The longest life of the Sun

Adapted from IOAA 2010 (Beijing), theory problem 5. We have restated it in our own words and kept the original data, adding the Sun's mass and luminosity from the IOAA 2025 data sheet. The solution was last checked on 16 October 2026.

If 0.8% of the Sun's initial mass could be turned into energy during its whole life, what is the longest the Sun could live, assuming that its luminosity stays the same? Take the Sun's mass as $1.988\times {10}^{30}$ kg and its luminosity as $3.828\times {10}^{26}$ W.

AnswerThe Sun could shine for at most about $1.2\times {10}^{11}$ years. Its real life on the main sequence is about ten times shorter, because only the hydrogen in its core, about a tenth of its mass, is ever turned into helium (Chapter 7).