The great conjunctions and the Star of Bethlehem
- Round
- Theory
- Points
- 20
- Level
- Silver
- Taught in
- Section 6.1
Adapted from IOAA 2017 (Phuket), theory problem 8. We have restated it in our own words and kept the original data. The solution was last checked on 23 October 2026.
A great conjunction is a conjunction of Jupiter and Saturn as seen from Earth. Take the orbits of Jupiter and Saturn as circles in the plane of the ecliptic, with sidereal periods of 11.86 and 29.45 years. The time between great conjunctions seen from Earth varies a little, but on average it is the same as for an observer at the centre of the Solar System. Ignore precession throughout.
(a) Find the average time between great conjunctions, in years, and the average angle round the Sun between one great conjunction and the next. [6 points]
(b) A great conjunction took place on 21 December 2020, 30.3° east of the Sun. In which constellation was it? [2 points]
In 1606 Johannes Kepler worked out that a great conjunction can happen three times in one year, because both planets loop back in retrograde motion, and that this happened in 7 BC. It may be the event remembered as the Star of Bethlehem.
(c) In which constellation did the great conjunctions of 7 BC take place? [8 points]
(d) In which constellation was the Sun at the second of the three conjunctions of 7 BC? [4 points]
- By (6.2),
- In that time Jupiter moves round by
- On 21 December, the December solstice, the Sun is at ecliptic longitude 270°. The conjunction was 30.3° east of it, at longitude 300.3°, which is in Capricornus.
- From 7 BC to 2020 is 2026 years, since there is no year 0. That is
- Three conjunctions in a year happen only when both planets are moving backwards, which they do around opposition. At the middle conjunction the planets were opposite the Sun, so the Sun was at longitude 202.0°. Virgo runs along the ecliptic to longitude 217.9°, where Libra begins.
Answer(a) The great conjunctions come every 19.86 years on average, each 242.7° further round the Sun than the last. (b) The conjunction of 2020 was in Capricornus. (c) Those of 7 BC were in Pisces. (d) The Sun was in Virgo. The official solution allows Aries and Libra as well, since an average period carried back over two thousand years cannot place the conjunction to better than a few degrees.
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.