Astronomical surveying with Polaris: for the determination of azimuth, Polaris is preferably observed when it is at which position?

Introduction / Context:
Polaris (the Pole Star) lies close to the north celestial pole and is commonly used in astronomical surveying to establish true azimuth. Measurement geometry impacts sensitivity and observational error.

Given Data / Assumptions:

• Clear sky observations near the horizon region where Polaris traces a small circle around the pole.
• Use of a theodolite or total station with astronomical capability.

Concept / Approach:
At elongation, Polaris attains its maximum angular displacement east or west of the meridian. The azimuth of Polaris varies most slowly near elongation, making azimuth determination less sensitive to timing errors and refraction, and therefore more accurate operationally.

Step-by-Step Solution:
Identify positions: culmination (upper/lower transit across the meridian) and elongation (max east/west azimuth).Recognize that at elongation, azimuth changes minimally with time compared to culmination.Therefore, observe at elongation for better azimuth accuracy.

Verification / Alternative check:
Survey manuals recommend elongation observations due to reduced rate of azimuth change and simpler corrections.

Why Other Options Are Wrong:

• Culmination: higher rate of azimuth change; more timing sensitivity.
• Neither/either: less precise guidance than the established best practice.
• Lower transit only: unnecessarily restrictive and not optimal.

Common Pitfalls:
Neglecting refraction and instrument collimation; inadequate timekeeping; poor identification of elongation times.

Final Answer:
At elongation