As others have stated, both Voyager probes are equipped with a radioisotope thermoelectric generator, or RTG. It’s essentially a tiny nuclear power plant.
Individual atoms of radioactive elements like uranium and plutonium are sort of like set mousetraps. These atoms were “set” in extremely violent events in the past of the universe, either at the core of a dying star, or at the collision sites of neutron stars. Nuclei of smaller atoms were crushed together under ridiculously high pressures and, by pure coincidence, some ended up getting “latched” like the spring of a mousetrap, storing energy. These set mousetrap atoms quietly floated through the universe, eventually ending up on Earth still in their set positions.
For quantum mechanical reasons, sometimes these latches will fail, completely at random, for no reason. Like a mousetrap that is triggered, it violently snaps, causing a big and sudden release of energy. For a mousetrap, that’s released as a loud snap noise (and possibly delivering a killing blow to an unlucky rodent that happens to be in the way). For a radioactive atom, that is mostly released as a burst of heat.
If you can somehow gather enough of these “mousetrap atoms” together in one place, all the atoms randomly snapping will create enough heat that your sample will get extremely hot. You can then, with some cleverness, use that heat to power a machine. That’s a thick nutshell description of how an RTG works: you find a way to gather enough of these atoms in one place so that it gets really hot, and wrap it in a container that can turn the heat into electricity.
Commercial nuclear power plants are essentially the same principle, although they go a step further and try to refine the process by using some of the shrapnel from the “mousetrap snapping” to trigger other mousetraps. YouTube videos will often visualize this with literal actual mousetraps with ping pong balls balanced on them, where the snapping of the mousetrap causes the ball to fly off and disrupt other nearby mousetraps, eventually setting most of them off. RTGs don’t usually bother with this, they purely rely on the mousetraps snapping of their own accord.
RTGs aren’t magic. They have a lifespan. Even though the atoms themselves decay completely at random, meaning it’s impossible to tell when any individual atom will do it, we can measure properties of the crowd. This is where the property of “half life” comes into play. Plutonium, the radioactive material in the RTGs above the Voyager probes, has a half life of about 88 years. That means we have no idea when any given atom of plutonium will snap, but if we gather a set of them in one place, we can expect that about half of them will have snapped after 88 years. Fewer mousetraps to snap means less heat over time, meaning the RTG will slowly make less and less heat. Eventually, the heat output gets so low that the electronics on board don’t have enough juice to function correctly, and the probes shut down.
Voyager 1 is almost 50 years old. By 2065, it will be making about half as much energy as it did when it launched. It isn’t quite as simple as saying it will only work half as fast, or it can only run half as many instruments. If you had a recipe that asked you to set an oven or stove temp to 400 F, you can’t just set it to 200 F instead and get the same result if you took twice the time. There are important thresholds where things are only possible above a certain value. So the Voyager probes will cease their function long before their RTGs stop producing heat. It’s already causing significant problems for one of them.
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