Prime vertical – which points does this great circle pass through? The prime vertical at an observing station is the vertical great circle that passes through which of the following points?

Introduction / Context:
In positional astronomy and geodetic surveying, great circles on the celestial sphere such as the meridian and the prime vertical are essential reference planes. The prime vertical is orthogonal to the local meridian and helps define azimuths and amplitude of rising/setting bodies.

Given Data / Assumptions:

• Local horizontal coordinate system (altitude–azimuth) is used.
• Vertical circles are great circles passing through the zenith and nadir.
• Cardinal points on the horizon are east, west, north, and south.

Concept / Approach:

Every vertical circle passes through the zenith and nadir by definition. The prime vertical is the particular vertical circle that also passes through the east and west points of the horizon (it is perpendicular to the local meridian). Therefore the set of points it must pass through includes the east point, west point, and, inherent to all vertical circles, the zenith and nadir.

Step-by-Step Solution:

Verification / Alternative check:

Textbook celestial sphere diagrams show the meridian (north–south) at right angles to the prime vertical (east–west), each passing through zenith and nadir.

Why Other Options Are Wrong:

Picking any single point omits the others that the prime vertical necessarily includes; only the comprehensive option is correct.

Common Pitfalls:

Confusing the prime vertical with the prime meridian; assuming the prime vertical passes through north–south points (it does not).

Final Answer:

All of the above