Do planetary moons also travel on elliptical orbits?
Yes they do. All bodies that orbit about a primary body which dominates the mass of the system, travel in elliptical orbits. The exceptions are if the satellite is a member of a complex system of moons such as around Saturn or Jupiter. Because of the numerous gravitational perturbations, over thousands of years the orbits do not close upon themselves but are actually precessing quasi-ellipses. After each complete orbit, the satellite has been sufficiently perturbed that it doesn’t return to exactly the same spot in space, but perhaps a few dozen kilometers from its previous location one orbit ago. The orbit does not close upon itself, but is however very close to being a true Keplerian ellipse. That’s why we can still talk about the satellite having a well-defined orbital period of a few days or months.
