horizon upward.

Concept / Approach:
Refraction increases sharply as altitude approaches the horizon and diminishes to negligible at the zenith. Practical tables show approximately 33 arcminutes near the horizon and nearly zero directly overhead; in general, correction follows functions proportional to cotangent of altitude.

Step-by-Step Solution:
At zenith: path through atmosphere is minimal → correction ≈ 0.At horizon: longest path → correction ≈ 33′.Between these, use altitude-based tables or formulae to interpolate corrections.

Verification / Alternative check:
Refraction tables in nautical almanacs/survey manuals confirm the quoted limiting values and altitude dependence.

Why Other Options Are Wrong:

• Each individual statement is correct; thus the combined choice is appropriate.

Common Pitfalls:

• Neglecting refraction at low altitudes, leading to large altitude errors.

Final Answer:
all the above