Missing stars in Perseus and Andromeda
- Round
- Observation
- Points
- 40
- Level
- Bronze
- Taught in
- Section O1.9
Adapted from IOAA 2009 (Tehran), observation problem 1. We have restated it in our own words and kept the original data. The original was solved partly by looking at the real sky, and its chart was drawn for the view from Tehran. Ours is redrawn as a map with north at the top. The original table calls ζ Persei by the name Atik, which the IAU has since given to ο Persei, so we list it by its Bayer letter. The solution was last checked on 18 October 2026.
The original chart showed the sky around Perseus and Andromeda, about 100° by 70°, as it was on 22 October 2009 at 21:00 local time in Tehran. Our chart shows the same part of the sky as a map with north at the top. Four bright stars of Perseus and Andromeda have been left off it. Find the four missing stars and give each its number from the table. Polaris is named on the chart.
| Number | Name | Bayer letter |
|---|---|---|
| 1 | Mirfak | α Per |
| 2 | Alpheratz | α And |
| 3 | ε Per | |
| 4 | Menkib | ξ Per |
| 5 | γ Per | |
| 6 | Algol | β Per |
| 7 | Almach | γ And |
| 8 | δ And | |
| 9 | 51 And | |
| 10 | Mirach | β And |
| 11 | ζ Per |
| Star | Tap a star on the chart. |
|---|---|
| Constellation | |
| Magnitude | |
| Angle between two stars | Tapping a second star gives the angle between them. |
- Three corners of the Great Square, Scheat, Markab and Algenib, are where they should be, but its north-eastern corner is empty. That corner is Alpheratz, number 2, 14.2° east of Scheat and 14.0° north of Algenib.
- The chain of Andromeda runs from Alpheratz through Mirach, number 10, which is on the chart 14.5° from the empty corner. The next star of the chain, Almach, number 7, should lie 12.5° beyond Mirach, and that place is empty too.
- The chain continues, bending only a little, to the curved line of Perseus. The line is there, with γ Per, number 5, and δ Per, but the place in its middle, 15.8° beyond Almach, is empty. That is where Mirfak, number 1, belongs.
- Algol makes a nearly right-angled corner with Almach and Mirfak, 12.1° from Almach and 9.3° from Mirfak, almost due south of Mirfak. That corner is empty too, and it is the place of Algol, number 6.
- The other candidates, ε Per, ξ Per, γ Per, δ And, 51 And, Mirach and ζ Per, are all on the chart, so the four missing stars are found.
AnswerThe missing stars are numbers 1, 2, 6 and 7, which are Mirfak, Alpheratz, Algol and Almach.
This problem also appears among the olympiad problems of Section O1.9, Problems for Chapter O1, which teaches the ideas it uses. Equation and figure numbers refer to the course.