# How can stars burn for billions of years?

Why don't stars run out of fuel?...
10 January 2023

## Question

Chris - Dwayne has said since stars are emitting so much energy constantly, how can they last for millions or billions of years? I would expect them to burn up much sooner.

Matt - It's a really good question. I think I'm going to give you an answer in two halves, I think. You wouldn't be alone in thinking they would burn up sooner. Around a hundred years ago, this was one of the real hot topics in physics. There was a famous physicist called Lord Kelvin around the start of the 20th century. He did a sort of back of the envelope calculation of how long the sun should last and came up with an answer of a handful of million years. He sort of imagined the sun burning like a gas fire or something and said, okay, it can last maybe 10 million years and therefore evolution has to be wrong. There's not enough time for animals to evolve. And he used that to argue against Darwin and of course he was completely wrong, right? The missing piece of the puzzle that he didn't understand was the process that the sun uses to create energy is called nuclear fusion. And it's extraordinarily efficient. You get an enormous amount of energy out of a really, really tiny amount of matter. Um, it's dictated by this very famous equation. E=mc squared. E is energy, m is mass, and c is the speed of light, which is a very big number. So C squared is an enormous number. So what e equals mc squared is really telling you is that a tiny, tiny bit of mass gives you an enormous amount of energy. Stars are very, very efficient. The other half of the answer is that stars are just really, really big. So even if they are churning through fuel at an enormous rate, they can still last a very long time. The sun burns through several million tons per second, which sounds unbelievable, right? You think that wouldn't be sustainable at all. But if you go and calculate it down maybe use your number sense, right? If you get a calculator to work out how many seconds in a year, multiply that by 10 billion years and multiply that by a million tons of seconds, you don't get to even a fraction of 1% of the sun's mass, right? So the sun can happily burn a million tons of seconds for billions of years and still be absolutely fine. And it's all down to the efficiency of E=mc squared.

Chris - One point though is that size matters when it comes to stars, doesn't it? Because if you are a very big star and you have a massive amount of fuel and a massive amount of gravity and mass driving it all together, you get very, very hot, very, very quickly. But you also burn off all that fuel much more quickly. So big stars burn faster and brighter than small stars.

Matt - Yeah, that's exactly true. It's almost counterintuitive, right? You would think ‘big star, more fuel, it would last longer’. But big stars really do sort of live fast and die young. They burn so hot, they burn through their fuel much, much more quickly than smaller stars. So a star like the sun, which is pretty small, would last about 10 billion years. That's about 10,000 million years, more or less. A massive star might last 10 million years, which sounds like a long time. It's sort of a blink of an eye compared to the sun. A little cold red dwarf star might last for longer than the age of the universe.

Chris - Thank you, Matt.