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But if you're not aiming for orbital velocity the earth's rotational speed doesn't make any difference -- the relative speed of start and end points are the same. It doesn't take more fuel to travel west than east because of the rotation of the earth (jet stream sure, but if rockets are affected by the jet stream there's something seriously wrong)

Disclaimer: my entire picture of orbital dynamics comes from KSP



Check your orbital velocity at the surface. It's not 0. The direction you head does matter.




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