Interesting question!For a fire, we’d need oxygen, fuel and heat. First off, let’s consider the atmosphere of the moon. We usually think of the moon as being surrounded by vacuum, but it does actually have a very thin atmosphere - it’s less than one trillionth of the density of Earth’s atmosphere (at sea level). The gases in this atmosphere come from the radioactive decay of elements in the crust of the moon, and also from the solar wind. The reason we don’t consider it to have an atmosphere, is because it has to be constantly replenished by these sources - the gases are continually being lost to space.The composition of the atmosphere isn’t well known, but it’s estimated to be around 80,000 atoms per cubic centimetre. Of these, around 40,000 are argon, 2,000-40,000 are helium, 70 are sodium & 17 are potassium; small amounts of oxygen have been detected, but this is a very small proportion. Since fire needs an atmosphere of around 16% oxygen to burn, the moon’s atmosphere wouldn’t contain enough.As far as fuel goes, we’d also be struggling. The moon’s crust is made of a variety of oxygen-containing compounds. The major compounds are silica (SiO2, ~45%), alumina (Al2O3, ~15-24%), calcium oxide (CaO, ~12-16%), iron oxide (FeO, ~6-14%), and magnesium oxide (MgO, ~7.5-9%). This mixture of compounds is non-combustible, so wouldn’t be able to act as a fuel for our fire, even if we could somehow provide enough oxygen and heat.So, in short, you couldn’t (easily) set fire to the moon!
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