Collision risk in Earth orbit

Since the beginning of the 90s, Paolo started to study the problem of the growth of the number of artificial objects in the circumterrestrial space, the space debris issue. In 1992 one of us (AR) published the first (Rossi and Farinella, ESA J., 1992) of a series of papers devoted to the evaluation of the collision risk for Earth orbiting objects, based on the method developed by Weatherill for the asteroid belt. Later on, in the late 90s, together with Paolo we developed new methods and tools, based on Opik's studies on impacts in the Solar System, that allowed us to study the complex dynamics of large orbiting systems like the satellite constellations in Low and Medium Earth Orbits and their interaction with large debris clouds originated from the fragmentation of a spacecraft. In particular, in a "Gedankenexperiment", we hypothesized a fragmentation of a satellite from the Iridium constellation and studied the time evolution of the collision risk between the cloud of fragments and the moving constellation planes. When, on February 10, 2009, a satellite from the Iridium constellation and a non operational Russian satellite collided at about 776 km of altitude, the experiment became real and we were able to verify the validity our computations. A brief summary of our studies in the field will be presented, and the new steps forward made in the last years will be outlined. Particular emphasis will be placed on what is required in the present times, in the light of the tasks now faced by the space community with the ever growing number of space debris and the need for the implementation of active collision avoidance procedures.