A hidden law of physics discovered by Isaac Newton allows an object to spin faster or slower without changing its distance from the center.
Everyone knows Newton's inverse square law for gravity, which governs how planets orbit the sun. This paper revisits a much more obscure inverse cube law that Newton also identified. This law has a unique geometric property that lets a particle scale its rotation speed independently of its radial motion. This strange effect remained buried in his work for centuries while the rest of his laws changed the world. It provides a new mathematical tool for understanding complex orbital mechanics and central forces.
The Inverse Cube Force Law
arXiv · 2604.24799
Newton's Principia is famous for its investigations of the inverse square force law for gravity. But in this book Newton also did something that remained little-known until fairly recently. He figured out what kind of central force exerted upon a particle can rescale its angular velocity by a constant factor without affecting its radial motion. This turns out to be a force obeying an inverse cube law! Here we discuss this and some other interesting features of the inverse cube force law.