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Currently that methane is coming from natural gas, and represents a tiny, tiny fraction of our current natural gas use. If we didn't want to use natural gas, methane can be made from hydrogen and carbon dioxide. This is critical to SpaceX's Mars plan, as they're planning on making their propellant for the return trip once they get there. If you can produce it on Mars, you can definitely produce it on Earth.
For example, hydrogen and oxygen are the 1st and 3rd most abundant elements in the universe, so liquid oxygen and liquid hydrogen fuel is always going to be an option
For example, Blue Origin and SpaceX are developing launchers that run on methane - fantastically plentiful on Earth in the form of natural gas. Delta IV runs on hydrogen, which can be synthesized through gasification or electrolysis. Falcon 9 and Atlas V burn kerosene, also very common.
The real issue is whether, at high launch rates, this will become a meaningful contributor to climate change; hopefully through use of space-based resources we can reduce the up-mass requirements enough to avoid that problem.
It's a slightly more complicated platform (using hydrolox for the upper stage, and optional strap-on solids for the booster), but the bulk of the propellant is methalox.
Aside from synthetic fuels, you can launch rockets on methane. Can't make methane? (You are a robot society by now, because it would mean there is no biosphere anymore). Still fine! We can convert our oceans into fuel (hydrogen + oxygen), given energy input. Energy can come from renewables, nuclear, etc.
No, we are not going to run out of fuel for as long as we have water.
I'd be more worried about conflicts breaking out due to mass migration due to parts of the world becoming harder and harder to eek out an exsistance in.
If they meant decaying in the "climate change is destroying the world" sense, then presumably the idea is that we've learned our lesson and won't destroy the next rock the way we have this one. Debatable, but at least the next rock is unlikely to have dead dinosaurs for use to dig up and burn.
If they meant decaying as in "the sun is eventually going to swallow us up", the presumably we will spread humanity across a bunch of decaying rocks, and continually migrate for the most decayed to newly formed rocks.
We don’t have them yet because they are expensive investments. It’s like flying NYC-SFO because building a 747 is cheaper than building the I-80 freeway — It seems like a no-brainer now we have Silicon Valley in one and Wall Street in the other, but imagine it from the point of view of Teddy Roosevelt rather than Franklin Roosevelt