In short, no. This is a common misconception based on simplified models of the atom to better depict certain aspects. While these models have their place, they do not accurately represent reality.
Unlike the orbital path of a planet/moon/etc. around a larger body, electrons do not move in such a manner. This is because they are governed by quantum mechanics as opposed to classical physics of motion. The electron cloud is effectively a group of probability density functions (one for each orbital), within which an electron can be at any place at any given time. These basically define a volume in which the electron will be present in it's current state. To the best of my knowledge its motion within the cloud is effectively random as there is no discernible path as such.
Very true, as is the case with many phenomena across chemistry and physics our method for defining the system is mistaken for a physical truth. Unfortunately such distinctions are not always easy to get across and that level of detail appeared to be above what the question required.
So obviously, while there must be a physical basis (as there is with everything whether we understand it or not) for the electron's motion within the orbital PDF, to the best of my knowledge it does not move in a similar manner to planets orbiting a sun. That being said I'm more than happy to be corrected and this is far from my speciality.
Laurence provides a correct general description of how the wave function of quantum mechanics represents the various resonance states into which electrons become captive of in atoms as being volumes within which the electron is likely to be found.
The conclusion that these were resonance states was reached by Louis de Broglie in the 1920's and this is what gave Schrödinger the idea to use the wave function to represent them.
The wave function however represents its energy as being spread evenly in this volume.
Heisenberg also came with a corresponding solution at about the same time, representing the energy of the electron as a probability density distribution that gives the highest level of density as corresponding to the ground orbit in the Bohr atom when applied to the isolated hydrogen atom.
There is also the path integral of Feynman that represents all possible trajectories that the electron can follow within the volume defined by the wave function.
Hello Andre/Laurence.......Well said....Same is the case with Eectron's spin....The way we consider the spinning electron.....In real that might not happen.....