Sirius and Canopus from Kraków
- Round
- Theory
- Points
- 10
- Level
- Silver
- Taught in
- Section 2.7
Adapted from IOAA 2011 (Katowice), theory problem 12. We have restated it in our own words and kept the original data. The solution was last checked on 17 October 2026.
Because of precession, the part of the sky that can be seen from a given place changes over time. Is it possible that at some time Sirius will not rise as seen from Kraków, while Canopus will rise and set? Assume that Earth's axis sweeps out a cone of angle 47°, so that it keeps a tilt of 23.5°. Kraków is at latitude 50.1° N, and the present coordinates of the stars are 6h 45m, −16°43′ for Sirius and 6h 24m, −52°42′ for Canopus.
- From Kraków a star never rises if its declination is less than
- Precession keeps each star's ecliptic latitude
- The first line of (1.26), with
- The declination of Sirius can range from −63.2° to −16.2°, so at times it will be less than −39.9° and Sirius will not rise from Kraków. The declination of Canopus can be no more than −52.4°, which is always less than −39.9°, so Canopus never rises there.
AnswerNo. Precession will at times take Sirius out of sight from Kraków, but Canopus can never rise there, whatever the date.
This problem also appears among the olympiad problems of Section 2.7, Precession and nutation, which teaches the ideas it uses. Equation and figure numbers refer to the course.