  We study energy integrals and discrete energies on the sphere, in particular,
analogs of the Riesz energy with the geodesic distance in place of Euclidean,
and observe that the range of exponents for which the uniform distribution
optimizes such energies is different from the classical case. We also obtain a
general form of the Stolarsky principle, which relates discrete energies to
certain $L^2$ discrepancies. This leads to new proofs of discrepancy estimates,
as well as the sharp asymptotics of the difference between optimal discrete and
continuous energies in the geodesic case.
