Definition of elongation of a star — condition in the astronomical triangle A star is said to be at “elongation” when which geometric condition is satisfied?

Introduction / Context:
Elongation is an important concept in astro-surveying, especially for using Polaris to determine true azimuth. At elongation, the star has maximum azimuth east or west of the meridian, simplifying azimuth computations.

Given Data / Assumptions:

• Astronomical triangle vertices: celestial pole, zenith, and the star.
• Observation of a circumpolar star such as Polaris.

Concept / Approach:

At elongation, the star’s hour circle is tangent to its diurnal circle. Geometrically, the angle at the star in the astronomical triangle is 90 degrees. This corresponds to the condition for extreme azimuth and is used in azimuth determinations in the field.

Step-by-Step Solution:

Verification / Alternative check:

Standard surveying texts derive azimuth-at-elongation formulae using this right-angle condition.

Why Other Options Are Wrong:

• (a) describes an apparent motion direction, not the defining condition.
• (c) describes circumpolarity, not elongation.
• (e) azimuth zero is meridian transit, not elongation.

Common Pitfalls:

• Mixing up elongation (max azimuth) with culmination (max/min altitude).

Final Answer:

When the angle at the star of the astronomical (spherical) triangle is 90°.