A binary seen face on
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 8.2
Adapted from IOAA 2010 (Beijing), theory problem S4. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
A binary star is 10 pc away. The largest angular separation of its two stars is 7.0″ and the smallest 1.0″. The period is 100 years and the orbit is face on, at right angles to the line of sight. The orbit of one star round the centre of mass has an angular semi-major axis of
- The semi-major axis of the relative orbit is half the sum of the largest and smallest separations,
- By (8.2),
- The other star's orbit is
AnswerStar 1, with the larger orbit, has 1.6 solar masses and star 2 has 4.8 solar masses.
This problem also appears among the olympiad problems of Section 8.2, Visual binaries and the masses of stars, which teaches the ideas it uses. Equation and figure numbers refer to the course.