A debris cloud from a fragmentation on orbit may be modeled by transformation of variables from the instantaneous velocity distribution at the fragmentation time to the spatial distribution at some elapsed time later. There are no Gaussian distributions assumed and the evolution map is quite nonlinear, being derived from the solution of the Lambert, two-point boundary value, problem and the state transition matrix for unperturbed propagation, so the traditional tools of analysis that assume these qualities fail dramatically. The transformation of variables technique does not suffer from any such assumptions, and unlike the Monte Carlo method, is not subject to sampling errors or approximations. Structures and features are evident in the density maps, and these structures show promise for simplified approximation of the density map. Most prominent of the structures is the well-known pinch point at the fragmentation location in inertial space. The anti-pinch line, or wedge, is also observed. Bands on the opposite side of the fragmentation are very noticeable, and their existence may be motivated from simple orbit dynamics. These bands make the anti-pinch line actually more of a set of anti-pinch line segments. By computing these density maps over time, the evolution may be studied. There is a density generator, a density band at roughly the same altitude as the pinch point, that cycles around the earth and appears a source of the bands, with newly created bands moving radially outward and diminishing in density. Although the initial velocity distribution affects the final spatial distribution, the Lambert solutions, which are the most time consuming to compute, need only be computed once. Therefore, different initial distributions may be changed and the results recomputed with relative speed. A comparison of the effects of initial distributions is shown in this paper.

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