Resistance Inside a Spinning Sphere express
Deep inside Earth lies a solid iron core about the size of the Moon. It floats in liquid metal and sways slightly, like a pit in a peach when you shake the fruit. Such oscillations are called Slichter modes: the core shifts both along the planet's axis and perpendicular to it.
Three forces act together to damp this motion. The viscous fluid envelops the core like molasses on a spoon. Earth's rotation makes the fluid spiral. And the magnetic field threads through the metal, resisting displacement. Previously, each force was described separately, but in nature they act together.
The authors of the paper assembled unified formulas for all three effects. They accounted for the fact that the core, fluid, and outer shell can have different electrical conductivities and magnetic properties. The calculations showed how oscillation energy dissipates as heat and magnetic waves. Computer simulations confirmed the accuracy of the formulas.
The new formulas are useful not only for Earth. Oceans hide beneath the icy crusts of Jupiter's and Saturn's moons. If they have solid cores, those cores also oscillate. By measuring the damping of these oscillations, we can infer ice thickness and water composition.
So the problem of a trembling pit inside a spinning peach helps us peer into the depths of distant worlds.
Earth's inner core rotates slightly faster than the rest of the planet: each year it gains about 0.2 degrees on the surface.
In Arthur C. Clarke's novel Rendezvous with Rama, explorers investigate a spinning cylinder with an internal ocean — oscillations of a solid core could reveal its structure.