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When a rocket takes off and heads into space it should be moving with the Earth's spin. I'm told that the atmosphere also spins with the Earth. When it leaves the atmosphere does it act like sling shot and continue in the direction it was spinning?
When a rocket leaves the Earth's atmosphere it is still within the Earth's gravitational pull. This means that the rocket will not go exactly in the direction it was spinning. Instead, it will continue onward but with a curve due to Earth's gravity. The farther the rocket moves the less pull Earth will have on it. However, space is a microgravity environment. This means, the rocket will always have a form of gravity pulling on it.