Radii and masses from an eclipse
- Round
- Theory
- Points
- 100
- Level
- Silver
- Taught in
- Section 8.4
Adapted from IOAA 2008 (Bandung), theory problem 1. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
An eclipsing binary has a period of 30 days. When the secondary star eclipses the primary star, the eclipse lasts 8 hours from first to last contact, and its flat bottom lasts 1 hour 18 minutes. Spectra show that the largest radial velocity of the primary star is 30 km/s and of the secondary star 40 km/s. The orbits are circular and the inclination is 90°. Find the radii and the masses of both stars, in solar radii and solar masses.
- The relative speed is
- The separation is
- With
- The primary moves more slowly, so it is the heavier star, with
AnswerThe primary star has a radius of 0.84 solar radii and a mass of 0.61 solar masses, and the secondary 0.61 solar radii and 0.46 solar masses.
This problem also appears among the olympiad problems of Section 8.4, Eclipsing binaries, which teaches the ideas it uses. Equation and figure numbers refer to the course.