Meridian altitude of a circumpolar star: At which position does a circumpolar star attain its maximum altitude as seen by an observer?

Introduction / Context:
Circumpolar stars never set for a given latitude and trace circles around the pole. Understanding where the altitude is maximum or minimum is fundamental for astronomical observations used in surveying.

Given Data / Assumptions:

• The star is circumpolar (declination sufficiently large for latitude φ).
• Upper and lower culminations occur when the star crosses the local meridian.
• Elongations occur when the star is farthest east or west of the meridian.

Concept / Approach:
At meridian transit (culmination), the star’s altitude is extremal. For circumpolar stars, the upper culmination corresponds to the highest altitude (closest approach to the zenith) while the lower culmination corresponds to the lowest altitude above the horizon. Elongations maximize azimuthal departure, not altitude.

Step-by-Step Solution:
Recognize that altitude extrema occur at meridian crossings.For circumpolar stars, the crossing above the pole (upper culmination) gives the maximum altitude.Therefore select “At upper culmination.”

Verification / Alternative check:
Altitude at upper culmination is approximately 90° − |φ − δ|, which is greater than altitude at lower culmination, approximately 90° − |φ + δ|.

Why Other Options Are Wrong:
East/west elongation: maximizes azimuth, not altitude.Lower culmination: gives the minimum altitude for circumpolar stars.

Common Pitfalls:
Confusing elongation with culmination; they address different extrema (azimuth versus altitude).

Final Answer:
At upper culmination.