The most likely way I see this being put together, is that the Orbiting Objects are Children of an Empty Game Object.That Empty Game Object is rotating too, causing all it's children to rotate with it.
So, Make your orbiting object a child of your Point, and rotate your point using the "Rotate" Action.
This'll get the movement you want, but now your orbitals are also rotating, so add an FSM to your orbitals, with the opposite rotation. (So if your Rotating your Centre Point "90" across the Z axis each frame, your children will be rotating "-90" across the Z Axis) keeping the orbitals upright.