The next great opposition of Mars
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 6.1
Adapted from IOAA 2010 (Beijing), theory problem 11. We have restated it in our own words and kept the original data. The solution was last checked on 23 October 2026.
Mars reached a great opposition, an opposition at which it came especially close to Earth, at 17h 56m UT on 28 August 2003. The next great opposition came in 2018. Estimate its date. The semi-major axis of Mars's orbit is 1.524 au. Take both orbits to be circles.
- By Kepler's third law Mars's sidereal period is
- By (6.2),
- From 28 August 2003 to 28 August 2018 is
- Seven synodic periods end
AnswerOur estimate puts the great opposition on 7 August 2018. The real opposition came 11 days earlier, on 27 July 2018. Mars's orbit is an ellipse, so its speed changes round the orbit, and the seven real intervals did not add up to seven average synodic periods.
This problem also appears among the olympiad problems of Section 6.1, Configurations and synodic periods, which teaches the ideas it uses. Equation and figure numbers refer to the course.