During the lifetime of the Solar System, collisions between small bodies have been relatively common. Low-velocity collisions (less than 0.1 kms-1) between planetesimals (bodies of size 1-10 km) led to the accretion of the present-day planets. On the other hand, in the primordial asteroid belt it is believed that the accretion process was interrupted, as soon as the initially gentle collisions were turned into destructive hypervelocity (about 6 kms-1) impacts. Subsequently, the collisional evolution of asteroids has given rise to a variety of phenomena and objects, which are currently studied through a mixture of observational, theoretical and experimental methods.
The so-called dynamical families, first identified by Hirayama (1918) are groups of main belt asteroids having some very similar orbital parameters. While the majority of asteroids are believed to have undergone significant collisional evolution, thus losing any significant record of their origin, the members of each of these families are generally thought to be fragments from a small number of catastrophic collisions - in the simplest model, each family arises from a single disruption event. The separation of the majority of families, in orbital element space, from members of the main asteroid belt means that they are statistically unlikely to have undergone many collisions. This makes the families very important in any consideration of laboratory simulations, when looking at fragment velocities and rotation rates from single impact events. More than 100 possible families have been identified by analysis of asteroid proper elements, and the statistical significance of some of these as having a common origin (in terms of taxonomy and composition) has been confirmed although the theory of asteroid families is still incomplete, and cannot explain some observations (see e.g. Chapman et al., 1989, for a review of data on asteroid families).
A general knowledge of the outcome of catastrophic fragmentation of asteroids by hypervelocity impact is relevant to the problem of both the origin and the nature (in terms of velocity and size distributions, etc.) of Earth-crossing asteroids and other short-lifetime asteroid orbital regions, such as the Kirkwood gaps, which have depletion mechanisms but no clearly identified source of re-supply.
Most hypervelocity impact experiments against macroscopic targets performed in the past and devoted to the simulation of catastrophic collisions between small solar system bodies have been carried out in evacuated target chambers, so as to reproduce the high vacuum conditions which exist in the interplanetary medium. However, in spite of various precautions (arenas, curtains, etc.), it has been impossible (i) to prevent fragments from undergoing secondary fragmentation against the walls of the target chamber, possibly affecting the final mass and shape distributions, and (ii) to record their uninterrupted ballistic trajectories, and thus gather further information about their spatial and velocity distributions and any structures present in them. In order to avoid the secondary fragmentation process and to record photographically the trajectories of the fragments, we performed a series of experiments in the open, on a flat area, at the proving ground of IMEG (Montemerano, Grosseto, Italy). A large amount of data was collected on each test - firstly by measuring the final positions of all recoverable fragments, and secondly by visual recordings using both monochrome CCD equipment and a fast-framing NAC E-10 camera operating at 700 frames per second. The film from the fast-framing camera was digitised and has been analysed using an Acorn Archimedes 440 computer system, and this has allowed us to (a) measure accurately the rotation rates of most fragments and their velocities in a plane perpendicular to the viewing direction, and (b) confirm the presence of collimated jetting (the ejection of a statistically significant number of fragments along some preferential direction). Some results, such as the angular dependence of the velocity distribution and the angular momentum distribution in space, are in good agreement with the semi-empirical model proposed by Paolicchi et al. (1989) as well as previous experimenters (see e.g. Fujiwara et al., 1987)
This experimental procedure has opened the door to a new approach to data collection and analysis - the number of individual fragments which could be measured accurately has increased by at least an order of magnitude compared with most previous experiments. On one hand, the possibility of analysing the parameters of individual fragments has pointed to an improvement in the quality of results. On the other hand, it has highlighted the enormous benefits and possibilities which result from a computer-based analysis of this type of experiment.
In spite of the large body of work which has been carried out in the field of catastrophic disruption, the amount of detailed data available, rather than average values, is surprisingly small. This lack of precise, fully reliable and high resolution data is due to the many problems associated with accurately recording the outcome of impact experiments of astrophysical interest. The main problem areas are;
b) secondary fragmentation against the walls of a target chamber, affecting (i) the distribution of the fragment aspect ratios[1], and (ii) interfering with any subsequent analysis of fragment positions on the floor of the chamber;
c) geometric problems arising from the use of a single camera. In most hypervelocity impact experiments performed to date, a single camera has been used, not so much because of the difficulty and cost of using 2 cameras (and thereby obtaining a stereo record), as the intrinsic difficulty of matching the two sequences of hundreds of fast-moving objects. This matching is essential for any 3D reconstruction of the disruption. The single camera is a relatively simple means of recording, but provides only a two dimensional projection of a three dimensional event and therefore suffers from the difficulties of deconvolving this 2D picture - especially if one cannot be absolutely sure of the axially symmetric distribution of the ejected fragment field.
A second advantage of increased data yield here is that minor but important effects - which might not have been apparent at all in previous experiments - can be studied perhaps for the first time, and from a strong statistical standpoint. Many previous investigators have been forced to use only average values from a number of experiments, due to the large errors in individual measurements. Although both average and specific data are of interest, the information provided by each is different.
With the above points 1.2.(a) to 1.2.(c) in mind, we have concentrated upon overcoming some of these difficulties. Furthermore, since the research on which this thesis is based was also aimed at the study of new types of targets, we have investigated the behaviour of targets provided with harder cores ('cored' targets) and compared and contrasted the outcome of their impacts with targets having the same geometric characteristics but without a core.
The main objectives of this work were to:
c) record the rotational properties of a significant number of ejected fragments, and to relate these measurements to other properties of the specific fragments;
a) study the effect of a core upon catastrophic fragmentation of macroscopic targets of artificial rock;
d) use two high-speed cameras to make a complete 3-dimensional record of the disruption;
e) search for, and collect evidence of, collimated jets of fragments; that is, statistically significant numbers of ejected fragments closely arranged about some preferential directions or planes - a result of fundamental importance in the study of the origins of asteroidal families.
The achievements of this research project can be classified under four headings:
2. The discovery of collimated jets of fragments with a high level of statistical significance under a c2 test - a result which is of great importance to the study of the collisional evolution of asteroids and asteroidal families.
3. The accurate measurement of rotation rates by measuring, for the first time, 'lightcurves' from real fragments, yielding rotation rate estimates which could be cross-checked against values found using other techniques.
4. A fairly exhaustive analysis of the fragment ejection field (i.e. individual angle and velocity values for each fragment) from the experiments carried out in 1989 using 2 uncored and 2 cored targets, including measurement of the rotation rates of over 400 fragments from the 4 shots in 1989 - more than an order of magnitude increase over previous studies of fragment rotation.
While the 3D work has achieved considerable success, this has so far been mainly concerned with the various problems of software development and data collection; only a small quantity of new physical data has been obtained. Chapter 4 of this thesis covers the analysis of the 2D experiments, reporting the results obtained during this project. In order to place the separate aspects of the analysis (velocity studies, fragment shapes, and so on) in the correct academic perspective, a short review of previous work is given with each sub-section in chapter 4.
One of the large outstanding problems in the field of catastrophic disruptions (see e.g. Fujiwara et al., 1989) is that of scaling between separate experiments within a research programme, between results from different programmes, and directly to asteroidal data. Most laboratory experiments have been carried out using macroscopic targets in the cm-sized regime. Not only is it impractical to attempt experiments with substantially larger targets (say, by factor of 100 in diameter) but there would remain the problem of the effects of gravitation - not significant until one considers fragmentation of kilometre sized bodies - and this cannot possibly be directly simulated in a laboratory. Experiments using an overpressure to simulate the volume-averaged stress in a gravity-dominated body have been carried out by Housen et al. (1991) but this technique is of limited usefulness because it does not offer any means of simulating the stress gradient within the body.
The problems addressed in this thesis do not require scaling in order to provide direct comparisons. This is primarily because our experiments have been conducted keeping constant any parameters (most importantly size and impact energy) which might affect the outcome of a catastrophic disruption. However, I shall touch upon this point whenever applicable to the discussion of the results presented here.
[1] We can associate three orthogonal axes with most solid bodies of irregular shape, and measure the three-dimensional shape of the bodies along these axes. These dimensions are usually referred to as a, b and c where a is the largest linear dimension of the body, followed by b and c. The ratios b/a and c/a are called the aspect ratios.