There is only one stable speed at which a planet can orbit in a circle; any slower, and it'll start falling in toward the star, and any faster and it'll start to move away from the star.

The only way to vary the speed is a powered orbit, and that's not likely to happen with a planet.

I respect that you reserved some room to be surprised.

For a given stellar mass and orbital radius (assuming a circular orbit), there's not really any wiggle room on how long the planet's orbital period is. Speeding up or slowing down the planet requires it to orbit at a different distance. If you meant the speed of a planet's rotation about its own axis, I guess the limit would basically be the point at which it tears itself apart by spinning so fast that its gravity no longer holds it together.

Yes, but that would be dictated by how fast can it spin before shattering into pieces. So mostly gravity/composition thing, I'd imagine. Many things in solar systems are (postulated to) derive from the rotation of the protoplanetary disk, via conservation of angular momentum - however, planets can also get spun up or down after forming by e.g. collisions with other objects, including extra-system objects.

Just realized, I meant orbit speed and not rotation aeound the planets axis. Shouldn't write in parallel to meetings... Your answer was very interesting so, thank you!

I see! In the other case, the answer is: velocity vector determines the orbit. For any given point at any given orbit, there's only one valid velocity vector relative to the star (direction and magnitude) - tweaking it tweaks the shape of the orbit.

One of the best way to get an intuition for orbits is to play Kerbal Space Program for a few hours :).

Going back to my buried physics knowledge, that is quite logic. Thanks again!

I am just afraid to touch Kerbal Space Program, I really cannot afford another time sink at the moment!

As one time ovner of a Star Wars RPG PC whos secret super weapon was his tremendous Astrogation skill, I really should so I guess!