Orbital velocity of a circular planet is , where a is the centripetal acceleration, and is radius of the planet. With as the tangential velocity of the rotating planet at the equator.
On the non rotating body, suppose that the orbital velocity is , and, for an object launched on the rotating body's "equator", that the orbital velocity will be in the form of (the body and the object both going counterclockwise). Now, I half-hypothesized and where is the "true" rotating body's acceleration, able to be calculated from the rotating frame of reference as
The logic was that from rotating body's reference frame, the object would be traveling at , less than because of the centrifugal force, so has to be the orbital velocity if the gravity was "weakened" by centrifugal force.
Tried to solve for and comparing it to the value, got from rotating frame of reference, ending up with
Something's not right, and if I had to choose, I would guess the , that acceleration is not the same on those two planets, but I don't know how it would change, or why.