The circumpolar stars are having polar distances
- Aequal to the latitude of the place of the observation
- Bless than the latitude of the place of the observationCorrect
- Ctwice the latitude of the place of the observation
- Dthrice the latitude of the place of the observation
Solution
Concept
Circumpolar stars
Formula
Circumpolar if polar distance < latitude
Step-by-step solution
1. A star never sets if its declination exceeds (90° − φ), i.e. its polar distance is less than the observer's latitude.
Explanation
Stars close enough to the celestial pole circle it without dipping below the horizon. Their polar distance is smaller than the latitude of the observer.
Why the other options are wrong
Polar distances equal to, or greater than, the latitude give stars that touch or cross the horizon.
Shortcut
Circumpolar: polar distance < latitude.
Common mistake
Choosing "equal".
Correct answer: B) less than the latitude of the place of the observation