The correct answer is: C. Distance from the pole must be less than the latitude of the observer.
A circumpolar star is a star that remains visible in the night sky throughout the year from a particular location on Earth. This is because the star’s declination is greater than or equal to the observer’s latitude. The declination of a star is its angular distance north or south of the celestial equator. The celestial equator is an imaginary line in the sky that lies directly above the Earth’s equator. The latitude of a location on Earth is its angular distance north or south of the Earth’s equator.
For example, if an observer is located at a latitude of 40 degrees north, then any star with a declination of 40 degrees or greater will be circumpolar for that observer. This is because the star’s declination is greater than the observer’s latitude, so the star will always be above the horizon.
The other options are incorrect. Option A is incorrect because the declination of a circumpolar star does not need to be 0 degrees. For example, the star Polaris has a declination of 89.2 degrees, and it is circumpolar for all observers located north of the Arctic Circle. Option B is incorrect because the declination of a circumpolar star does not need to be 90 degrees. For example, the star Vega has a declination of 38.7 degrees, and it is circumpolar for all observers located north of 51 degrees north latitude. Option D is incorrect because the hour angle of a star is the angle between the star’s right ascension and the observer’s local meridian. The hour angle of a circumpolar star does not need to be 180 degrees.