Collision risk: a new method for assessing and visualizing it

A new method to assess and visualize the collision risk for an orbiting spacecraft, based on a concept derived from Opik's studies of the close approaches between comets/meteoroids, and the planets of the Solar System, is presented. The space debris population is represented in a suitable parameter space with respect to the orbit of a possible target object (selected a priori), by analyzing the dependence of the specific orbital energy of any member of the population upon its impact velocity, U, with the target body. Taking sections of this space at constant U values, by plotting the objects in terms of their specific orbital energy as a function of the inclination of their orbital plane relative to the target's orbit and exploiting Opik's simple analytical expression for the intrinsic collision probability (expected impact rate per unit target cross-section), the curves of iso--probability, in particular those corresponding to relevant hazard thresholds for target spacecraft of any given lifetime, can be visualized in the diagrams. Placing all the individual potential projectiles in these diagrams and estimating the corresponding cumulative probability, a quantitative picture of the collision risk posed by a given debris population is obtained. Useful insights into the dynamics of the overall debris population with respect to selected target orbits is obtained. The method is also useful to study the effects of single fragmentation events occurring on specific orbits. Particular emphasis is given here to two test cases: a fragmentation of an object in an orbit close to the International Space Station and a fragmentation of an Iridium satellite.