Modelling the Long-Term Evolution of Orbital Debris

by Luciano Anselmo

Current space missions around the earth have to deal with a problem mostly ignored just 25 years ago: man-made orbital debris. Besides the more than 9,000 objects (50% of which are break-up fragments) routinely tracked by the U.S. Space Surveillance Network, typically larger than 10-20 cm and with a combined mass exceeding 5,000 metric tons, the circum-terrestrial space is populated by a very large amount of smaller particles, down to sub-millimetre sizes, which is continually being replenished by international space activities.

While the impact of large objects is potentially able to induce catastrophic fragmentations, particles in the millimetre and centimetre size range can severely damage critical spacecraft sub-systems. A cost effective shielding against millimetre sized debris is sometimes feasible, but avoiding penetration following the impact of a particle close to one centimetre is considerably more difficult and expensive, as International Space Station designers know well.

The best approach to investigate the future evolution of orbital debris and the practical effectiveness of mitigation measures is to develop models and software codes able to realistically describe the relevant physical processes (orbital dynamics, air drag, on-orbit explosions, slag discharge from solid rocket motors, collisions, surface degradation, etc…) and the operational practices (launches, release of mission related objects, disposal options) connected to the space activities in orbit around the earth. However, this becomes a very demanding task, in particular if the goal is to model the orbital debris evolution over several decades or more.

In spite of the inherent difficulties and limitations involved, a few groups around the world have developed a quite complex set of computer codes to simulate in detail the long-term evolution of the debris population. One of these groups is based in Pisa, at the Space Flight Dynamics Laboratory of ISTI-CNR. Since the 1990’s, under three European Space Agency (ESA) contracts, this group has developed a couple of dedicated software tools, plus several support programs. One of these tools, the Semi-Deterministic Model for Space Debris Mitigation analysis (SDM), has been continuously upgraded to include more and more sophisticated traffic and mitigation options.

In its various versions, SDM has been used in several international studies, eg research promoted by the Inter-Agency Space Debris Coordination Committee (IADC), to investigate the relative effectiveness of some mitigation measures, such as on-orbit explosion prevention and satellite end-of-life de-orbiting, proposed in order to control the growth of orbital debris. The results have contributed to discussions at the United Nations (Technical Report on Space Debris, United Nations, New York, 1999) and to the adoption of internationally recognized mitigation guidelines and codes of conduct (IADC Space Debris Mitigation Guidelines, Inter-Agency Space Debris Coordination Committee, 2002; European Code of Conduct for Space Debris Mitigation, European Debris Mitigation Standard Working Group, 2004).

There are only a few sources of orbiting objects able to catastrophically fragment by impact spacecraft and rocket bodies: launches, on-orbit explosions and, of course, collisions. Because at present the catastrophic collision probability is still very low, new launches – involving satellites, upper stages and mission related objects – and explosions are the leading sources of sizeable objects and this explains why a large international effort has been initiated in order to passivate spent rocket stages and remove spacecraft at the end-of-life from critically important regions of space (eg the geostationary ring and low earth orbits, below the altitude of 2000 km).

As far as the sinks are concerned, aside from high eccentricity orbits, for which the luni-solar perturbations may produce an effective reduction of the orbital lifetime, the only mechanism able to remove sizeable objects from space is the air drag from the residual high atmosphere. However, its effectiveness is proportional to the local atmospheric density and the area-to-mass ratio of space objects. Thus, it is not very efficient in removing large orbital debris above 650 – 700 km. This means that even maintaining the current relatively modest level of space activity, the amount of abandoned satellites, spent upper stages and large debris is destined to grow, at altitudes greater than 650 km, providing one of the ingredients of a possible collisional chain reaction.

Assuming an updated business-as-usual scenario, and taking into account the recent evolution of space activities and the most probable future trends, the Monte Carlo simulations carried out with SDM have shown that only the adoption of drastic mitigation measures, such as upper stage and spacecraft explosion prevention and end-of-life manoeuvring to limit the residual permanence in the most crowded regions of space, are able, in low earth orbit, to stabilise, and then progressively reduce, the number of objects larger than 10 cm. However, the final outcome critically depends on the break-up models adopted. In certain cases, the low earth orbit population of objects larger than 10 cm is growing, though slowly, even in the mitigated scenarios, and the long-term onset of an exponential growth cannot be avoided, unless old abandoned spacecraft and rocket bodies are actively de-orbited (a prospect prohibitively expensive with the limits of existing technology).

Figure 1
Figure 1: Long-term evolution below 2000 km of the number of objects larger than 10 cm.

Figure 1 shows the long-term evolution, below the altitude of 2000 km, of the number of objects larger than 10 cm, according to different mitigation scenarios investigated with SDM. Each line was obtained by averaging twenty Monte Carlo runs. The reference case is characterised by the current launch activity, taking into account the phasing out of obsolete launchers and the introduction of new rocket families. Mission-related objects are released according to present practices, while break-up prevention measures are progressively introduced, leading to no more explosions after 2030. In the increased scenario the number of space launches is augmented by 1% per year. In MIT_1 no mission related object is released after 2020, while in MIT_2 through MIT_5 the satellites launched after 2010 are manoeuvred at the end-of-life, in order to reduce their residual permanence in low earth orbit to 75, 50, 25 and 0 years, respectively.

Figure 1 Figure 1
Figure 2: Space debris impacts on a panel of the Long Duration Exposure Facility, left in orbit for 5.7 years (by courtesy of NASA). Figure 3: Hole in an antenna of the Hubble Space Telescope due the impact of a centimetre sized orbital debris. The external surface of the telescope is pitted by more than 1500 impacts (by courtesy of NASA).

At present, in the framework of a fourth ESA contract (2004-2007), SDM is undergoing broad and profound changes, in terms of overall concept and architecture, trajectory propagators, collision risk evaluation and debris mitigation options, to be better suited for investigating high earth orbital regimes, in particular those associated with high eccentricity orbits and with navigational and geosynchronous satellites. The technical manager of this contract is Alessandro Rossi, Carmen Pardini and Luciano Anselmo are work package leaders. The ESA technical supervisor is Rüdiger Jehn, of the European Space Operations Centre in Darmstadt, Germany.


Please contact:
Luciano Anselmo, Space Flight Dynamics Laboratory, ISTI-CNR, Italy
Tel: +39 050 315 2952