On planetary systems as ordered sequences

A planetary system consists of a host star and one or more planets, arranged into a particular configuration. Here, we consider what information belongs to the configuration, or ordering, of 4286 Kepler planets in their 3277 planetary systems. First, we train a neural network model to predict the radius and period of a planet based on the properties of its host star and the radii and period of its neighbors. The mean absolute error of the predictions of the trained model is a factor of 2.1 better than the MAE of the predictions of a naive model which draws randomly from dynamically allowable periods and radii. Second, we adapt a model used for unsupervised part-of-speech tagging in computational linguistics to investigate whether planets or planetary systems fall into natural categories with physically interpretable "grammatical rules." The model identifies two robust groups of planetary systems: (1) compact multi-planet systems and (2) systems around giant stars ($\log{g} \lesssim 4.0$), although the latter group is strongly sculpted by the selection bias of the transit method. These results reinforce the idea that planetary systems are not random sequences -- instead, as a population, they contain predictable patterns that can provide insight into the formation and evolution of planetary systems.