  We consider the problem of recovering the initial value, from the trace on
the light cone, of the solution of an initial value problem for the wave
equation. When the space is odd dimensional, we show that the map from the
initial value to the traces of the (even or odd in time) solutions on the light
cone is an isometry and we characterize the range of this map and construct its
inverse. We do this by relating the problem to the recovery of a function from
its spherical means over all spheres through the origin, which in turn is
related to the Radon transform inversion via the inversion map on R^n.
