  The dynamics of sedimenting particles under gravity are surprisingly complex
due to the presence of effective long-ranged forces. When the particles are
polar with a well-defined symmetry axis and non-uniform density, recent
theoretical predictions suggest that prolate objects will repel and oblate ones
will weakly attract. We tested these predictions using mass polar proalte
spheroids, which are composed of 2 mm spheres glued together. We probed
different aspect rations ($\kappa$) and center of mass offsets ($\chi$) by
combining spheres of different densities. Experiments were done in both
quasi-two-dimensional (2D) and three=dimensional (3D) chambers. By optically
tracking the motion of single particles, we found that the dynamics were
well-described by a reduced mobility matrix model that could be solved
analytically. Pairs of particles exhibited an effective repulsion, and their
separation roughly scaled as ~$(\kappa-1)/\chi^{0.39}$, i.e. particles that
were more prolate or had smaller mass asymmetry had stronger repulsion effects.
In 3D, particles with $\chi>0$ were distributed more uniformly than $\chi=0$
particles, and the degree of uniformity increased with $\kappa$, indicating
that the effective 2-body repulsion manifests for a large number of particles.
