Plutonium is a pretty valuable resource in Starbound, and it can be very tricky to find, especially if you don’t know where to look. Plutonium is particularly valuable because of the ability to use it as fuel. One Plutonium Ore can produce six units of fuel, making it a lot more effective than ordinary coal. Just don’t get reckless when using it; these aren’t easy to come by.
You’ll have the best chances of finding Plutonium on high-risk planets if you search deep underground. It can also be found on moons and meteorites. But again, you’ll have to dig deep if you hope to have any chance of even seeing it. Even if you do manage to find Plutonium, they’re often available only in very small pockets, so it’s unlikely you’ll ever find plutonium goldmine in the game as it is right now.
You can also try searching in asteroid belts where there are a lot of rare ores floating about, as well as near moon fuel deposits. Players have also reported that moons near radioactive stars are more likely to contain Plutonium Ore as well. If you’re planning on going Plutonium hunting in Starbound, these few areas will likely be your best bet to obtaining some.