How Does the Sun Burn Without Oxygen?

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We all know that fire cannot burn without oxygen. We also know there is no oxygen in outer space. So how does the sun burn without oxygen?

—Christine Spraut, Fleetwood, Pennsylvania

“Burn” is an earthly term that we use to describe the activation
of a chemical reaction between a fuel and an oxidant. The most familiar example involves atmospheric oxygen, such as striking a match to produce a flame. The sun, by contrast, gives off its great heat and light by smashing hydrogen atoms together in its core. This is a nuclear reaction, and the process is known as nuclear fusion. If such a process could be safely harnessed, it would surely solve the energy needs of the world.

Related: How Much Light is Received at the Poles?