VISUALIZING IMPACT PROBABILITIES OF SPACE DEBRIS
, A. ROSSI
and P. FARINELLA
I.A.S., Planetologia, Area di Ricerca C.N.R., Via Fosso del Cavaliere 100, I-00133 Roma, Italy
CNUCE, C.N.R., Area della Ricerca di Pisa, Via Alﬁeri, 1, Loc. San
Cataldo, 56010 Ghezzano – Pisa, Italy;
Universit´e de Paris 7, Observatoire de Paris Meudon, DESPA, 5
Place Jules Janssen, F-92195 Meudon, France;
Dipartimento di Astronomia, Universit`a di Trieste, Via
Tiepolo 11, I-34131 Trieste, Italy
(Received 5 July 1999; Accepted 29 August 2000)
Abstract. We present a new method to assess and visualize the collision risk due to space debris for an
orbiting spacecraft. It is based on a parameter space derived from
Opik’s studies of close approaches between
small Solar System bodies and the planets. By means of this representation, many useful insights into the
dynamics of the overall debris population with respect to a selected target can be obtained. The method can
also be applied to estimate the increase in impact hazard (e.g., for the International Space Station) associated
to fragmentation events occurring on a speciﬁc orbit.
Keywords: fragmentation, impact probability,
Opik’s theory, visualization
The space around the Earth is increasingly crowded by a population of orbiting objects of
widely different sizes. This population is the source of a signiﬁcant collision risk for the
operational spacecraft which often play a vital role in the present society and economy.
In particular, the current decade is characterized by a growing use of the polluted Low
Earth Orbit (LEO) by a number of satellite constellations for telecommunications, which
will soon account for a large fraction of all the sizable objects present in circumterrestrial
space. More than the conventional space missions, these constellations require huge long-
term investments and suffer from a speciﬁc vulnerability, as their effectiveness relies on
the simultaneous availability of a number of spacecraft, all orbiting in the same debris
environment (Rossi et al., 1999).
Therefore, in the last few years, several models have been developed to study the envi-
ronment in which a satellite will orbit during its operative life (e.g., Sdunnus, 1995; Kessler
et al., 1996). Moreover, since the early work of Kessler (1981), several researchers have
studied the problem of the collision risk with the orbiting debris (e.g., Rossi and Farinella,
1992; Klinkrad, 1993; Pardini and Anselmo, 1998).
In this paper, we present a new method to study and visualize the collision risk for an
orbiting spacecraft. It allowsus to provide a clear, synthetic picture of the environment faced
by a satellite in a speciﬁc orbit, giving also interesting information on the orbital dynamics
of the population of potential projectiles with respect to the target. We are going to use
Author for correspondence (Tel.: 503152953; Fax: 503138091; E-mail: email@example.com).
Space Debris 1, 143–158, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.