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We knew the earth rotates, but the moon is tidally locked.

To tell that another planet is rotating, you have to be able to distinguish its surface (I guess?). Who first did this?

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Mercury's surface was virtually unknown until Mariner 10 flew by and Venus is covered in clouds. Of the terrestrial planets, that leaves Mars.

It was likely Christiaan Huygens in November 1659 who first realised Mars was rotating when he tried to map it. His estimate of roughly 24 hours was fairly close.

I believe Galileo's earlier observations on Jupiter were with a telescope not powerful enough to resolve smaller 'surface' features (like the Great Red Spot), which may have either proven that Jupiter rotates, or at least that something on the surface is moving across it.

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    Nice answer! It might be better to link to both the Wikipedia article and the paper The Mapping of Mars separately, rather than linking to the footnote. (PDF also available). Wikipedia articles are constantly changing so a link to a footnote could disappear at any moment. – uhoh Sep 11 '17 at 23:45
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    Wikipedia supports your view on Galileo, suggesting that the first sighting was either by Hooke in 1664 or Cassini in 1665 - https://en.wikipedia.org/wiki/Great_Red_Spot . Galileo died in 1642. – MartinV Sep 12 '17 at 13:21
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    True, I imagine the Great Red Spot was identified before anything else of note (apart from the cloud bands), which was after Galileo's time. Interestingly, Galileo was among the first to infer that the Sun was rotating, by watching the movements of sunspots. –  Sep 12 '17 at 13:46