Analytic model for orbital debris environmental management

A differential equation expressing the time rate of change of the number of objects on orbit has been developed. This approach, referred to as the "particles-in-a-box" (PIB) model, allows for the examination of orbital debris sources and sinks in a fashion that identifies the physical parameters of the low Earth orbit (LEO) environment with the coefficients of the differential equation. The PIB equation has at least two uses: 1) to test the stability of the LEO environment against runaway growth via a simple evaluation of the coefficients, and 2) as the basis for a numerical model of the environment. It has been determined, relative to the first of these two uses, that the present environment is slightly unstable to catastrophic growth—a condition that could be improved by the employment of active debris reduction techniques. Relative to the second of these uses, and under the simplest implementation of the PIB model—a single "equivalent" particle species in a single environmental box—the number of particles on orbit will continue to increase until approximately 2250 to 2350 A.D., reaching totals of 500,000 to 2,000,000. The model is expandable to the more realistic (complex) case of multiple species in a multiple-tier system.