I will discuss various manoeuvres of a flying saucer, i.e. an object with a disc or saucer-shaped body, in Euclidian 3-space. It turns out tha the configuration space of such an object is a 5-dimensional contact manifold. I will point out that certain special manoeuvres of flying saucers equip this manifold with three different 5-dimensional parabolic geometries, namely Penrose's null twistors CR structure, a flat para-CR structure and G_2 contact structure of Friedrich Engel. If time permits an excerpt from the `Star Wars' motion picture will be shown with a visualisation of these manoeuvres.