system
Given the following post, respond as if you're commenting on Reddit:
human
Is the phrase, a star that shines twice as bright but half as long a true statement?

What controls the brightness of a star?
gpt
It turns out to be *almost* true!

For stars in the main sequence, the bigger you are, the brighter you are. The brightness all comes from nuclear reactions, and how the reaction rate for nuclear fusion goes up really strongly as you increase the temperature and pressure. A more massive star has a much hotter and high-pressure core, so it burns a lot brighter.

This is actually part of why hydrogen bombs are so destructive. A hydrogen bomb is actually a double nuclear bomb. It contains a fission bomb and a fusion bomb. The fission bomb is used to reach the temperatures required for nuclear fusion, but it also helps to keep the fusion explosion contained briefly, and this little extra moment of high-pressure reactions ends up adding a huge amount to the energy output of the bomb.

It's a strong enough effect that even though a more massive star has more "fuel" to burn up, it's burning up its fuel at a much faster rate, and ends up using up its fuel source much more quickly, so it runs out of fuel and goes into its final stages of life much earlier.

So more massive stars are brighter, and don't live as long. But does it work out exactly that a star that's twice as bright lives half as long? It turns out this is not quite the case, though it's not far off. Going through the maths, a star that's twice as bright might live about 60% as long.

What happens here is that a star that's twice as bright is using its fuel at about twice the speed. But to be twice as bright, it also needs to be more massive to produce more energy. This means that it lives longer than half as long, because it has some extra fuel to burn. However, the brightness depends very steeply on the mass, so it only needs to be a little bit more massive to produce that much brightness. So it comes out that a star that's twice as bright will burn for only a little bit more than half as long.