There is an old joke about the limitations of physics and its need for mathematical abstraction, the punchline of which runs, “We assume a spherical chicken⃛”. In trying to model the collisional evolution of asteroids, however, theorists have been unable to avoid assuming a spherical chicken. To create the present asteroid belt, asteroids must have been undergoing collisions throughout the age of the Solar System, but to make tractable analytical calculations of what happens when one asteroid hits another, one is forced into the unrealistic assumption that the bodies are spherical and rigid.
Now at last we can do something better: as reported on page 437 of this issue1, Asphaug and his co-authors (along with several other research groups) are progressing beyond analytical calculations to detailed numerical models of what happens when irregular, inhomogeneous asteroids suffer high-velocity impacts. Of particular interest are the near-Earth asteroids — not just ‘making’ them, but the possibilities for ‘braking’ one that might chance to be on a collision course with the Earth (the subject of a couple of Hollywood productions, Deep Impact and Armageddon, which either have been or will shortly be released).
Such detailed modelling has now become possible, partly because we now know the shapes of a few asteroids from radar mapping and spacecraft imaging, but mostly because high-speed supercomputers and advanced hydrodynamic codes are becoming available for non-military applications. Although the ‘peace dividend’ has yet to pay any obvious cash rebates, it appears to be yielding some research benefits. Over the past few years, similar computations have yielded realistic models of the tidal breakup2 of the progenitor of comet Shoemaker-Levy 9 by Jupiter in 1992; models of the impacts and plume formations3 of those fragments as they plunged into the atmosphere of Jupiter in 1994; similar models of the entry into the Earth's atmosphere of giant meteoroids such as the Tunguska bolide4 of 1908; and simulations of the formation of the Moon by an enormous glancing collision between some large body and the Earth, early in the Solar System5. A rich suite of problems has become ripe for solution with the advent of these powerful computing tools.
An important question about the structure and evolution of asteroids is whether they are monolithic bodies or ‘rubble piles’ — that is, loose agglomerations of debris fractured by past collisions but not quite dispersed into separate bodies. Asphaug et al. conclude that this is likely for many asteroids, but that it may depend critically on the first impact suffered by an initially monolithic body (Fig. 1). Once fracture zones are created, they tend to protect the material on one side from damage due to impacts on the other side, as the shock wave is absorbed, reflected or attenuated by the smaller rocks in the zone. Generally speaking, these effects tend to make the asteroid more resistant to global disruption, and hinder the rate at which further fracturing occurs to convert the entire mass into a ‘rubble pile’. A few large pieces can survive.
There is observational evidence that even very small asteroids are rubble piles, from the statistics of spin rates6. It seems that no asteroids spin so fast that they would be in a state of tension. Among very small asteroids, the average rate of spin is fast enough that there appears to be a barrier in the distribution of spins at the rate corresponding to this limit, suggesting that most asteroids indeed have no tensile strength, as would be the case for heavily fractured bodies. On the other hand, rubble pile structure does not help to explain the few very slowly spinning asteroids. 253 Mathilde, for example, imaged in detail by the NEAR spacecraft last year, is one such very slowly spinning body, with a rotation period of around 17 days. The images returned were astonishing for the number and large size of craters revealed, so it is not plausible that Mathilde somehow avoided spin-inducing impacts. However, the very large craters found on Mathilde do indicate a rubble pile structure, because according to the results of Asphaug et al. a monolithic body struck hard enough to produce such large craters would probably be blown apart, whereas a ‘sandbag’ might avoid complete disruption. The low bulk density of Mathilde found by its gravitational perturbations on the NEAR spacecraft also supports the idea that this is a structure with a lot of vacuum in among the rock7.
Perhaps the most interesting aspect of this work for the general public is the implication for defence against asteroid impacts on the Earth. If an asteroid were found to be on a collision course with the Earth, could we avoid it? The front-running technique is to explode a nuclear bomb some distance from the asteroid, vaporizing a thin layer of its surface on one side, and thus giving it a nudge. But most studies8 of this process have suffered from the spherical chicken problem, modelling the offending asteroid as a coherent solid body rather than a loose collection of debris. The new work may mean that deflecting an asteroid from a collision course would be more like clearing a landslide off the road than pushing a boulder aside. If the only thing holding the body together is gravity, then one cannot apply an impulsive change in its motion greater than the escape velocity from the surface without disrupting the body into many pieces. This means a kilometre-sized body can be given a change of course of only about a metre per second. Such a small impulse would have to be applied a fair fraction of a year before the projected time of collision in order to accumulate a change of path of a couple of Earth radii. The smaller the object, the smaller the impulse allowed, so the concept of a ‘Star Wars’ type shield protecting the Earth from imminent impacts is seriously flawed; better to discover asteroids far in advance in an orderly survey, allowing plenty of time to respond.
Asphaug, E., Ostro, S. J., Hudson, R. S., Scheeres, D. J. & Benz, W. Nature 393, 437–440 (1998).
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International Journal of Impact Engineering (2002)
Advances in Space Research (2002)
Journal of Mathematical Physics (2000)
Monthly Notices of the Royal Astronomical Society (2000)
Earth, Planets and Space (1999)