Axial rotation, orbital revolution and solar spin–orbit coupling

The orbital motion of the Sun has been linked with solar variability, but the underlying physics remains unknown. A coupling of the solar axial rotation and the barycentric orbital revolution might account for the relationships found. Some recent published studies addressing the physics of this problem have made use of equations from rotational physics in order to model particle motions. However, our standard equations for rotational velocity do not accurately describe particle motions due to orbital revolution. The Sun’s orbital motion is a state of free fall; in consequence, aside from very small tidal motions, the associated particle velocities do not vary as a function of position on or within the body of the Sun. In this note, I describe and illustrate the fundamental difference between particle motions in rotation and revolution, in order to dispel some part of the confusion that has arisen in the past and that which may yet arise in the future. This discussion highlights the principal physical difficulty that must be addressed and overcome by future dynamical spin–orbit coupling hypotheses.