Three stars missing from the Magelang sky
- Round
- Observation
- Points
- 60
- Level
- Silver
- Taught in
- Section O1.9
Adapted from IOAA 2015 (Magelang), planetarium problem 1. We have restated it in our own words and kept the original data, adding the latitude and longitude of Magelang. The original was shown in a planetarium, and our chart redraws that sky as a map of the whole sky above the horizon. The solution was last checked on 18 October 2026.
A planetarium shows the sky of Magelang, Indonesia, at latitude 7.5° S and longitude 110.2° E, for 28 July 2015 at 21:00 local time (UTC+7). Three bright stars are missing from the image. Find them, and name them by their Bayer letters. The stars that may be missing are α Pav, α Lyr, α Aql, α Vir, α CrB, α Gru, α Ser, α Cen, α Cyg, α Oph, α Cru, α Boo, α PsA, α Sco, β Aqr, β Cru, β Oph, β Peg, γ Sco, γ Cyg, δ Pav, ε Peg and ε Boo. The star called γ Sco in this list is the one now named σ Lib.
| Star | Tap a star on the chart. |
|---|---|
| Constellation | |
| Magnitude | |
| Angle between two stars | Tapping a second star gives the angle between them. |
- At 21:00 local time, 14:00 UT, the local sidereal time is about 17h 45m, so the meridian runs through Ophiuchus and Sagittarius, and Antares is 64° up, west of the meridian. All 23 stars of the list are above the horizon at that moment, the lowest being β Peg at 5°, so none can be struck off for being set, and each pattern has to be checked on the chart.
- The Southern Cross is low in the south-south-west, with Acrux 11° and Mimosa 14° up, and Hadar is beside it. The brighter Pointer, α Cen, should be 4.4° from Hadar, on the side away from the Cross, but that place is empty. α Cen is missing, at an altitude of 27° and an azimuth of 203°.
- Corvus is in the west. The line along its northern edge from Gienah through Algorab leads on, almost straight, for 14.5° to an empty patch of sky where Spica should be. α Vir is missing, 26° up at an azimuth of 261°.
- In the north-west the kite of Boötes is on the chart, with ε Boo, δ Boo, β Boo and γ Boo, and Corona Borealis beside it, but the bright star at the southern tip of the kite, 10.4° from ε Boo, is missing. That star is α Boo, Arcturus, 32° up at an azimuth of 298°.
AnswerThe missing stars are α Cen in the south-south-west, α Vir in the west and α Boo in the west-north-west.
This problem also appears among the olympiad problems of Section O1.9, Problems for Chapter O1, which teaches the ideas it uses. Equation and figure numbers refer to the course.