Astronomical corrections: the standard correction for parallax (in arcseconds) expressed as a function of zenith distance α is which of the following?

Introduction / Context:
Topocentric parallax arises because observations are made from the Earth’s surface rather than its center. For solar/lunar or stellar observations in classical navigation and surveying tables, small empirical corrections (in arcseconds) are applied to convert apparent positions to geocentric ones.

Given Data / Assumptions:

• Correction magnitude given as a small constant multiplier (arcseconds).
• α denotes zenith distance (complement of altitude).
• Sign convention assumes subtracting the correction from the apparent altitude where appropriate.

Concept / Approach:
For small parallax corrections, a cosine dependence on zenith distance is common, since the projection of the observer’s displacement from Earth’s center onto the line of sight involves cos α. A negative sign indicates the observed (topocentric) altitude is greater than the geocentric altitude and needs reduction.

Step-by-Step Solution:
Recognize parallax term structure: proportional to cos α.Adopt the empirical coefficient 8.8 arcseconds for the stated context.Apply sign: correction = − 8.8 cos α arcsec.

Verification / Alternative check:
For α = 0° (object at zenith), cos α = 1, largest correction in magnitude; for α = 90° (horizon), cos α = 0, vanishing correction—consistent with geometry.

Why Other Options Are Wrong:

• + 8.8 cos α: wrong sign.
• ± 0.8 sin α or + 8.8 sin α: wrong angular dependence and/or magnitude.
• Duplicate punctuation “- 8.8 cos α.” is effectively the same as option (a) but presented ambiguously; standard form is without trailing dot.

Common Pitfalls:
Mixing refraction and parallax corrections; confusing altitude (h) and zenith distance (α = 90° − h).

Final Answer:
- 8.8 cos α