A severing rate model for tape tethers based on experimental ballistic equations

Abstract

A model for the severing rate of tape-like tethers under the impact of small space debris is presented and combined with three ballistic limit equations already proposed in the literature. One of them is based on the classical assumption that particles with 1/3 of the width of the tether can sever it. The other two rely on experimental and numerical results and take into account the impactor-to-tether relative velocity. As a result, the severing rate formula is a triple integral involving the differential flux of debris as a function of the debris size, velocity and impact angle. In order to evaluate the severing rate, a database of the differential flux for different orbit altitudes and inclinations was constructed by using Master 8.03. After implementing and verifying a numerical code, several parametric analyses were conducted to understand the effect of the three ballistic limit equations and the impoverished state of the space debris population on the severing rate. As compared with the simple 1/3 ballistic limit equation, the severing rates found with the two experimental ballistic limit equations are a factor of two lower (or more, depending on the orbit) for the same debris flux and similar among them. However, the growth of the space debris flux over the last decade counteracted this improvement; the severing rate found with the updated debris flux database and the experimental ballistic limit equations is similar to the one found in the past by using older epochs and the classical tether cut assumption.