Stars from Mount Damavand
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 1.4
Adapted from IOAA 2009 (Tehran), theory problem 5. We have restated it in our own words and kept the original data. The solution was last checked on 15 October 2026.
Mount Damavand stands in the north of Iran, near the southern coast of the Caspian Sea. An observer on its summit (latitude 35°57′ N, longitude 52°06′ E,
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From sea level and without an atmosphere, a star is circumpolar when it is still above the horizon at lower culmination, which by (1.14) means
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From the summit the edge of the sea lies below the horizontal by the dip of the horizon,
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Refraction raises a star seen at the horizon by about 34′, as in the common errors above, so a star is still seen when its true direction is 34′ below the edge of the sea.
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By (1.13), the altitude of the star at lower culmination is
AnswerThe smallest declination is about +51°05′. Without refraction the limit would be +51°39′, and from sea level with no atmosphere +54°03′.
This problem also appears among the olympiad problems of Section 1.4, What you can see from where you stand, which teaches the ideas it uses. Equation and figure numbers refer to the course.