This video explains why it isn't faster to fly west if earth is spinning to the east. Let's break this down to really picture the scenario. You've got one Earth, which is rotating eastward. And you've got one airplane, flying just above the Earth's surface going westward. Put the two together, and the plane's destination would then, logically, be moving toward the plane as the Earth rotates. The result should be a super short flight from Chicago to San Francisco, with a little longer travel time on the return flight. Right? Well, no. That supposedly quick trip is complicated for a few reasons.
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