In positional astronomy for surveying, the angle between Earth’s rotation axis and the local vertical at the observation station is termed what?

Introduction / Context:
Precise terminology in spherical astronomy helps convert celestial observations into terrestrial coordinates. The relationships among latitude, co-latitude, and the local vertical are fundamental for geodetic work and astro-orientation.

Given Data / Assumptions:

• The local vertical is the line through the observer’s zenith and nadir.
• Earth’s rotation axis defines the celestial poles.
• Astronomical latitude (φ) is the angle between the local vertical and the equatorial plane.

Concept / Approach:
The angle between Earth’s axis and the local vertical equals the complement of the astronomical latitude, i.e., co-latitude (90° − φ). Since the axis is 90° from the equatorial plane, the vertical-to-axis angle must be 90° − φ.

Step-by-Step Solution:
Define astronomical latitude φ as the angle between the equatorial plane and local vertical.Recognize that the angle between the vertical and the axis = 90° − φ.Therefore the required term is ‘‘astronomical co-latitude.’’

Verification / Alternative check:
Star elevation at the pole equals φ; consequently, pole distance from the zenith is 90° − φ, matching the vertical–axis angle.

Why Other Options Are Wrong:

• Astronomical latitude is φ, not the complement.
• Co-declination and declination refer to a star's position, not the station's orientation.

Common Pitfalls:

• Confusing star-based quantities (declination) with site-based quantities (latitude/co-latitude).

Final Answer:
astronomical co-latitude