The influence of the fragmentation threshold on the long term evolution of the orbital debris environment

By means of the code STAT, developed in the past four years in Pisa under an ESA contract, we have carried out a number of numerical simulations of the long term evolution of the orbital debris population, and monitored the growth in time of the number of objects larger than 1 mg in mass. Previous work had shown that after a phase of gradual, quasi-linear growth due to launches and explosions, collisions in the low-orbit population lead to a kind of a chain reaction, yielding a runaway proliferation of fragments. The epoch at which this behavior takes place as well as the characteristic time constant of the nearly-exponential growth phase are sensitively related to some parameters of the physical model adopted for the collisional outcomes. The most critical of such parameters is the fragmentation threshold Q∗, defined as the limiting value of the ratio between the projectile kinetic energy and the target mass which discriminates between small scale “cratering” impacts and disruptive collisions. Here we report on the results of a set of simulations performed by varying Q∗ by plus or minus a factor two with respect to the nominal value of 4.5 × 104 J/kg, inferred from laboratory experiments. The main results of these simulations are the following: first, we confirm that a phase of nearly-exponential runaway growth of the small-size debris population is always observed, but the initial “waiting time” interval is at least ≈ 200 years for our range of Q∗ values: second, the onset time for the exponential regime as well as its characteristic time constant are growing functions of Q∗; and third, this behavior agrees well with the forecasts of much simpler mathematical models developed earlier (Farinella and Cordelli, Science & Global Security 2, 365–378, 1991). Our results highlight the need for more extensive experimental estimates of the fragmentation threshold parameter and its dependence on the size, shape and structure of the space objects. Such estimates should then be incorporated into a future generation of more realistic simulation models.