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It should be possible to light a strike anywhere match in space because the head is essentially a firework and contains both fuel and oxidiser but the match would quickly go out once the oxidiser was all used up and the wooden stick would not burn.Lighter flints would probably not spark in space because the small metal particles need oxygen in the air to glow brightly however a fast grindstone grinding steel may produce rather dim sparks because the particles of metal ripped off by the grindstone are initially red hot but they cannot burn in space.
I was thinking about this; to get the particles of steel hot enough to ignite in the first place, they would need to be glowing brightly due to the striking, so they must start of bright even before any combustion takes place. So I say that there would be sparks, visible, but not so long -lived as there would be in air.
There is another factor: in a vacuum, the cooling effect would be less than in air and that could affect how long the trails of hot, 'unignited' steel particles appeared to be.
You could be right about the fast combustion; as they are moving fast through the air they have a 'forced draught', effectively. It all depends upon what the minimum temperature is for steel to burn.
Have you seen those new magnesium alloy / steel firelighters? They produce a fantastic shower of sparks when struck right. You can get a fire going with virtually no 'backwoods' skills at all - it's like a blow torch for a brief period. It would be interesting to try it out in an inert atmosphere -nitrogen, for instance- and see the 'glow'.
high temperature Mg combining with N2
You can buy these things in camping / out door shops everywhere in the UK. Very impressive. Treat yourself to one and experiment; they're cheap enough.