1. Introduction.

Our planet has been under a constant barrage of objects from space since its formation more than four billion years ago. These objects range from the very small to the very large; every day thousands of dust particles enter our atmosphere, over longer periods, objects with a diameter of a few kilometres hit the Earth with devastating consequences for life as a whole. In the past there was an unwillingness to recognise that the Earth was not a closed system however, knowledge obtained over the last century or so has brushed that notion aside.

It is now widely accepted that an impact on the Yucatan peninsula caused the climate changes that ended the long dominance of the dinosaur family some 65 million years ago (Alvarez et al, 1980). The huge Barringer carter in Arizona was created some 50,000 years ago, and in 1908 thousands of acres of forest were destroyed in Tunguska. An equivalent impact on a city would eliminate everything within a 40 kilometres radius. More recently we have witnessed small land impact or atmospheric explosions, in 2007 in Peru, in 2008 in Sudan and less than a month ago in Indonesia.

This bombardment is integral to life on our planet. The Earth was formed through the same material (Joseph, 2009): without water and carbon life as we know it would not exist. Periodic impacts have revised the conditions and shaped the course of evolution (Elewa, 2009). On the one hand we can rejoice in them, on the other, we can fear for our future (Chyba and McKay, 1997; Napier, 2009).

Understanding the threat from Near Earth Objects (NEOs) is relatively recent. The first Earth crossing asteroids, Apollo and Adonis, were discovered in 1932 however it wasn’t until 1988 that the Spacewatch programme, to survey and catalogue NEOs, began. The spectacle of comet Shoemaker-Levy 9, impacting with planet Jupiter in July 1994, with at least 21 cometary fragments of a couple of kilometres in diameter, causing massive explosions, sparked public interest, while technically risible Hollywood productions such as Armageddon, Asteroid and Deep Impact added to public concern. This however set the seeds for the widespread, and at times hysterical, media reporting that followed the discovery of asteroid 99942 Apophis. First detected in December 2004, it presented a 2.5% probability of impact in 2029; this was later discounted following more accurate orbit determination but currently there still is a small possibility (0.002%) of a resonant return with a possible impact in 2036.

Most of the practical and theoretical work on the subject has been carried out by the United States with NASA leading the way, but more recently the European Space Agency and its member states have started addressing the problem. In Britain a debate took place in the House of Commons in March 1999 and a Task Force to the Minister for Science to report on potentially hazardous Near Earth Objects was established in January 2000. The Task Force, which released its findings in August 2000 stated that "at a time when we understand better than ever before the consequences for the world as a whole, an international effort of research, coordination and anticipatory measures is required in which British science, technology and enterprise should play an important part."

There are countless numbers of asteroids and comets in the Solar System in well-defined regions far from Earth, such as the Kupier Belt. The gravitational forces of the outer planets, mainly Saturn and Jupiter, together with collisions with other asteroids, slowly alter the orbits of these small bodies. Following many deflections, an asteroid or comet may become a Near Earth Object, when its orbit either intersects that of the Earth or is within 0.3 Astronomical Units. Such an object is said to be potentially hazardous when its orbit brings it even closer to Earth, at a mere 0.05 AU, and has a diameter of at least 150 metres (Binzel, 2000). So far over 300 potentially hazardous objects have been catalogued, but the number increases almost on a daily basis as the survey continues. Given enough accurate measurements of the position of an asteroid or comet, astronomers can predict their orbits over very long periods of time. However, as they move around the Solar System they continue to suffer small deflections so their orbits may not be completely predictable far into the future.

2. DEFLECTING ASTEROIDS

For the first time in history there are possibilities for mitigating or removing the risks of Near Earth Objects impacting the Earth (Barbee and Nuth, 2009; Cambier et al., 2009; Crowther, 2009). This depends on first improving our ability to detect such objects well in advance and to accurately measure their orbital parameters and physical properties. It is only recently that space agencies around the world have started to direct their exploration ideas towards comets and asteroid; not only to improve the current knowledge of these small celestial bodies but also to start developing the technological capabilities should a deflection mission become necessary. Missions such as Giotto, Deep Impact, NEAR-Shoemaker, Stardust, Hyabusa, Rosetta and Dawn are testament to the increased interest in this subject by space agencies all over the world.

Over the last couple of decades a number of possible deflection methodologies have been proposed and investigated in more or less detail. The underlying concept of most of these approaches is to impart a change in the asteroid’s linear momentum, thus producing a change in its orbit. The consequence and end result of this is to increase the distance of the asteroid from the Earth. Broadly speaking the deflection approaches can be categorised in two main groups: impulsive deflections which deliver an almost instantaneous change to the velocity vector of the asteroid and long term deflections which act on the asteroid for extended periods of time.

2.1 Impulsive Approaches

Impulsive approaches are conceptually very simple (Barbee and Nuth 2009; Cambier et al., 2009). An impact with the asteroid or a large explosion produces an instantaneous change in the magnitude and direction of the velocity vector of the asteroid. The consequence of this change is that the trajectory of the asteroid is altered thus eliminating the possibility of an impact with the Earth. The main drawback of such an approach is that the energies released by these strategies are very close to the energy required to catastrophically disrupt an asteroid. If fragmentation is a result of the impact/explosion this may pose increased risks to Earth (Barbee and Nuth 2009; Cambier et al., 2009).

2.1.1 Nuclear Detonation

Nuclear devices provide the highest energy density among all possible deflection strategies (Cambier et al., 2009). . Nuclear detonation can be accomplished in three different ways: the explosion occurs at a certain distance from the asteroid; the explosion takes place ion the surface of the asteroid; the explosion occurs inside the asteroid’s surface. In the last two cases the ejected mass from the asteroid would be obviously larger than in the first case. The stand off explosion is however more robust against uncertainties in the composition and shape of the asteroid. The total Δv delivered by the nuclear detonation will be given by the sum of the different radiation components as well as the debris resulting from the explosion:

The main contribution to the total change on velocity generally comes from the neutron radiation which, penetrating deeper into the asteroid, produces more evaporation. Occasionally however, x-ray radiation becomes the dominating contributor (Hammerling and Reno, 1995).

2.1.2 Kinetic Impact

The kinetic impactor is without a doubt the most conceptually, technologically and politically simple approach to deflecting a potentially hazarous asteroid. The linear momentum of the asteroid is altered by impacting a mass into it. The impact is modelled as an inelastic collision mediated through a momentum enhancement factor due to the blast of expelled material.

(2)

where β is the momentum enhancement factor, m_a and m_imi is the relative velocity of the impactor with respect to the asteroid. To improve the efficiency of this approach we would therefore need large masses, but this is currently limited by launch capabilities. Alternatively we would need to design trajectories that maximise the impact velocity, and this can be achieved through the use of retrograde orbits (McInnes, 2004).

2.1.3 Artificial Spin Up

While not strictly an impulsive method, artificial spin up requires nevertheless a destructive approach to asteroid deflection. The underlying idea is to increase the spin rate of the asteroid to such a level that the stress induced on the asteroid’s core by the centrifugal load, initiates a fragmentation process (Bombaredelli 2007; Bombardelli 2009). The spin rate that needs to be imparted to an asteroid of bulk density ρ and diameter d to achieve fragmentation is:

(3)

where G is Newton’s gravitational constant and σ is tensile strength of the asteroid material. The use of chemical or electrical thrusters attached to the asteroid’s surface appears to be both inefficient due to the relatively small torques that could be produced, as well as problematic as the thrusters may be thrown off the surface due to centrifugal forces. A more realistic and efficient approach would be to anchor a spacecraft close to the spin axis of the asteroid and release a couple of tethered masses. In this case very high inertia/mass ratios can be achieved as well as providing a large lever arm (in the order of several kilometres) for a torque applied by thrusters positioned on the tethered masses.

2.2 Long Term Approaches Conceptually opposite to impulsive approaches, long-term approaches interact directly or indirectly, with the asteroid over an extended period of time, possibly lasting several years. The finale outcome of any long term approach is a change in the physical characteristics of the asteroid or in its orbital elements that produces the required deflection. These approaches can be further divided into techniques that actively produce a controlled thrust on the asteroid – mass driver, gravity tug, in-situ propulsion, surface ablation – and approaches that passively produce a thrust by varying the optical and thermal properties of the asteroid (Barbee and Nuth, 2009; Cambier et al., 2009; Crowther, 2009).

2.2.1 In-situ Propulsion

This approach requires the spacecraft to land on the surface of the asteroid and use its propulsion system to modify the asteroid trajectory. Chemical propulsion provides a higher thrust but its low exhaust velocity makes it less efficient than a low thrust propulsion system. This approach is however not without a number of technological challenges first and foremost an appropriate anchoring system between the propulsion system and the asteroid. Secondly, the surface operations may lead to the creation of a transient atmosphere of loose regolith that could negatively affect the propulsion system’s operations and hardware (Scheeres, 2004). Finally due to the rotation period of the asteroid the thrust vector will not maintain a constant direction so this will require the propulsion system to be switched on and off (Scheeres and Schweickart, 2004).

Two approaches, both hinging on modifying the spin rate of the asteroid, have been suggested to address this problem. The first approach requires the propulsion system to at first nullify the spin rate of the asteroid, then to impose a spin rate, which matches the asteroid’s orbital period and finally deflect the asteroid. The second approach requires a re-orientation of the asteroid’s rotational pole

2.2.2 Surface Ablation

The idea to concentrate energy on an asteroid to sublimate the surface material, creating a jet of gas and dust was first suggested in the mid 90s (Melosh et al, 1994). The ablated material produces a minute but continuous thrust which ultimately alters the orbit of the asteroid. The energy can be either sunlight focused through one or more mirrors (Maddock et al, 2007) or produced by a laser beam. While the way in which the energy is delivered to the asteroid surface, is different, the end result for the two approaches, is conceptually the same. The acceleration, aabl, which the asteroid experiences due to the surface ablation is:

(4)

where ζ is a scattering factor that accounts for plume dispersion, EMBED Equation.3 is the average velocity of the gas particles, EMBED Equation.3 is the total sublimated mass flow and M_a is the mass of the asteroid, which changes as a function of time due to sublimation process.

2.2.3 Gravity Tug

This methodology exploits the mutual gravitational attraction between the asteroid and a spacecraft to divert it from an impact trajectory (Lu and Love, 2005). This concept was suggested as a deflection approach robust enough to overcome the inherent uncertainties in the asteroid composition, morphology and spin rate. While this approach is robust to asteroid uncertainties it is however in no way immune (Broschart and Scheeres, 2005; Kawaguchi et al., 2008). Obviously, the closer the spacecraft is to the asteroid, the larger the gravitational attraction, and therefore the ability to pull the asteroid off its trajectory. The exhaust gases of the engines must however not impinge on the asteroid, as this would cause the centre of mass of the spacecraft-asteroid system to remain unperturbed. This means that the engines of the spacecraft must be tilted outwards. To avoid canted thrusters, displaced non-Keplerian orbits have been suggested as a fuel-efficient approach to towing asteroids (McInnes, 2007).

A spacecraft in a displaced orbit will however need to be approximately 3 times heavier than a hovering spacecraft for the same standoff distance, or will need to be substantially closer for the same spacecraft mass. An interesting approach for displaced orbits is the possibility of using multiple spacecraft, resulting in an increased Δv capability as well as inherent redundancy and enhanced mission flexibility (Lappas and Wie, 2008).

2.2.4 Mass Driver

The mass driver system produces a change in the linear impulse vector of the asteroid by shooting into space part of the asteroid’s surface. The asteroid crust is excavated by means of a drilling device and accelerated into space through an electromagnetic railgun (Olds et al, 2004). The variation in velocity, Δv, of the asteroid is given by:

(5)

where M_a is the mass of the asteroid, which changes as a function of time due to the excavation process; v_e is the excess velocity of the expelled mass, m_exp. Each impulse therefore produces a small and finite variation in the orbital elements of the asteroid. Similarly to the in-situ propulsion approach the performance of the mass driver is independent of the shape of the asteroid and affected only by its spin rate.

2.2.5 Yarkovsky Effect

This methodology requires the alteration of the surface properties of an asteroid through highly reflective or absorptive substances. The change in surface properties would amplify the Yarkovsky effect, which is the thermal radiation force acting on an asteroid due to the anisotropic emission of photons (Chesley et al., 2003). This is a consequence of the time required for the asteroid surface to warm up or cool down.

In general there are two components to the Yarkovski effect: a diurnal and a seasonal effect. In general, the magnitude of the effect will depend on the asteroid size dependent, and will affect the semi-major axis of smaller asteroids, while leaving large asteroids practically unaffected. For kilometre-sized asteroids the Yarkovsky effect is minuscule over short periods: 6489 Golevka is subjected to a force of approximately 0.25 N, yielding a net acceleration of 10⁻¹⁰ m/s^². This effect is however steady, and over a sufficiently long time, probably several decades, an asteroid's orbit can be perturbed enough to divert it from a collision course with the Earth.

3. CONCLUSIONS

Over the last decade the possibility of an asteroid, large enough to cause world-wide destruction, impacting the Earth has stimulated an intense debate among the scientific community on possible deflection methods. A large range of mitigation strategies have been proposed and compared in literature (Barbee and Nuth, 2009; Cambier et al., 2009; Crowther, 2009; Sanchez et al, 2009). The broad overview presented in this paper does not intend to rule out other possible methods not analysed here, although some could be considered as a combination of the methodologies introduced above. For the first time in the history of mankind, we have the technological capabilities and scientific know-how to protect ourselves from a catastrophe of truly cosmic proportions. We cannot rely on statistics alone to protect us from catastrophe; we cannot afford to wait for the first modern occurrence of a devastating NEO impact before taking steps to adequately address this threat. It is now time for mankind to develop practical and viable strategies to protect Earth from asteroid impact; if not we will go the way of the dinosaurs…

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