In general relativity, freely-falling test objects follow geodesics of the background spacetime in which they live. In a sense, this feature is a mere rephrasing of Einstein’s equivalence principle. In 1968, Brandon Carter showed that the geodesic motion of objects orbiting a Kerr black hole was integrable, in the sense of Hamiltonian mechanics, by discovering a fourth constant of motion that now bears his name. This “universality” of geodesic free fall is, however, but an approximation: In general, two different bodies will follow two distinct paths, depending on how they spin and deform.