Backscattering from the rough surface of a sphere illuminated by a moving source

Electromagnetic waves are launched and collected by the same directive radar antenna located on a reentry vehicle. The scattering obstacle is the fireball resulting from a nuclear detonation. The objective of this communication is to determine approximately the incoherent power scattered from the rough surface of the sphere available at the source at a specified time. The received power depends on many factors including the scattering cross section per unit area of the sphere and the area illuminated. The area illuminated is determined by the intersection of the sphere with a volume of space that is a function of the radar pulsewidth and the time of interest.