A cloud near the centre of the Galaxy
- Round
- Theory
- Points
- 2
- Level
- Bronze
- Taught in
- Section S4
Adapted from IOAA 2007 (Chiang Mai), theory problem 1.12. We have restated it in our own words and kept the original data. The solution was last checked on 16 October 2026.
Atomic hydrogen at rest gives out radio waves of frequency
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The cloud's line is seen at a higher frequency than the rest frequency, so its wavelength is shorter and the cloud is coming towards us.
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For a speed much less than that of light the fractional shift in frequency equals
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The exact second line of (S.30) gives 262.5 km/s, so the low-speed form is accurate enough here.
AnswerThe cloud is coming towards us at about 262 km/s.
This problem also appears among the olympiad problems of Section S4, Physics toolkit, which teaches the ideas it uses. Equation and figure numbers refer to the course.