  Geodesic orbit spaces are those Riemannian homogeneous spaces (G/H,g) whose
geodesics are orbits of one-parameter subgroups of G. We classify the simply
connected geodesic orbit spaces where G is a compact Lie group of rank two. We
prove that the only such spaces for which the metric g is not induced from a
bi-invariant metric on G are certain spheres and projective spaces, endowed
with metrics induced from Hopf fibrations.
