Astronomical surveying — multiple equivalent definitions of geographic latitude Which statements correctly describe the latitude of an observer's position on Earth?

Introduction / Context:
Geographic latitude is a fundamental coordinate in astronomical and geodetic surveying. There are several equivalent ways to define it, each useful for different observational procedures, reductions, or conceptual explanations involving the celestial sphere and the local horizon system.

Given Data / Assumptions:

• Observer at a point on Earth with a well-defined local meridian.
• Standard celestial sphere relations hold.
• Any small deflection of the vertical is neglected for basic definitions.

Concept / Approach:
For an observer in the northern hemisphere, the altitude of the elevated pole (near the pole star Polaris) equals the local geographic latitude. The zenith's declination is also numerically equal to the latitude because the zenith lies along the observer's meridian at an angular distance from the celestial equator equal to the observer's latitude. Fundamentally, latitude is the angular distance along the meridian between the equator and the observer's position, reckoned north or south according to hemisphere.

Step-by-Step Solution:

Verification / Alternative check:
Simple star-altitude observations (e.g., Polaris) confirm that measured pole altitude equals local latitude to first order, matching these equivalent definitions.

Why Other Options Are Wrong:

• Options (a)–(d) are all correct statements. Therefore, the comprehensive choice is (e).

Common Pitfalls:
Confusing astronomical declination (celestial coordinate) with terrestrial latitude, although they are numerically equal for the zenith; neglecting the small corrections due to atmospheric refraction and local vertical deflection in precise work.

Final Answer:
All of the above