Velocity distribution of satellite breakups

It is shown that the change in velocity, Delta nu, of each piece of a satellite breakup causes a rotation of the plane of the satellite through an angle alpha about the radius vector, r, at the time of the breakup. The angle alpha for each piece can be measured from the classical orbital parameters of inclination and longitude of the ascending node of the satellite and the breakup piece. The 3-dimensional period-eccentricity-alpha scatter plot of the breakup pieces shows the distribution of the shape of the perturbed orbits as well as the orientation of the perturbed orbital planes relative to the orbital plane of the satellite prior to its breakup. It is shown that this 3-dimensional scatter plot is a nonlinear transformation of Delta nu of the breakup pieces, which depends on the magnitude of the radius vector, r, and the velocity vector, nu, of the satellite at the time of its breakup. This transformation can be analytically inverted to solve for Delta nu. This inverse transformation is applied to an actual satellite breakup to obtain the distribution of Delta nu of the pieces.