What is the formula for calculating whether a star is circumpolar viewed from a northerly latitude?

Answer 1

"Circumpolar" means the star doesn't set, and is always above the horizon.

It does that if it's within (your north latitude) of the north celestial pole (roughly the North Star).

At the north pole . . . your north latitude is 90 degrees. All stars within 90 degrees

of the North Star are circumpolar. The North Star is directly over your head, and the

whole sky just goes round and round it. Nothing ever sets.

On the equator . . . your north latitude is zero. All stars within zero of the North Star are

circumpolar. The North Star is on your horizon. Everything sets ... nothing is circumpolar.

If you're reading lists of objects and their celestial (sky) coordinates in a directory or astronomical

catalog of some kind, the number you're interested in is the star's 'declination'. That's its angle

measured from the equator of the sky. Subtract your north latitude from 90 degrees. Then,

any star with a declination more than that number is circumpolar.

Example:

You live near Chicago.

You might live on my street, because your latitude is 42.05° north.

Subtract that from 90°, get 47.95° .

Anything in the sky is circumpolar if its declination is more than 47.95° .

Answer 2

Stars within an angle of (your latitude) from the celestial pole never set. That's the

same as saying: Any star whose declination is (90 minus your latitude) or more.