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how do rockets work in a vacuum
In 1920 a newspaper scoffed that rockets can't work in space, since there is no air to push against. That was wrong, and here is why.
A rocket burns fuel and throws hot gas out of its back at enormous speed. It pushes on the gas it throws, not on the air.
Newton's third law: push the gas down, and the gas pushes the rocket up. A little gas moving very fast balances a heavy rocket moving slower.
In fact, a vacuum helps. At sea level the air pushes back on the exhaust. One engine, the R-S twenty-five, makes 1,860 kilonewtons there and 2,279 in space.
How fast can a rocket get? The rocket equation: speed gained equals exhaust speed times the natural log of full mass over empty mass.
With hydrogen engines, exhaust near four point four kilometers a second, a rocket that is ninety percent fuel gains about ten kilometers a second.
So, the whole idea: the rocket throws gas back, the gas pushes it forward, no air needed. Space is not a problem, it is where engines do best.
A rocket brings its own thing to push on, the exhaust it throws, so empty space is all it needs.