A spectrum during microlensing
- Round
- Theory
- Points
- 5
- Level
- Bronze
- Taught in
- Section 5.8
Adapted from IOAA 2023 (Katowice), theory problem 3. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.
A faint star in the bulge of the Milky Way, normally of magnitude 20.4 in the I band, brightened to magnitude 15.2 for a while, because the gravity of a star passing in front of it bent more of its light towards us. During the brightening, astronomers took a high-resolution spectrum of it with the UVES spectrograph on the Very Large Telescope, whose mirror is 8.2 m across. How large a telescope would be needed to take a spectrum of the same quality, with the same instrument and exposure time, of the star at its normal brightness? The sky background is negligible.
- The star brightened by
- The spectrum depends only on the number of photons collected, so a telescope that collects 120 times as much light from the star at its normal brightness gives the same result. By (5.1) its diameter must be
- The telescope would have to be
AnswerA telescope about 90 m across would be needed, more than twice the size of the largest telescope now being built.
This problem also appears among the olympiad problems of Section 5.8, Spectrographs, photometry and astrometry, which teaches the ideas it uses. Equation and figure numbers refer to the course.