If a planet had a perfectly flat surface (no mountains, etc.), and had no atmosphere, would it be possible to orbit it at one cm above the ground?

The planet might be perfectly flat but still have a planetary bulge like at Earth’s equator. So you’d have to account for all of that to clear over it.

That being said, no orbit is completely round. Every orbit has different degrees of eccentricity. However, if you could get a perfectly round orbit around a geometrically perfect spherical planet with no atmosphere, and you were at the planet’s equator launching precisely East, then the answer would be yes!

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