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Methane is apparently the most easily available hydrocarbon. It is also a flammable, and highly combustible fuel; does burning methane provide sufficient power-weight to be used to launch artificial satellites and their ilk into Earth Orbit?

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Probably possible, rockets have been built that used kerosene and even Hydrogen peroxide. Liquid natural gas stores a lot of energy per volume, but hydrogen is very light and so offers a huge amount of energy per kg. And in trying to accelerate your rocket vertically upward at several 'g' it's kg that matter.

Energy density plot

Note: data from http://en.wikipedia.org/wiki/Energy_density