Three bodies and no solution

Abstract

One of the most intriguing science fiction novels written by Isaac Asimov —Nightfall — includes much concerning celestial mechanics. The action takes place on a planet orbiting inside a multiple star system. Because of the rare occurrence of the night on the planet, the habits of the people are quite peculiar — especially as far as psychological and social aspects are concerned. Science is also deeply affected. Due to the joint action of several massive stars the orbit of the planet is far from resembling an ellipse, and gravitation becomes difficult to discover, even for an alien Newton. So how can be explained, in a simple way, the entangled trajectories of a planet driven by the simultaneous attraction of several stars? — especially knowing that an incredibly high level of complexity is reached, even if we restrict our attempts to the orbital paths resulting from the mutual influences of only three bodies.