2017
The Large Magellanic Cloud in Phuket
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 1.7
Adapted from IOAA 2017 (Phuket), theory problem 1. We have restated it in our own words and kept the original data. The solution was last checked on 15 October 2026.
The Large Magellanic Cloud has right ascension 5h 24m and declination −70°00′. Phuket is at latitude 7°53′ N and longitude 98°24′ E, in the time zone UT+7. On what date of the year does the Large Magellanic Cloud culminate at 21:00 as seen from Phuket? The Greenwich sidereal time at 0h UT on 1 January is about 6h 43m.
At culmination the local sidereal time equals the right ascension. The sidereal time at a given clock time is about 3 min 56 s later each day than the day before.
- At upper culmination the local sidereal time equals the right ascension, 5h 24m. The cloud does rise at Phuket, since it culminates
- Phuket is 98°24′ east, which is 6h 33.6m, so at that moment the Greenwich sidereal time is
- 21:00 in Phuket is 14:00 UT. During 14 hours of ordinary time the sidereal time advances by
- Setting this equal to 22h 50.4m gives
- 31 days after 1 January is 1 February, when the cloud culminates about 3 minutes after 21:00, and on 2 February it culminates about 1 minute before.
AnswerThe Large Magellanic Cloud culminates at 21:00 in Phuket on about 2 February.
This problem also appears among the olympiad problems of Section 1.7, Problems for Chapter 1, which teaches the ideas it uses. Equation and figure numbers refer to the course.