system
Given the following post, respond as if you're commenting on Reddit:
human
Can a geosynchronous orbit happen on every planet? Or does it need specific circumstances like certain rotation/revolution speed? And can you do it with any object?
gpt
If the rotation is too slow then the orbit would have to be so far away that it would be unstable (not clearly inside the Hill sphere of the object). While you can calculate the height of a stationary orbit and the radius of the Hill sphere in each case there is a surprisingly simple relation: The planet needs to rotate several times per orbit. Everything else cancels out. 13 times per orbit would give a system like Sun/Earth/Moon.