A sky from somewhere on Earth
- Round
- Observation
- Points
- 26
- Level
- Bronze
- Taught in
- Section O3.2
Adapted from IOAA 2019 (Keszthely), planetarium problem 2. We have restated it in our own words, left out one part about comets, and drawn the sky again from a star catalogue at the latitude and time of the original. The solution was last checked on 20 October 2026.
The dome below shows the sky from somewhere on Earth, with no Solar System objects.
| Star | Tap a star on the dome. |
|---|
(a) What is the latitude of the place, and in which hemisphere is it? (3 points)
(b) Name the three brightest stars on the dome, in order, and estimate the azimuth of each, measured from north through east. The dome draws α Centauri, a pair too close to split by eye, at the magnitude of its brighter star, −0.01, and the eye sees the pair as one star of magnitude −0.28. (12 points)
(c) Name nine constellations that contain stars that never set at this place. (9 points)
(d) Mintaka, δ Orionis, is setting at this moment. Roughly how many hours ago did it rise? (2 points)
- (a) The long axis of the Southern Cross points down to the south celestial pole, which stands about 25° above the south point. The place is at latitude 25° S, in the southern hemisphere.
- (b) The brightest star is Sirius, low in the west at azimuth about 262°. The second is Canopus, in the south-west at about 222°.
- (b) The third is α Centauri, at about 151° in the south-east. Seen as one star of magnitude −0.28, by (4.3), it is brighter than Arcturus, at −0.05, in the north-east.
- (c) At latitude 25° S, stars south of declination
- (d) A star on the celestial equator is above the horizon for half of each sidereal day, as Section 1.4 showed, so Mintaka rose about 12 hours ago.
AnswerThe place is at latitude 25° S. The brightest stars are Sirius at azimuth 262°, Canopus at 222° and α Centauri at 151°. Any nine of the seventeen constellations in the solution answer part (c), and Mintaka rose about 12 hours ago. The official solution gives the azimuths as 82°, 42° and 331°, which are 180° away from these, as if they had been measured from south. From 25° S, α Centauri never strays more than 33° in azimuth from due south, so 331° cannot be measured from north, and measured from north, as the question asks, the azimuths are the values given here.
This problem also appears among the olympiad problems of Section O3.2, Finding the latitude, which teaches the ideas it uses. Equation and figure numbers refer to the course.