Where Vega and Altair are heading
- Round
- Theory
- Points
- 3
- Level
- Bronze
- Taught in
- Section S3
Adapted from IOAA 2018 (Beijing), theory problem 10, part (c). We have restated it in our own words and kept the original data. The solution was last checked on 16 October 2026.
In the year 2000, Vega was moving across the sky by 200.94 mas a year eastwards and 286.23 mas a year northwards, and Altair by 536.23 mas a year eastwards and 385.29 mas a year northwards, where 1 mas is a thousandth of an arcsecond. Find the position angle of the proper motion of each star, that is, the direction in which it moves on the sky, measured from north through east.
- Measured from north, a vector with eastward component
- For Vega,
- For Altair,
AnswerVega is heading towards position angle 35.07° and Altair towards 54.30°, both towards the north-east of the sky. Section 1.5 restates parts (a) and (b) of the same problem, which find the angle and the distance between the two stars.
This problem also appears among the olympiad problems of Section S3, Maths toolkit, which teaches the ideas it uses. Equation and figure numbers refer to the course.