Polaris (Pole Star) on its small diurnal circle Polaris describes a small circle around the north celestial pole. What is the approximate radius of this circle (angular distance of Polaris from the pole)?

Introduction / Context:
Polaris, commonly known as the Pole Star, lies close to the north celestial pole and is a crucial reference for astronomical observations, surveying, and navigation. Although it appears nearly fixed, it actually traces a small circle around the pole as Earth rotates. Knowing the approximate radius of this circle helps observers anticipate its slight nightly motion and plan precise pointing or latitude checks.

Given Data / Assumptions:

• The question asks for an approximate angular radius (order-of-magnitude knowledge).
• Polaris is near, but not exactly at, the north celestial pole.
• Long-term changes due to precession are ignored for a typical exam-level estimate.

Concept / Approach:
The angular radius of Polaris’s apparent circle equals its angular distance from the pole (90° minus Polaris’s declination). Modern values place Polaris within about 1° of the pole, historically hovering somewhat under a degree; for standard surveying/astronomy exams, this is commonly rounded to approximately 1°.

Step-by-Step Solution:

Verification / Alternative check:
Star charts and almanacs show Polaris within roughly a degree of the pole in recent centuries, confirming the conventional approximation used in fieldwork.

Why Other Options Are Wrong:

• 2°, 3°, 4°: all significantly overstate the polar distance for Polaris.
• “None of these” is unnecessary because 1° is a valid rounded value.

Common Pitfalls:
Assuming Polaris is exactly at the pole (radius 0°) or overestimating the radius by several degrees; neglecting that the exact value changes slowly over centuries due to precession.

Final Answer:
1°