the Saari's theorem

Saari's theorem states that in a gravitational system of multiple bodies, like planets or moons, the long-term stable configurations (called relative equilibria) are those where the bodies are arranged in symmetrical patterns that minimize the system's potential energy for a given angular momentum. It essentially means that over time, such systems tend to settle into the most balanced, symmetric arrangements, making these configurations inherently stable. This theorem helps explain why certain celestial patterns, like planets orbiting in stable configurations, persist over long periods.