How much of the sky do stars cover?
- Round
- Theory
- Points
- 10
- Level
- Silver
- Taught in
- Section 4.5
Adapted from IOAA 2011 (Katowice), theory problem S9. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.
The distances between stars are huge compared with their sizes, so a star cluster or a galaxy without gas and dust hides almost nothing behind it. We look towards a galaxy whose surface brightness is 18.0 magnitudes per square arcsecond. Assume that its stars are all like the Sun, and estimate what fraction of the sky in that direction is covered by the discs of its stars.
- Surface brightness does not depend on distance, so the disc of every star like the Sun has the Sun's surface brightness,
- If the discs of the stars cover a fraction
- Here
AnswerThe stars cover only about
This problem also appears among the olympiad problems of Section 4.5, Surface brightness and photon counts, which teaches the ideas it uses. Equation and figure numbers refer to the course.