What about smaller scales, from asteroids, meteors, and comets up to planets, stars, stellar clusters, and galaxies themselves? Could there be a simple scale-free rule that would unite these disparate shapes and sizes? At first glance these objects appear as different as can be. Yet each has at least two things in common: gravitation and rotation. Each has mass, and each spins about an axis. Not to say that these masses and spins are at all identical—in fact, they are very different. However, what if there were a simple combination of mass and spin that is itself scale-free? Such a construction would represent a neat way of categorizing the properties of a vast range of astronomical objects.
Many amusement parks have rotor rides, best avoided after a hearty lunch. If you haven’t eaten recently, let’s take a spin on one of these contraptions. After handing over your ticket and waiting in a half-hour queue, you walk into a large metal cylinder. Following the lead of others, you stand with your back against the wall. Soon the contraption begins to rotate—slowly at first, then faster and faster. As the floor beneath you starts to drop, you find your back pinned against the metal surface. Inertia, you realize, as you remember the story of Newton’s bucket. If it weren’t for the wall, you’d be flying off toward the roller coaster. The surface against your back acts to keep you moving in a circle, exerting what physicists call a “centripetal force,” which creates an inward directed “centripetal acceleration,” enabling your circular motion. Then, before you can work out the equations, you see the ride operator pull the lever to end the ride. The floor rises, the whirling stops, and you get off. Had fun?
As you disembark, you realize to your dismay that everything still seems to be spinning—from the churning of your stomach to the agitation in your head. The delicate fluid in your inner ear presses uncomfortably upon special nerves, producing the loathsome sensa-