2013
Splitting the light of a binary
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 4.2
Adapted from IOAA 2013 (Volos), theory problem S8. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.
A binary star cannot be split in a telescope and is seen from Earth as one star of magnitude 5.00. One of its stars is twice as bright as the other. What are the magnitudes of the two stars?
Write the fluxes of the two stars as
- Let the fainter star give flux
- The fainter star gives a third of that flux, so by (4.2) it is fainter by
- The brighter star gives two thirds of the total, so it is fainter than the pair by
- As a check, the two differ by
AnswerThe brighter star has magnitude 5.44 and the fainter 6.19.
This problem also appears among the olympiad problems of Section 4.2, The magnitude scale, which teaches the ideas it uses. Equation and figure numbers refer to the course.