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I noticed that East and West appear swapped on maps of the Sun, even though the Sun rotates around its polar axis in the same sense as Earth.

See for example below Sun disk with a Venus transit diagram or also here.

So, at least for the Sun, East and West are defined from an Earth observer viewpoint. This makes me wonder: How are East and West defined on other bodies of our solar system?

solar map

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Actually, it is a bit contentious. The IAU defined the North Pole of a planet to be that axis of rotation which lies north of the solar system's invariable plane. Which means that it is possible for bodies to rotate retrograde, and Venus and Uranus are considered to rotate retrograde with this definition. This definition is not universally accepted.

From early periods when solar maps were drawn, they have been labelled such that features appear on the "Eastern" limb of the sun and move to the "Western" limb, though this means that they are moving from Earth's East to Earth's West. This convention hasn't changed, though things have changed for the moon, just to confuse things.

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Since the direction of revolution of all the planets is the same, the direction of angular velocity vector on the planet is taken to be North, and the direction of revolution is said to be east.

Just like Earth.

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Actually, Venus rotate the other way, Uranus axis is tilted near 90 degrees and Mercury rotates synchronously with its orbit. –  LocalFluff Apr 20 at 8:22
    
@LocalFluff But that doesn't change the defn of directions. We say Earth rotates from West to East, and Venus from East to West. I have never read anything on the lines about Uranus. To be blank, in all the sci. literature that I've read, they just talk in terms of numbers with respect to certain conventions. East/West barely pops up. I am not really sure on this, either. –  Cheeku Apr 20 at 8:33

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