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Is ISS orbiting with or against the rotation of Earth? Is it important in any aspect for the space station?

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The ISS orbit is prograde - in the direction of the Earth rotation. Prograde orbits are orbits with inclination less than 90 degrees. ISS inclination is 51.6 degrees.

These orbits are slightly easier to reach, because they don't require as much fuel, as you get additional "kick" from the Earth during launch. Retrograde (opposite direction) orbits are rare, because they require more fuel to reach. It would be inefficient to build the ISS in retrograde orbit, because all the craft would have to spend additional fuel to get there. The ISS orbit was chosen to make it accessible from the key launch sites in United States (Florida) and Kazakhstan (Baikonur).

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There's only one space launch site in the world that I know of that regularly launches satellites into retrograde orbits and that's the Israeli launch site of Palmachim. They launch retrograde mostly due to the hostile relations between Israel and it's neighboring countries to the east, and a rocket carrying a satellite can very very difficult to distinguish from a rocket carrying a warhead, especially if you're trying to figure it out after it's launched and is heading (potentially) towards you. –  Nickolai Mar 24 at 14:05
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Actually, it is very easy to differentiate between them. They fly VERY different trajectories, with VERY different motor burn profiles. Orbit identification from a small number of observations used to be a routine undergraduate astrodynamics computer programming homework problem. (See [Bate, Mueller, White] "Fundamentals of Astrodynamics", Dover Books, for more details.) –  John R. Strohm Mar 24 at 20:52
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