Stellar fusion is the source of energy inside of stars, including of course our sun. Through stellar fusion, stars convert lighter elements into heavier elements, producing energy along the way. The reason that this works is that heavier elements have smaller masses, because as they get bigger, they need less energy to bind the nucleus together per particle. The reasons for this are somewhat esoteric and involve virtual particles and The Strong Force, and other such things that we don't normally encounter. But if we just take it as an axiom that producing heavier elements, (up to iron) means less mass, it follows from Einstein's famous equation that all of that missing mass has to turn up as something, and it does, as energy in the form of intense gamma radiation that helps the star from collapsing in on itself. There are a number of ways that a star does this, in a small to medium sized star, such as our sun, it mostly uses the proton-proton chain, fusing hydrogen into helium; and as a star runs out of its normal fuel, it synthesizes heavier elements through the CNO Cycle or through Alpha Capture. Along with creating energy, this also creates heavier nuclei that the star will release through its stellar wind or through a stellar explosion.

All of this is perhaps familiar to the reader, and is covered elsewhere on here in more technical detail. But there is a point about stellar fusion that I never worked out until quite recently, and which is probably surprising and interesting. Which is that the process of stellar fusion happens very, very slowly. It may be interesting to ask yourself now "How often do atoms collide deep in the core of the sun?" and then compare the answer after reading the below:

According to Nasa's fact sheet, the sun converts about 4,300,000 tons of matter a second. Since this represents the mass difference between four protons and a helium nucleus is about one part in 139, this equals about 600,000,000 tons of hydogen being burnt a second. Which certainly seems like a lot. But, the density of material in the core of the sun is about 150 tons a cubic meter. For water at normal density, that would be about 800 meters cubed a second. But the gas in the center of the sun is 150 times as dense, meaning that it only fills 4 million cubic meters. Now, taking the cube root of that shows that the amount of hydrogen burned through a second would be the cube root of 4 million, or about 150 meters on a side. In other words, about the volume of a medium-sized lake.

But of course, that is just every second, and there have been plenty of seconds since the sun started to shine. Counteracting that is the fact that the sun is very, very large. Six hundred million tons of material is a lot by human standards, but the sun has a mass of 10^30 kilograms. If we round up that 600,000,000 tons to a billion tons, and then convert it into kilograms, the sun burns 10^12 kilograms a second. So in an average second, there is a 10^-18 chance that any particular hydrogen atom in the sun will undergo fusion. (As a side note, the chances are much higher in the dense core of the sun, and much lower to non-existent in much of its mass). To put this in terms that may clarify the picture a little, a normal gas tank that runs on gasoline may have around 10^27 molecules of octane in its tank. If a car was burning gasoline as slowly as the sun was burning hydrogen, it would be burning about 1,000,000,000 molecules a second, or about 100 femtograms. This is a very small quantity, obviously.

When I contemplate the universe, I end up usually thinking along two lines: amazement that anything exists at all, and slight disappointment that everything works so poorly and awkwardly. The sun, seeming to be so amazing, is actually a ball of gas that is half-heartedly fusing in order to prevent its collapse. And the sun is fairly large, for a star. Inside of a red dwarf, the reactions are probably going along at a rate that I would have to use a ridiculous comparison to the Queen Mary's fuel tank burning an ethane atom every four years, or something suitably ridiculous. Of course, if the sun was fusing happily and quickly, at even a millionth of the rate that a gas tank reacted, it would have long ago burned itself out.

Two caveats about this: first, despite the fact that the sun is not really that energetic on the large scale, do not stare at it, taunt it, or point at it, laughing mockingly. It is still very large and by the standards of your covalently bonded body, can evaporate and heat stress you very quickly. Secondly, many of the calculations I used to figure out the suns rate of burning and its equivalent for normal combustion using perfectly spherical cows. I must admit that dealing with powers of tens in such things as the solar mass and Avogardo's number was beyond the usual maths that I am required to do. So some of my particular calculations may be in error, although I believe the general outline I have described is correct.

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