2007
Solar days and sidereal days
- Round
- Theory
- Points
- 2
- Level
- Bronze
- Taught in
- Section 1.3
Adapted from IOAA 2007 (Chiang Mai), theory problem 1.3. We have restated it in our own words and kept the original data. The solution was last checked on 15 October 2026.
From noon on 1 July to noon on 31 December is 183 solar days. How long is this interval in sidereal days?
The stars come back to the same place in the sky every sidereal day, 23 h 56 min 4 s.
- A solar day is 24 h and a sidereal day is 23 h 56 min 4 s, or 23.9344 h, so each solar day holds
- The interval is therefore
- The same follows from counting turns. In a year of 365.25 solar days Earth turns 366.25 times relative to the stars, one turn more than relative to the Sun because it also goes once round the Sun (Chapter 2). So 183 solar days are
AnswerThe interval is 183.50 sidereal days, half a sidereal day more than the number of solar days.
This problem also appears among the olympiad problems of Section 1.3, Right ascension, declination and hour angle, which teaches the ideas it uses. Equation and figure numbers refer to the course.