Astronomical surveying: which coordinate pairs can fully specify the position of a celestial body on the celestial sphere for an observer on Earth?

Introduction / Context:
In astronomical surveying and navigation, we describe the position of a heavenly body on the celestial sphere using angular coordinates. Several coordinate systems are in common use, each suited to a different observational or computational task, but any complete pair from a standard system uniquely fixes the body’s apparent position at a given time.

Given Data / Assumptions:

• The observer is at a fixed location on Earth at a given instant.
• Standard spherical coordinate systems are well defined.
• Refraction and parallax are neglected for the core concept of coordinate specification.

Concept / Approach:
Three principal systems are relevant: (1) the horizontal (altitude–azimuth) system tied to the observer’s horizon; (2) the equatorial (declination–hour angle) system tied to the local meridian; and (3) the equatorial (declination–right ascension) system tied to the celestial equator and vernal equinox. Any complete pair from one system specifies a unique point on the celestial sphere.

Step-by-Step Solution:
Alt–Az: altitude is angular height above the horizon; azimuth is bearing along the horizon. Together they fix the line of sight.Dec–HA: declination is north/south of the celestial equator; hour angle measures how far west the object is from the observer’s meridian.Dec–RA: declination paired with right ascension (measured from the vernal equinox) gives a time-independent sky map coordinate; local sidereal time converts RA to hour angle.

Verification / Alternative check:
Given any one pair, the other pairs are convertible through known transformations involving the observer’s latitude and local sidereal time, confirming their completeness.

Why Other Options Are Wrong:
“None of these” is incorrect because each listed pair is indeed sufficient.

Common Pitfalls:
Confusing right ascension with hour angle (they differ by local sidereal time), or assuming altitude–azimuth are global rather than local coordinates.

Final Answer:
All the above