Sun-like stars above the disc
- Round
- Theory
- Points
- 10
- Level
- Silver
- Taught in
- Section S3
Adapted from IOAA 2010 (Beijing), theory problem 10. We have restated it in our own words and kept the original data. The solution was last checked on 16 October 2026.
The number of stars like the Sun, which astronomers call main-sequence stars of type G (Chapter 7), per unit volume in the disc of the Milky Way falls off exponentially with height above the middle plane of the disc, with a scale height of 300 pc. What fraction of its value in the middle plane does it have at heights of 0.5 kpc and 1.5 kpc?
- By (S.6) the number per unit volume at height
- At 0.5 kpc, which is 500 pc,
- At 1.5 kpc, which is 1500 pc,
AnswerAt 0.5 kpc the number per unit volume is 0.189 of its value in the middle plane, just under a fifth, and at 1.5 kpc it is 0.0067, about a hundred and fiftieth.
This problem also appears among the olympiad problems of Section S3, Maths toolkit, which teaches the ideas it uses. Equation and figure numbers refer to the course.