The celestial pointer
- Round
- Observation
- Points
- 10
- Level
- Bronze
- Taught in
- Section O1.9
Adapted from IOAA 2007 (Chiang Mai), observation problem 1. We have restated it in our own words and kept the original data, adding the latitude of Chiang Mai and the size of the region to search in the last part, which the original left open. The solution was last checked on 18 October 2026.
An observer in Chiang Mai, Thailand, at latitude 18.8° N, has a pointer to show objects in the night sky. The examiner asks for the following.
- Move the pointer along the celestial equator. (1 point)
- Aim the pointer at the vernal equinox. (1 point)
- Aim the pointer at the brightest star of the Great Square of Pegasus. (2 points)
- Aim the pointer at α Ari. (2 points)
- Start at Aldebaran, α Tau, turn the pointer 35° northward and then 6° westward in equatorial coordinates, and aim at the brightest star within about 10° of that point. (4 points)
- The celestial equator is the great circle through the east and west points of the horizon. It crosses the meridian in the south at an altitude of
- The vernal equinox is the March equinox point, where the Sun crosses the equator northward. It lies in Pisces with no bright star to mark it, 15.5° from Algenib, a little west of due south, which is about the length of the eastern side of the Great Square, 14.0°.
- The four corners of the Great Square are Alpheratz, magnitude 2.07, Scheat, 2.44, Markab, 2.49, and Algenib, 2.83. The brightest is Alpheratz, at the north-eastern corner, even though it belongs to Andromeda.
- α Ari is Hamal, magnitude 2.01, the brightest of the short bent line of three stars that makes up Aries.
- Aldebaran is at right ascension 4h 35.9m and declination +16.5°. Turning 35° north brings the pointer to declination +51.5°, and turning 6° west takes 6° off the right ascension, which brings it to 4h 11.9m. The point is in Perseus. Within 10° of it the brightest star is Mirfak, magnitude 1.8, 7.7° away, brighter than δ Per, magnitude 3.0, 6.0° away. If the 6° is measured along the sky instead, the point is at 3h 57m, and Mirfak, 5.5° away, is still the brightest. Capella is brighter, but it is 12° away.
AnswerThe equator runs from east to west, 71.2° high in the south and just north of Mintaka. The vernal equinox is in Pisces, 15.5° from Algenib, a little west of south. The brightest star of the Square is Alpheratz, α Ari is Hamal, and the last star is Mirfak.
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.