Introduction

The most important requirement, scientific or otherwise, for any impact mitigation is the recognition of the hazard, since, in the absence of a perceived impact risk, there is neither the incentive nor the capability to address the threat. Therefore, the success of any potential mitigation effort will rely heavily upon our ability to discover, track, and analyze threatening objects. In this chapter we will consider the effectiveness of the present surveying and monitoring capabilities by bombarding the Earth with a large set of simulated asteroids that is statistically similar to the impacting population.

Our objective is to determine where on the sky impactors may most readily be detected by search instruments and to evaluate current search techniques for their effectiveness at detecting asteroids on impact trajectories. We also consider the likelihood that existing survey efforts would find previously undiscovered impactors with just weeks to months of warning time. We discuss the factors that affect whether an impactor detection is actually recognized as a near-Earth asteroid (NEA) discovery and announced to the community for further analysis, including impact monitoring. We close with an example demonstrating how automatic impact monitoring can detect a distant impending impact immediately after discovery, when the impact probability is very low, and how the threat gradually grows more severe during the discovery apparition. In many cases the threat will not be alarming until the object is re-detected at a subsequent apparition. This can substantially diminish the effective warning time, and hence shorten the time available to mitigate the impact.

Introduction

The known NEA population contains a confusing variety of objects: there are many different “animals in the zoo” of near-Earth asteroids. Some NEAs are thought to be largely metallic, indicative of material of high density and strength, while some others are carbonaceous and probably of lower density and less robust. A number of NEAs may be evolved cometary nuclei that are presumably porous and of low density but otherwise with essentially unknown physical characteristics. In terms of large-scale structure NEAs range from monolithic slabs to “rubble piles” and binary systems (asteroids with natural satellites or moons). An asteroid that has been shattered by collisions with other objects may survive under the collective weak gravitational attraction of the resulting fragments as a cohesionless, consolidated, so-called rubble pile. A rubble pile may become a binary system if it makes a close approach to a planet and becomes partially disrupted by the gravitational perturbation. More than 20 NEAs in the currently known population are thought to be binary systems and many more are probably awaiting discovery.

The rate of discovery of NEAs has increased dramatically in recent years and is now seriously outstripping the rate at which the population can be physically characterized. The NEA population is still largely unexplored.

Which physical parameters are most relevant for mitigation considerations? Preventing a collision with an NEA on course for the Earth would require total destruction of the object, to the extent that the resulting debris poses no hazard to the Earth or, perhaps more realistically, deflecting it slightly from its catastrophic course.

Introduction

The current Spaceguard Survey classifies each known near-Earth asteroid (NEA) as either non-threatening or deserving of additional astrometric attention. For any possibly threatening object, the dominant issues are the uncertainty in its trajectory and physical nature as well as what can be done to reduce that uncertainty. Morrison et al. (2002) note that

Thus reduction in uncertainty is tantamount to ensuring that unnecessary costs are avoided and that necessary actions are undertaken with adequate warning.

Ground-based radar is a knowledge-gathering tool that is uniquely able to shrink uncertainty in NEO trajectories and physical properties. The power of radar stems largely from the precision of its measurements (Table 3.1). The resolution of echoes in time delay (range) and Doppler frequency (radial velocity) is often of order 1/100 the extent of a kilometer-sized target, so several thousand radar image pixels can be placed on the target. Delay-Doppler positional measurements often have a fractional precision finer than 1/10 000 000, comparable to sub-milliarcsecond optical astrometry.

The single-date signal-to-noise ratio (SNR) of echoes, a measure of the number of useful imaging pixels placed on a target by a given radar data set, depends primarily on the object's distance and size.

Introduction

Mitigation of any hazard begins with a comprehensive understanding of the forces to be reckoned with. Reckoning – taking measure – is being done with great efficiency on one front: the first-order census of kilometer-scale near-Earth objects (NEOs) may be complete in the next few decades (Jedicke et al. 2003). But the most basic physical properties of these bodies remain unknown: how they are assembled, how they respond to tidal and impact stress, and how they will respond to the artificial perturbations that will one day be required.

This chapter provides an introduction to comets and asteroids and their geophysical evolution, and concludes with recommendations for theoretical and laboratory effort and spacecraft reconnaissance. Little is known for sure. Comprehensive introductions to the rapidly evolving science of comets and asteroids are found in the University of Arizona Press review volumes Asteroids III (Bottke et al. 2002) and Comets II (Festou et al. 2004).

Comets

Not long ago, interplanetary space near Earth was believed to be far emptier than it now appears. The only luminous entities besides the Moon were the passing comets, whose comae and tails can form some of the most extensive structures in the solar system, and which have been scrutinized since the dawn of astronomy. While these centuries of observation have led to an understanding of the dynamics and compositions of cometary envelopes, cometary nuclei – compact objects ranging from a few hundreds of meters to a few hundreds of kilometers diameter – remain a tight-wrapped mystery (Jewitt 1999; Meech et al. 2004).

Introduction

Mitigation and detailed characterization of asteroids and comets require some period of close proximity operations about them. To support close proximity operations requires an understanding of dynamics of natural material on and about small bodies, and the dynamics, navigation, and control of artificial objects on and about small bodies. In this chapter we discuss some of the controlling issues that relate to close proximity operations, and draw connections between this issue and the design of spacecraft and mission concepts to carry out close proximity operations.

Since the field of astrodynamics and celestial mechanics is often considered to be a mature field, it is relevant to ask why the control of spacecraft about small solar system bodies is considered to be a difficult problem. There are a number of reasons for why this is the case, which we review here and explain in additional detail throughout this chapter. A clear rationale for why this is true can best be expressed through the following chain of facts.

Introduction

It is a demonstrable fact that asteroids of all sizes and less frequently cometary nuclei suffer collisions with the Earth's surface. The impact hazard, which is defined in Morrison et al. (2002) as “… the probability for an individual of premature death as a consequence of impact,” has undergone considerable analysis with the conclusion that the greatest risk is from the very rare collisions of relatively large asteroids that can create a global scale catastrophe in the biosphere (Chapman and Morrison 1994). In the last decade, the question of how to deal with the hazard has led to considerable activity and advocacy on the part of the interested scientific community, and activity at government level has been stimulated in the United States, Europe, and Japan (a detailed overview is given by Morrison et al. 2002): there are now survey programs to search for objects that could be potentially hazardous; there are high-level calls for increased observational efforts to characterize the physical and compositional nature of near-Earth objects (NEOs) (e.g., The UK NEO Task Force report: Atkinson et al. 2000); an impact hazard scale has been invented to provide the public with an assessment of the magnitude of the hazard from a particular object; there have been considerable advances in the accuracy of orbit determination and impact probability.

Nevertheless, it seems that the question of how governments should go about preparing to mitigate the hazard needs some further attention.

Introduction

Some investigations of the surface or sub-surface of near-Earth objects (NEOs) that are needed to support mitigation demand contact with the surface. The main examples are:

• Seismological methods, requiring both sources and receivers, to examine the internal structure of NEOs and look for cracks and voids that may influence the mitigation strategy and its effects.

• Surface and sub-surface mechanical properties measurements, to determine the material's response to drilling, digging, hammering, impacts, explosive detonations, etc. The type of measurements performed would depend on the mechanical interaction involved in the mitigation strategy being pursued (e.g., whether low or high strain rate).

• Measurements of sub-surface thermal properties and volatile content, with a view to using non-gravitational forces (outgassing) for mitigation.

• Emplacement of a radio beacon to help refine predictions of a NEO's future orbit.

• Radio transmission tomography, to examine the interiors of NEOs.

There are of course many other potential investigations requiring surface contact that appear to be rather less important for mitigation, being motivated wholly by science or space resources studies. For example, mitigation studies would seem to require compositional information no more detailed than that that can be determined remotely (e.g., by X-ray and infrared (IR) spectroscopy) and by comparison with meteorite analogs. An object's response to a mitigation technique is determined more directly by a set of key physical properties – particularly mechanical, thermal, and structural.

Introduction

In the 1994 book edited by Gehrels, Hazards due to Comets and Asteroids, chapters by Ahrens and Harris (1994), Shafer et al. (1994), Simonenko et al. (1994), Solem and Snell (1994), and Melosh et al. (1994) present and study a number of ways of preventing an oncoming asteroid from colliding with the Earth. Most methods considered nudging it sufficiently at 10 or so years before the impending collision to change its course so it would miss the Earth.

The methods studied include the use of conventional or nuclear explosives on or below the surface, the impact by large masses at high velocities, the blowing off of material by standoff nuclear weapons or by the concentration of solar energy using giant mirrors or by zapping it with lasers, and more gentle methods such as simply attaching a propulsion rocket, a solar sail or launching surface material off at sufficient velocity to escape the asteroid.

The analyses of the different methods rely primarily on data and estimates accumulated for cratering and disruption using the material properties of terrestrial materials. In most cases those were silicate materials with mass densities of ∼3 g cm–3 or iron asteroids of density ∼8 g cm–3. However, it is becoming generally accepted that many of the asteroids are re-accumulated rubble pile bodies of very low density and strength, and comets have been thought for some time to have that structure.

Introduction

Understanding the inventory and size distribution of those bodies which during their orbital evolution can intersect the orbit of the Earth with a non-zero probability of collision is a high priority task for modern planetary science. Apart from obvious considerations about mitigation of the impact hazard for the terrestrial biosphere, this is also a challenging theoretical problem, with important implications for our understanding of the orbital and physical evolution of the minor bodies of our solar system.

Several mechanisms have been discovered and analyzed in recent years to explain the steady influx of bodies from different regions of the solar system to the zone of the terrestrial planets. Several unstable regions in the orbital element space have been identified in the asteroid main belt, which can lead bodies to be decoupled from the belt and evolve into near-Earth object (NEO) orbits (Morbidelli et al. 2002). Both conventional collisional mechanisms and dynamical non-gravitational mechanisms (Yarkovsky effect) can be responsible for a steady injection of main-belt asteroids into these unstable orbits. Even in the absence of unstable regions, the Yarkovsky effect can cause a continuous drift in semimajor axis and eccentricity, eventually leading to a close encounter with a terrestrial planet, and removal from the main asteroid belt (Spitale and Greenberg 2001, 2002). The NEO production rate and the resulting NEO inventory and size distributions can be theoretically estimated and compared with observations (Bottke et al. 2002). It should be noted that the effectiveness of the different supply mechanisms is eminently size dependent.

This book describes the two main applications of plasma physics, laboratory research on thermonuclear fusion energy and plasma-astrophysics of the solar system, stars, accretion discs, etc., from the single viewpoint of magnetohydrodynamics (MHD). This provides effective methods and insights for the interpretation of plasma phenomena on virtually all scales, ranging from the laboratory to the Universe. The key issue is understanding the complexities of plasma dynamics in extended magnetic structures.

The book starts with an exposition of the elements of plasma physics, followed by an in-depth derivation of the MHD model. By means of the conservation laws, different model problems for laboratory and astrophysical plasmas are formulated. The spectral theory of MHD waves and instabilities is then developed in analogy with quantum mechanics. The centrepiece is the analysis of inhomogeneous plasmas with intricate spectral structures that provide a unified view of waves and instabilities in plasmas as different as tokamaks and coronal flux tubes. This is illustrated by the magnetic structures and dynamics observed in the solar system, and analysed in detail for cylindrical flux tubes. Advanced chapters on wave damping and resonant heating expose the wonderful interplay of physics and mathematics.

In order to provide the student with all the tools that are necessary to understand plasma dynamics, the classical MHD model is developed in great detail without omitting steps in the derivations. The necessary restriction to ideal dissipationless plasmas, in static equilibrium and with inhomogeneity in one direction, is more than compensated by the insight gained in the intricacies of magnetized plasmas. With this objective the size of the original manuscript, including advanced topics of magnetohydrodynamics, became impractical so that we decided to split it into two volumes.

Plasma dynamics in laboratory and nature

In this chapter we will make an excursion to the vast territory of magnetic structures and dynamics of the different plasmas encountered in the solar system, in particular the Sun and the planetary magnetospheres. While laboratory plasma confinement for the eventual goal of energy production also provides a rich diversity of magnetic structures, their topology and dynamics is always constrained by the presence of a fixed set of coils with programmed currents that should control the spatial and temporal behaviour of the magnetic fields. The reason is clear: for the success of thermonuclear energy production, plasma dynamics and complexity are not really desired. The best thing would be to extract energy from a plasma that just sits quietly inside a toroidal vessel and the engineering approach to plasma confinement is to try to approach this ideal as closely as possible. The history of thermonuclear fusion research demonstrates impressive progress along this line but also the immense obstacles, due to complex plasma dynamics, that have to be overcome. In astrophysical plasmas, on the other hand, no such human engineering constraints exist: plasmas and their associated magnetic structures appear to be almost free to exhibit the bewildering variety of different dynamics that are observed on virtually all length and time scales.

Space missions in the second part of the twentieth century have played an important role in demonstrating the different magnetic structures and dynamics of plasmas in the solar system.

The ideal MHD equations

The dynamics of magnetically confined plasmas, as exploited in laboratory nuclear fusion research and observed in astrophysical systems, is essentially of a macroscopic nature so that it can be studied in the fluid (MHD) model introduced in Chapter 2. The ‘derivation’ of the MHD equations in Chapter 3 provided indications about the range of validity and the limitations of the equations. In the present chapter, we will develop the MHD model for the interaction of plasma and magnetic field in detail and, thus, obtain a powerful ‘picture’ for the dynamics of the mentioned plasmas.

Recall from the introduction of Chapter 3 that the equations of magnetohydrodynamics can be introduced either by just posing them as postulates for a hypothetical medium called ‘plasma’ or by the much more involved procedure of averaging the kinetic equations. Whereas Chapter 3 was mainly concerned with the second method, in the present chapter we exploit the first method: we simply pose the equations and use physical arguments and mathematical criteria to justify the result. We continue the exposition of Section 2.4.1, where we already encountered the relevant equations.

Postulating the basic equations

The ideal MHD equations describe the motion of a perfectly conducting fluid interacting with a magnetic field. Hence, we need to combine Maxwell's equations with the equations of gas dynamics and provide equations describing the interaction.

First, consider Maxwell–s equations, already encountered in Chapters 2 and 3.

Stability: intuitive approach

Two viewpoints

How does one know whether a dynamical system is stable or not? Consider the well-known example of a ball at rest at the bottom of a trough or on the top of a hill (Fig. 6.1). There is a position (indicated by the full circle) where the potential energy W due to gravity has an extremum W0. Displacing the ball slightly to a neighbouring position (at the open circle) results in either a higher or a lower potential energy W1. This corresponds to a stable system in the first case (W1 > W0) and an unstable system in the second case (W1 < W0).

Already at this stage some important observations can be made, viz.:

1. (a) We have tacitly assumed that the constraining surface is curved, i.e. either convex or concave, so that there is a position of rest, which is called the equilibrium position. In this case, one may rescale the potential energy such that the equilibrium state corresponds to W0 = 0, and W1 becomes the potential energy of the displacement, which is called the perturbation.

2. (b) If the constraining surface is flat and inclined, the system is not in equilibrium and the ball simply rolls along the plane. This lack of equilibrium, when W has no extremum, should be well distinguished from neutral or marginal stability, when W1 = W0. The latter situation occurs when the surface is horizontal, so that the value W = 0 may be assigned to both W0 and W1.

Motivation

Under ordinary circumstances, matter on Earth occurs in the three phases of solid, liquid, and gas. Here, ‘ordinary’ refers to the circumstances relevant for human life on this planet. This state of affairs does not extrapolate beyond earthly scales: astronomers agree that, ignoring the more speculative nature of dark matter, matter in the Universe consists more than 90% of plasma. Hence, plasma is the ordinary state of matter in the Universe. The consequences of this fact for our view of nature are not generally recognized yet (see Section 1.3.4). The reason may be that, since plasma is an exceptional state on Earth, the subject of plasma physics is a relative latecomer in physics.

For the time being, the following crude definition of plasma suffices. Plasma is a completely ionized gas, consisting of freely moving positively charged ions, or nuclei, and negatively charged electrons. In the laboratory, this state of matter is obtained at high temperatures, in particular in thermonuclear fusion experiments (T ∼ 108 K). In those experiments, the mobility of the plasma particles facilitates the induction of electric currents which, together with the internally or externally created magnetic fields, permits magnetic confinement of the hot plasma. In the Universe, plasmas and the associated large-scale interactions of currents and magnetic fields prevail under much wider conditions.