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So, I've read a bunch of articles about how, somewhat contrary to intuition, it's usually faster to fly with the rotation of the earth versus against it. All the answers have to do with wind and adding vectors, assuming you launched yourself from the spinning planet. What about in this scenario?

Setup:
- There's a spinning planet, same size and rotation speed as earth (rotation speed measured w.r.t. something like earth's sun), but with no atmosphere, so it's basically in a vacuum.
- You're flying from outer space towards the planet. Specifically, you're flying directly towards the center of the planet (i.e., along a line that's orthogonal to a plane tangent to the planet's surface).
- Then, you redirect (to avoid crashing) so that you are flying parallel with the surface (or parallel to a plane tangent to the surface). You are flying several miles above the planet's surface along something akin to earth's equator.

Now, in terms time (measured by a clock situated at point A on the surface of the planet) to get from point A back to point A, circumnavigating the planet with a given level of thrust, is it faster to fly with or against the rotation of the planet?

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  • $\begingroup$ You must stay in orbit and for that situation it doesn't matter as for you have to gain the entire orbital speed. Thus is better to fly counterplanet $\endgroup$ – Alchimista Feb 15 '18 at 23:04
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The path to be traveled is much shorter when traveling counter-rotation. Thus that is the faster way.

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If you're in an airplane, in air that moves with the planet, a tailwind always helps. So in temperate latitudes fly east. In tropical latitudes fly west.

If there is no wind, i.e. the air just goes with the planet, then you should travel in the same direction as the rotation, because you're going around a circle, and since your speed adds with the earth rotation speed, you will have more centrifugal force, making you lighter, and being lighter means you need less power, or you can go faster with the same power. (On earth, the change in weight is a fraction of a percent. But scales that need to be really accurate have calibration weights.)

If the planet has no atmosphere, go against the rotation, for the obvious reason.

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