Sidereal time zero twice in a day
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 2.5
Adapted from IOAA 2018 (Beijing), theory problem 5. We have restated it in our own words and kept the original data. The solution was last checked on 17 October 2026.
On one particular day of each year, the Greenwich mean sidereal time is 00:00:00 twice. (a) Roughly what is the right ascension of the Sun on that day? (b) Estimate the date of this day in 2018, given that GMST was 6.706 h at 0h UT on 1 January 2018 (JD 2 458 119.5).
- (a) Sidereal time 0h comes round once every sidereal day, which is shorter than a solar day, so it can fall twice on one date only if the first time is within 3 min 56 s after midnight. GMST is then about 0h at midnight UT, when the meridian of Greenwich points away from the Sun. So the meridian at midnight has right ascension 0h, the Sun is opposite it, at right ascension 12h, and the date is near the September equinox.
- (b) GMST at 0h UT grows by
- After 263 days, at 0h UT on 21 September 2018, GMST is
Answer(a) The Sun is near the September equinox, at a right ascension of about 12h. (b) It happens on 21 September 2018. The official solution states 18h in part (a), which does not fit its own reasoning about the September equinox, where the Sun's right ascension is 12h.
This problem also appears among the olympiad problems of Section 2.5, Sidereal time on any date, which teaches the ideas it uses. Equation and figure numbers refer to the course.