the Saari's conjecture

Saari's conjecture is a question in celestial mechanics that suggests: for systems where multiple bodies (like planets or stars) move under mutual gravity, the only way the total kinetic energy (motion energy) remains constant is if the bodies stay in a fixed, shape-preserving configuration—specifically, they form a constant pattern, like a uniform rotation. In essence, it proposes that in the "cloud" of possible motion, only these steady, rotating arrangements can have unchanging total energy, implying that any other motion would involve changing energy over time.