  Test particles infalling from infinity onto a compact spherical star with a
mildly super-Eddington luminosity at its surface are typically trapped on the
"Eddington Capture Sphere" and do not reach the surface of the star. The
presence of a sphere on which radiation pressure balances gravity for static
particles was first discovered some twenty five years ago. Subsequently, it was
shown to be a capture sphere for particles in radial motion, and more recently
also for particles in non-radial motion, in which the Poynting-Robertson
radiation drag efficiently removes the orbital angular momentum of the
particles, reducing it to zero. Here we develop this idea further, showing that
"levitation" on the Eddington sphere (above the stellar surface) is a state of
stable equilibrium, and discuss its implications for Hoyle-Lyttleton accretion
onto a luminous star. When the Eddington sphere is present, the cross-section
of a compact star for actual accretion is typically less than the geometrical
cross-section (pi Rsquared), direct infall onto the stellar surface only being
possible for relativistic particles, with the required minimum particle
velocity at infinity typically ~1/2 the speed of light. We further show that
particles on typical trajectories in the vicinity of the stellar surface will
also be trapped on the Eddington Capture Sphere.
