Introductory

Which stars never set?

An observer stands at latitude $\phi = 47^\circ 55'$ N (Ulaanbaatar). Determine the range of declinations $\delta$ for which a star is circumpolar, i.e. never sets below the horizon. What fraction of the celestial sphere is permanently visible?

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Reading resources

Material that covers the physics behind this problem.

Spherical AstronomyRobin M. Green
The definitive treatment of the celestial sphere, spherical trigonometry and time systems. Dense but authoritative.
Textbook
Astronomy NotesNick Strobel
Free, well-illustrated introductory notes covering the whole syllabus at a conceptual level.
Lecture notes
Stellarium WebStellarium
Browser planetarium. Indispensable for checking coordinate, rising/setting and constellation questions against the real sky.
Website