Sources of planetary rotation: Mapping planetesimals' contributions to angular momentum

A systematic study of the motion backward and forward in time from a uniform distribution of bodies entering a planet's Hill sphere yields a mapping of the contribution to the planet's rotation from planetesimals as a function of their source in heliocentric orbital element space. The mapping allows determination of the contribution to rotation from any assumed distribution of heliocentric planetesimal orbits. For example, it can systematically reproduce earlier results from Monte-Carlo studies of contributions to rotational angular momentum. With our method of calculation, contributions to planetary rotation can be interpreted in terms of the arrival geometries at the planet's Hill sphere and the subsequent two-body motion inside the Hill sphere leading to impact. Prograde rotation is strongly favored if a planet grows in a relatively quiescent population of planetesimals with accretion nibbling at the edges of its feeding zone. However, if the impacting population were dominated by large bodies with high relative velocity, the direction and magnitude of rotation would be random.