Main Question or Discussion Point
What is non geodesic motion?
Why spinning particles don't have a geodesic path?Just to elaborate quickly on what HallsofIvy said: in general relativity, the world line of a (nonspinning) test particle is a geodesic, i.e. a curve with zero path curvature. More generally, the path curvature at any event on some world line is just the magnitude of acceleration experienced by the corresponding particle. For example, a charged particle in an "electrovacuum solution" of the Einstein field equation (EFE) will experience a nonzero Lorentz force, whose magnitude (at each event on the world line of the particle) agrees with the path curvature.
I didn't quite say that. However, in gtr, a spinning object immersed in a nonzero gravitational field (perhaps caused by a much larger nearby and spinning object) will in general experience a tiny "spin-spin" force and thus will be pushed off a geodesic path. However, these forces would be much too small to measure in any currently envisioned solar system experiments (at least, not any I know of). See for example "Dixon-Papapetrou equations" in Stephani, General relativity.Why spinning particles don't have a geodesic path?