Distance, luminosity and radius of a star

Adapted from IOAA 2013 (Volos), theory problem S6. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.

A star has effective temperature 8700 K, absolute magnitude 1.6 and apparent magnitude 7.2. Ignoring extinction, find (a) its distance, (b) its luminosity, and (c) its radius. Take the absolute magnitude of the Sun as 4.83 and its luminosity as $3.828\times {10}^{26}$ W.

AnswerThe star is 132 pc away, about 20 times as luminous as the Sun at $7.5\times {10}^{27}$ W, and $1.36\times {10}^9$ m in radius, about twice the Sun's.