Beauty in chaos: the hidden art and sacred geometric designs of trajectories in multi-body gravitational systems

Abstract

The Earth–Moon gravitational system is naturally chaotic, and mathematical models such as the Circular Restricted Three-Body Problem (CR3BP) employ layers of ordered assumptions in order to enable both trajectory generation and analysis. However, even within this simplified mathematical construct, the underlying chaos of multi-body gravitational systems introduces a pseudo-instability that yield a dynamic and sometimes drastic evolution of trajectory geometry despite seemingly insignificant changes in the initial position and/or velocity of an object. Three-body trajectories feature a natural artistry reminiscent of artistic styles and spiritual motifs originating from diverse time periods and cultures, ranging from sacred geometry and mandalic-like designs indicative of Buddhist and Hindu symbolism, to Spirograph art, and modernist and post-modernist minimalism. This work will analyze the artistic qualities of two classes of three-body trajectories within the Earth–Moon system: (1) cislunar periodic and near-periodic orbits, and (2) the mixture of quasi-periodic and chaotic trajectories of debris particles following a catastrophic breakup event. Overall, this work sets to prove that even in a chaotic multi-body environment, beauty and order emerges through a fine balance of initial conditions.