  Using the theory of determinantal point processes we give upper bounds for
the Green and Riesz energies for the rotation group SO(3), with Riesz parameter
up to 3. The Green function is computed explicitly, and a lower bound for the
Green energy is established, enabling comparison of uniform point constructions
on SO(3). The variance of rotation matrices sampled by the determinantal point
process is estimated, and formulas for the L2 -norm of Gegenbauer polynomials
with index 2 are deduced, which might be of independent interest. Also a simple
but effective algorithm to sample points in SO(3) is given.
