2010
The distance to a quasar
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 13.6
Adapted from IOAA 2010 (Beijing), theory problem 3. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
A quasar has a redshift of
The official solution turns the redshift into a speed with the relativistic Doppler formula and then uses the Hubble–Lemaître law. Compare it with the comoving distance.
- The relativistic Doppler formula gives
- A flat universe of matter alone gives a comoving distance
- Our model, with
AnswerThe quasar is about 750 to 800 Mpc away. The official solution accepts 750 Mpc from the Doppler route or about 735 Mpc from a flat universe of matter alone. Our model gives 794 Mpc. For a flat universe of matter alone the formula gives 726 Mpc, a little less than the official 735 Mpc.
This problem also appears among the olympiad problems of Section 13.6, Distances in an expanding universe, which teaches the ideas it uses. Equation and figure numbers refer to the course.