The radiant of two meteors
- Round
- Theory
- Points
- 24
- Level
- Silver
- Taught in
- Section 6.6
Adapted from the 2020 Global e-Competition on Astronomy and Astrophysics (Estonia, online), held in place of the IOAA that year, theory problem 7, parts (b) to (d). We have restated it in our own words and kept the original data. Part (a), the sidereal time, is in Section 2.5. The data put the radiant 14° below the observer's horizon. Meteors can come from below the horizon only if they graze the upper air far away, so a real shower is seen while its radiant is up. The solution was last checked on 23 October 2026.
From Chiayi, Chinese Taipei (latitude 23.5° N), at a local sidereal time of 21h 20m 50s, an observer saw two meteors of the same shower. The first appeared on the horizon due west and ran to a point 15° above the northern horizon. The second began at altitude 23.5° and azimuth 210° and ended at altitude 75° and azimuth 255°. Azimuths are measured from north through east. (b) Find the altitude and azimuth of the radiant. (16 points) (c) Find its right ascension and declination. (6 points) (d) Which of Crux, Dorado, Pavo, Tucana and Triangulum Australe is it closest to? (2 points)
- With
- The cross product of the two ends of each trail is the pole of its great circle, and the cross product of the two poles points along the line where the great circles cross. Of its two ends, the radiant is the one behind the start of each trail, since the meteors fly away from it.
- This gives the radiant at azimuth 201.9° and altitude −14.0°. The other crossing, at azimuth 21.9°, lies ahead of the meteors and is ruled out.
- By the formulas of Section 1.3, the declination is −67.2° and the hour angle is 4.61 h, so the right ascension is
- At right ascension 16h 44m and declination −67°, the radiant lies in Triangulum Australe.
Answer(b) Azimuth 201.9°, altitude −14.0°. (c) Right ascension 16h 44m, declination −67.2°. (d) Triangulum Australe.
This problem also appears among the olympiad problems of Section 6.6, Asteroids, comets and meteors, which teaches the ideas it uses. Equation and figure numbers refer to the course.