  The paper deals with some problems related to recovering information about an
obstacle in an Euclidean space from certain measurements of lengths of
generalized geodesics in the exterior of the obstacle. The main result is that
if two obstacles satisfy some generic regularity conditions and have (almost)
the same traveling times, then the generalized geodesic flows in their
exteriors are conjugate on the non-trapping part of their phase spaces with a
time preserving conjugacy. In the case of a union of two strictly convex
domains in the plane, a constructive algorithm is described to recover the
obstacle from traveling times.
