Vega and Altair
- Round
- Theory
- Points
- 15
- Level
- Silver
- Taught in
- Section 1.5
Adapted from IOAA 2018 (Beijing), theory problem 10, parts (a) and (b). We have restated it in our own words and kept the original data. The solution was last checked on 15 October 2026.
For the year 2000, Vega has right ascension 18h 36m 56.49s, declination +38°47′07.7″ and parallax 130.23 mas, and Altair has right ascension 19h 50m 47.70s, declination +8°52′13.3″ and parallax 194.95 mas, where 1 mas is a thousandth of an arcsecond.
(a) Find the angular distance between Vega and Altair. [9 points]
(b) Find the distance between the two stars in space, in parsecs. [6 points]
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(a) In degrees, the right ascensions are 279.2354° and 297.6987°, which differ by 18.4634°, and the declinations are
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The two terms of (1.23) are
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(b) Vega is
so
Answer(a) The stars are 34.20° apart in the sky. (b) They are 4.49 pc apart in space, which is closer than either of them is to the Sun.
This problem also appears among the olympiad problems of Section 1.5, The astronomical triangle, which teaches the ideas it uses. Equation and figure numbers refer to the course.