Furthermore, NEAs are distinct from the asteroids that inhabit the famous asteroid belt between Mars and Jupiter. With a total of 450,000 asteroids currently known and only 6,407 of them being NEAs, main belt asteroids are clearly far more numerous. The orbits of main belt asteroids may evolve so that they eventually become NEAs, but this happens on a very long time scale.

2.1 Orbit Classifications

NEAs are generally classified according to their orbit and (perceived) composition. In terms of composition, approximately 75% of them are carbonaceous, 17% are silicaceous, and 8% are metallic (nickel–iron). In terms of their orbits, some NEAs are Earth–crossing asteroids, falling into either the Aten or Apollo categories, while others are Mars–crossing (Earth–approaching) asteroids classified as Amors. Aten asteroids have a semi–major axis < 1 AU and a perihelion distance > 0.983 AU, while Apollo asteroids have a semi–major axis > 1 AU and a perihelion distance < 1.017 AU. Amor asteroids have a perihelion distance > 1 AU but < 1.3 AU. These orbital families are depicted in Fig. 2, an illustration created by The European Space Agency (ESA).

Figure 2: Near–Earth asteroid orbital families.

An important sub–category of NEAs according to orbit are the Potentially–Hazardous Asteroids (PHAs). These asteroids have a Minimum Orbit Intersection Distance (MOID) with Earth < 0.05 AU and an Absolute Magnitude (H) of 22.0 or brighter (H < 22.0), which corresponds to a minimum size of 150 meters. Absolute Magnitude for Solar System bodies is defined as the apparent magnitude of an object if it were 1 AU from the Sun and the observer, and at a phase angle of zero degrees. H = 22.0 generally corresponds to a size range of 110 – 240 meters, but for the purpose of defining PHAs an albedo of 13% is also assumed, in which case H = 22.0 corresponds to 150 meters. However, it is important to note that carbonaceous asteroids could have albedos less than 3%, making them both harder to detect and more dangerous (larger) when they are found. At the time of this writing there are 1078 known PHAs, with more being discovered on a continual basis. The count of known PHAs is maintained on http://neo.jpl.nasa.gov/neo/groups.html. While a PHA will not necessarily strike Earth, the chances of a collision at some point in the future are greater and therefore these objects bear careful monitoring.

2.2 The Search for NEOs

In 1993 and again in 1998 the U.S. Congress held hearings and mandated that NASA should conduct a survey to locate and track more than 90% of asteroids whose diameters equal or exceed one kilometer. In 2005 this limit was decreased and the new mandate is to find more than 90% of asteroids with diameters of 140 meters and larger before 2020.

When Congress originally sent NASA on the hunt for asteroids, less than 10,000 were known. Since the hunt began, more than 450,000 new asteroids have been discovered with several additional bodies added to this total each and every day. For most asteroids only their orbital elements and their absolute magnitude (brightness) at the time of their discovery are known (albeit with limited accuracies). We do not know the mass, chemical composition or physical structure of most asteroids.

Although an asteroid classification system does exist, based on the observed reflectance of the object from the blue to the near infrared, only about 5000 of the nearly 500,000 known asteroids have been spectrally classified. Unfortunately, although it is possible to classify any specific asteroid according to its spectral type, we do not currently understand what such classifications actually mean in terms of chemical composition or structure. It would therefore be impossible to use such information to design a mission to divert an asteroid from a collision with the Earth on a short time scale.

2.3 Spectral Classifications

Studies of meteorites have yielded a wealth of scientific information based on highly detailed chemical and isotopic studies possible only in sophisticated terrestrial laboratories. Telescopic studies have revealed an enormous (> 10⁵) number of physical objects ranging in diameter from a few tens of meters to nearly one thousand kilometers, orbiting not only in the traditional asteroid belt between Mars and Jupiter but also throughout the inner solar system. Many of the largest asteroids are classed into taxonomic groups based on their observed spectral properties and are designated as C, D, X, S or V types (as well as a wide range in sub-types) as shown in Fig. 3. These objects are certainly the sources for the meteorites in our laboratories, but we generally don’t know which asteroids are the sources for these meteorites.

Figure 3: The Bus–DeMeo taxonomy key.

These spectral classes are nominally correlated to the chemical composition and physical characteristics of the asteroid itself based on studies of the spectral changes induced in meteorites due to exposure to a simulated space environment. While laboratory studies have produced some notable successes (e.g. the identification of the asteroid Vesta as the source of the Howardites, Euchrites, and Diogenites meteorite classes), it is unlikely that we have samples of each asteroidal spectral type in our meteorite collection. The correlation of spectral type and composition for many objects will therefore remain uncertain until we can return samples of all of the specific asteroid types to Earth for analysis. The best candidates for sample return are asteroids that already come close to the Earth. Nearly 60,000 asteroids were discovered in 2007: just over 1% of these asteroids were NEAs. We cannot possibly send spacecraft to all such bodies, either for in–situ analysis or for sample return. It is unlikely that we can significantly improve our understanding of these asteroids based on meteoritic studies since we cannot typically connect a meteorite to its parent asteroid. Telescopic observation and spectral classification of the asteroid population is the only practical means of cataloging such a large and diverse set of objects. Unfortunately, although our current classification scheme can successfully bin objects based either on their orbital characteristics or on their spectral properties, detailed interpretation of this orbital or spectral information in terms of the chemical composition or structural integrity of a specific body is based more on faith and inference than on actual measurements of the properties of asteroids of specific type.

2.4 Motivations

These relatively broad classifications of NEAs serve to give structure to our overall understanding of their population and help provide context for our efforts to detect and track those that might prove hazardous to us. However, much more detailed information about a particular NEA will be required in the event that we have to design and deploy an effective spacecraft system to deflect an incoming object. Details such as mass, size, spin state, composition, density, and internal structure are absolutely critical inputs to the design of most deflection system concepts, particularly those that can be effective on short notice.

However, details such as these cannot currently be determined accurately (or at all) from ground–based observations. This means that a precursor science mission to the threatening asteroid would be required prior to the design and construction of the actual deflection system. Unfortunately, if the warning time is too short, there might not be time for a precursor science mission, leaving us in the difficult predicament of needing to design and deploy a deflection system with too little information when life as we know it on Earth hangs in the balance.

The proposed advancements in asteroid science described herein aim to eliminate this dilemma by allowing us to derive accurate physical data for a particular asteroid from ground–based observations of reflectance spectra.

Besides the need to defend ourselves against asteroid impact, it should be possible to mine the NEA population for most of the raw materials required for the development of space. It is simply not practical to bring tons of raw materials up the massive gravity well of the Earth, yet tons of materials will be required to provide the radiation shielding necessary to make living in space possible. Similarly, it will become much more efficient to manufacture simple structural materials such as steel beams and plates in space where they will be used rather than spend the tens of thousands of dollars needed to launch each kilogram of payload from the surface of the Earth. Once we know how to interpret an asteroid’s spectral signature to predict its chemical composition, it will be a simple matter to survey gravitationally advantageous NEAs for the resources required: iron, rock, water, carbon and nitrogen are all present in the NEA population. From a purely scientific perspective, studying asteroids provides critical insight to the understanding of the origins and evolution of our own Solar System. Applying that knowledge can also allow us to predict the long term behavior of other stellar systems, including the potential for the origin of life on worlds around other stars.

The Solar Nebula has proven to be an extremely complex dynamic system with chemical consequences that were unexpected as little as a decade ago. Just recently NASA’s Stardust mission returned samples from the Kuiper Belt CometWild 2 that had never come closer than 40 AU to the sun. When Stardust was launched in 1999, it was expected to return pristine samples of materials from the sun’s natal cloud stored unchanged for more than 4.5 billion years. Most scientists believed that gas and dust only fell closer to the sun with time: a one–way trip only interrupted if material could grow large enough to overcome the drag of ambient nebular gas and attain an independent orbit. What was actually returned was a mix of the expected pre–solar materials together with grains formed at very high temperatures, close to the sun. These samples conclusively proved that large–scale circulation patterns, shown in Fig. 4, existed in the nebula that mixed materials processed in the inner nebula out to the regions where comets formed. These findings completely revised our views of nebular dynamics and chemistry.

Figure 4: Circulation patterns in the natal solar cloud (Nuth, 2001).

2.5 Previous Asteroid Science Missions

Much of what we do understand today about NEOs is thanks to the various asteroid/comet science missions that have been flown in recent years. The Near–Earth Asteroid Rendezvous (NEAR)–Shoemaker mission (1996–2001) performed a flyby of the asteroid Mathilde during which mass and density measurements were collected (Yeomans, 1997), rendezvoused with and orbited the asteroid Eros, and culminated with a soft landing on Eros. Deep Space 1 was launched in 1998 and performed flybys of the asteroid Braille and the comet Borrelly. The Stardust mission was launched in 1999, investigated comet Wild 2 and its coma, and returned samples of the coma material in 2006. The Hayabusa/MUSES–C mission was launched in 2003, rendezvoused with the asteroid Itokawa, shown in Fig. 5 (image credit: ISAS/JAXA - Japanese space agency), in 2005, possibly collected samples, and will attempt to return any samples collected in 2010.

Figure 5: Asteroid Itokawa as seen during the Hayabusa/MUSES–C mission in 2005.

The Deep Impact mission was launched in 2005 and delivered a small impactor to comet Tempel 1 in the same year; the impactor created a crater on the comet, producing ejecta for the main spacecraft to study during a flyby. The impact event as seen by the monitoring spacecraft is shown in Fig. 6.

Figure 6: Collision of the impactor with comet Tempel 1 during the 2005 Deep Impact mission.

In 2007 approval was granted for Stardust to embark upon a secondary mission in which it will further study comet Tempel 1. Stardust is scheduled to fly by Tempel 1 in early 2011. The Dawn mission was launched in September of 2007 and will study the asteroid Vesta (the second most massive main belt asteroid) in 2011. The Dawn spacecraft will then proceed to rendezvous with the dwarf planet Ceres, also in the main belt, concluding its primary mission in 2015.

3 Asteroid Impact Events and Consequences

We see evidence of impacts, such as impact craters, on other celestial bodies. Our own Moon provides an excellent example quite close to home. The lunar surface is covered by impact craters that remain visible because there are no geological or meteorological processes to erode or disguise them, as seen in Fig. 7.

Figure 7: Lunar impact cratering.

This stands in sharp contrast to Earth; while our planet has an even richer impact history (as its gravitational field presents a much larger capture cross–section than the smaller lunar field), the evidence of this has been largely hidden from view by geological processes, meteorological processes, vegetation, and the fact that much of Earth’s surface is covered by oceans. Nevertheless, terrestrial impact craters have been discovered and more are being found. Known Earth impact craters as of the year 2000 are shown in Fig. 8 from the Lunar and Planetary Institute. More terrestrial impact craters have been discovered in the nine years since.

Figure 8: Locations of Earth impact crater structures discovered as of the year 2000.

3.1 Close Approaches

On October 16th, 2009 (essentially at the time of this writing), a small asteroid designated 2009 TM8 will pass within approximately 348,000 km of Earth, just a bit closer than our Moon. It was discovered about a day prior to its closest approach to Earth. The asteroid is only about 7 meters in size and so would burn up or explode high in our atmosphere before having a chance to do any damage. It is estimated that objects of this size pass within the orbit of our Moon several times per month.

While close approaches by asteroids of this size (< 10 meters) are frequent and difficult to detect, the small size of the objects prevents them from being a serious threat. Other asteroids that have closely approached Earth would not have been so benign if they had struck us. For instance, in March of 1989 an asteroid passed within 700,000 km of Earth that would have delivered the energy equivalent of more than 1 million tons of TNT and created a crater 7 km wide.

More distant but still relatively close (within 6 million km of Earth) approaches of large asteroids have occurred throughout the 20th century: Apollo in 1932, Adonis in 1936, Hermes in 1937, Icarus in 1968, and Geographos in 1969.

Of immediate concern is a significant close approach that will occur 20 years from now. The asteroid Apophis will closely approach our planet on Friday, April 13th, 2029 at an altitude of approximately 32,000 km (closer than our geosynchronous satellites). The size of Apophis is currently estimated at 270 m. While the asteroid’s size is well below the 1 km threshold for globally catastrophic impact effects, if it were to strike Earth it would deliver an energy of approximately 500 Mt, causing tremendous local and regional devastation. While we know that Apophis will not collide with Earth in 2029, the 2029 close approach will cause the orbit of Apophis to be radically altered due to Earth’s gravity. The precise manner in which Apophis flies past Earth in 2029 will have a tremendous effect on the asteroid’s post–flyby orbit, making it very difficult to predict the future threats that the asteroid may pose to Earth. Until recently the probability of Apophis striking Earth in 2036 was 1 out of 45,000 and new observations have reduced this probability to 1 out of 233,000. The fact that these numbers are only estimates, the size of the asteroid, how extremely close it will come to our planet, and the lack of in–situ orbital or physical observations of the asteroid all mean that it continues to merit our close attention.

Although Apophis is classified as a type Sq asteroid, we know little enough about the structure of this object that the European Space Agency (ESA) is considering a mission that would send a spacecraft to learn more about it on the chance that it becomes necessary to divert it from an Earth impact in the future. However, the case of Apophis begs the question of what might happen if an asteroid of sufficient size to penetrate our atmosphere were discovered only a short time until its predicted impact. Without enough time for a precursor science mission, there would be no source for the information required to inform a mission to successfully deflect the asteroid.

Another asteroid of concern is 2007 VK184, an asteroid estimated to be 130 meters in size that has a 1 out of 3030 chance of striking Earth in 2048. If the asteroid strikes Earth it will deliver 150 Mt of energy, more than the largest nuclear weapon ever tested.

3.2 Impact Events

On October 8th, 2009, a small asteroid estimated to have been about 10 meters in size collided with Earth, creating an approximately 50 kt explosion high above an island region of Indonesia. Events of this magnitude occur approximately once every 2 to 12 years, according to the NASA Jet Propulsion Laboratory (JPL). October 7th, 2008 was the first time that we were able to predict an impact before it occurred. The asteroid designated 2008 TC3, approximately 2–5 meters in size, struck our atmosphere over Sudan at 02:46 UTC while traveling at 12.8 km/s, producing a 1 kt explosion some tens of kilometers above the ground. The asteroid was only discovered 20.5 hours before impact. Meteoritic fragments of the asteroid were later recovered.

On June 6th, 2002 an asteroid approximately 10 meters in size collided with Earth and exploded in the atmosphere far above the Mediterranean Sea, releasing 26 kt of energy. It was critical that this event was monitored and identified as a natural occurrence since tensions were particularly high between Pakistan and India at the time.

In 1908, a small asteroid thought to be approximately 20 meters in size exploded 5 to 10 km above the ground over the Tunguska river in Siberia. The energy released was likely equal to about 10 to 15 Mt and devastated 2000 square kilometers, an area approximately the size of Washington, DC. A map showing the location of the event and a photograph showing just some of the damage are presented in Fig. 9.

Figure 9: Map with Tunguska event location and a photograph showing an example of the damage.

50,000 years ago a nickel–iron meteorite approximately 50 meters in size slammed into the ground about 55 km east of Flagstaff, Arizona. This resulted in an approximately 2.5 Mt explosion that created a 1,200 meter wide, 170 meter deep crater, shown in Fig. 10, killed all life within 4 km instantly, leveled everything out to 22 km, and generated hurricane–force winds out to 40 km.

Figure 10: The Barringer meteor crater in Arizona.

Some researchers have identified a periodicity to species extinctions found in the fossil record. while the mechanism behind this phenomenon remains unknown, we do have evidence that NEO impacts have played a role in the evolution of life on Earth. It is interesting that a strong 62 3 million year cycle has been identified (Rohde and Muller, 2005) with the extinction of the dinosaurs having occurred 65 million years ago.

3.2.1 The Extinction of the Dinosaurs

A fast moving streak of light crossed the skies of the northern hemisphere approximately 65 million years ago, and when it collided with the Earth in what is now the Yucatan Peninsula of Mexico, it changed the course of history. The impact of the 10–20 kilometer diameter asteroid sent tidal waves over Cuba and hundreds of miles up the Mississippi river valley. The energy released started fires throughout North, Central and South America. Mountain–sized rocks and debris were flung round the globe; their impacts ignited huge fires where they struck the land and spawned tidal waves where they fell into the oceans. The clouds of fine dust lofted into the stratosphere by the impact, combined with smoke generated by the global firestorms, brought darkness to the surface of the Earth.

This artificial night lasted for a minimum of 6 months, and some researchers believe that it may have lasted for several years. The unending darkness and brutal cold quickly killed virtually all large animals. Most of the photosynthetic plants spared from the global wildfires, such as sea–dwelling plankton, could not survive this seemingly endless night. The food chain broke down on both the land and in the oceans and those creatures that had been unlucky enough to survive the first few days of the catastrophe slowly starved over the next several months. The final survivors were small furry scavengers, plants, and some of the smallest land– dwelling reptiles and birds. The 250 million year reign of the dinosaurs had ended and the age of mammals had begun.

Our understanding of this cataclysmic event began in 1980 when the father–son team of Louis and Walter Alvarez and their colleagues Frank Asaro and Helen Michael proposed that an asteroid impact had wiped out the dinosaurs, and indeed, most life on Earth 65 million years ago (Alvarez et al., 1980). While this hypothesis was initially treated with extreme skepticism, the discovery of world–wide deposits of the very rare element iridium together with carbonaceous ash in a very thin layer dated to be on the order of 65 million years old lent support to their argument. Although structures such as Meteor Crater in Arizona had been shown to have been caused by the impact of a 50 meter diameter body of extraterrestrial iron, such events were deemed by most geologists to be exceedingly rare and thought to affect only very localized areas. However, observation of the terrestrial surface from space has since revealed hundreds of previously unknown impact craters.

3.2.2 Jupiter Impacts

A startling event that helped inaugurate the era in which the asteroid threat to Earth has been taken seriously was the collision of comet Shoemaker Levy–9 with Jupiter in 1994. The comet had passed within Jupiter’s Roche Limit in 1992 and was torn into 22 fragments. These fragments created a spectacular display when they collided with Jupiter two years later. The scars visible on Jupiter from the collisions are shown in Fig. 11.

Figure 11: Collision scars on Jupiter after the 1994 impact of comet Shoemaker Levy–9.

Then on July 19th, 2009, exactly 15 years after the Shoemaker Levy–9 collision, an object collided with Jupiter again, though the asteroid (or comet) was not observed prior to the collision and hence we cannot be sure which object it was. Nevertheless, studying the impact scar on Jupiter has led to the conclusion that it was a single object (not torn into fragments as comet Shoemaker Levy–9 was) no more than 1 km in mean diameter.

4 Asteroid Deflection Methods

When two objects are on intersecting trajectories and the speed and timing of those objects along their trajectories is such that the objects will attempt to occupy the same point in space at the same time, they will collide unless something about the situation is altered in advance of the collision. This is the scenario when an asteroid is on a collision course with Earth. The emerging engineering science of planetary defense is generally concerned with mitigating the hazard posed to Earth by NEOs, and is particularly concerned with preventing the collision of NEOs with Earth.

4.1 Asteroid Collision Prevention Modes

We begin with the premise that Earth is to be protected from the incoming asteroid and therefore we do not seek to move the Earth from the collision point. That would of course be both undesirable and unachievable for myriad reasons. Therefore we seek to act upon the asteroid. Annihilating the asteroid, either by vaporizing it or pulverizing it into a fine grain dust cloud is nowhere near achievable with current or foreseeable technology. Breaking an asteroid into fragments in a controlled fashion is possible in theory, but studies have shown that the required technology is not yet within our reach (Barbee et al., 2007). Fragmenting an incoming asteroid in an uncontrolled fashion is highly undesirable because there is no way to guarantee that all the fragments will be small enough to burn up harmlessly in our atmosphere should they go on to hit the Earth, or that all fragments of sufficient size to do ground damage would miss the Earth subsequent to the fragmentation of the asteroid (Sanchez et al., 2008).

Effectively removing the asteroid by altering its orbit dramatically enough that it moves into a much higher or lower orbit around the Sun requires far more momentum than we can conceive of imparting to an asteroid. In fact, we can impart only enough momentum to the asteroid under the best of circumstances to amount to a mere perturbation to the asteroid’s orbit. However, if performed optimally and with sufficient lead–time, a tiny perturbation can indeed cause an incoming asteroid to miss Earth. This is asteroid deflection, the most practical mode for preventing an asteroid from colliding with Earth, and a variety of methods and systems have been proposed to achieve it.

4.2 Asteroid Deflection Modes

A deflection can be applied to an asteroid in one of two ways: gradually via the application of a relatively small force over a long period of time, or impulsively via the application of a relatively large force in a short period of time (effectively instantaneously).

While these methodologies, and the technologies and systems required to enact them, differ substantially, the fundamentals of asteroid deflection from the perspective of Astrodynamics apply in all cases. Various studies have shown that the best direction in which to apply the deflection force is generally along the asteroid’s inertial velocity vector (Barbee and Fowler, 2007). The exception to this is the case in which a deflection is being applied during the asteroid’s final solar orbit prior to the time of undeflected impact. In this case the best direction for the deflection force acquires more and more of a radial component (though remaining in the asteroid’s orbit plane) as the time interval between when the deflection is applied and when the asteroid would have otherwise struck Earth decreases (Barbee and Fowler, 2007). Additionally, if the deflection is applied very shortly before the undeflected collision time, the best deflection force direction generally also has a component out of the asteroid’s orbit plane (Barbee and Fowler, 2007).

However, deflections applied during the asteroid’s final orbit around the Sun before Earth impact are generally infeasible, as the data that follows demonstrates. Ideally we would like to be applying the deflection much earlier, on the order of several years or, even better, several decades prior to the undeflected collision time. This gives the cumulative change in the evolution of the asteroid’s deflected position enough time to differ substantially from the undeflected motion of the asteroid, serving to maximize the overall deflection. In this case, not only do we want to apply the deflection force along the asteroid’s inertial velocity direction, we also want to apply the deflection when the asteroid is at or near its perihelion. It is a result of orbital dynamics that deflection forces applied at perihelion result in significantly larger deflections of an asteroid’s trajectory (Barbee and Fowler, 2007). This is especially relevant since virtually all asteroid orbits have appreciable eccentricity.

4.2.1 Gradual Asteroid Deflection

Gradual asteroid deflection systems work by applying a very small force to the asteroid over a long period of time. Proposed systems for achieving this include the Gravity Tractor (GT), the solar concentrator, and the Yarkovsky Effector (YE). Other gradual deflection system concepts have been proposed, but the three listed here show the most promise (though all of them are still only conceptual at this time).

The Yarkovsky Effect is anisotropic re–radiation of thermal energy absorbed by the asteroid from the Sun. As the asteroid rotates/tumbles about its center of mass, portions of its surface will alternately face towards and away from the Sun. When facing towards the Sun, solar energy is absorbed and this energy is then radiated away when facing away from the Sun. However, the radiation of the absorbed energy is not symmetrical and thus a net force is induced on the asteroid. The asteroid’s orbit that brings it to a collision with Earth is the result of all the natural forces acting upon the asteroid, including the Yarkovsky Effect. So, if the asteroid’s surface properties are modified (e.g., by covering the asteroid’s surface with some reflective material) in a way that causes its absorption or radiation of energy to change from what it would have been naturally, this will cause a small, gradual change in the evolution of the asteroid’s motion. If this change is induced far in advance of the undeflected collision time, then the cumulative change in the asteroid’s position over time will cause it to miss Earth. While there are various technical hurdles to be crossed before a YE system can be made practical, a key factor is that the asteroid’s physical properties (albedo, thermal properties, etc.) must be well known in order to accurately predict the result of applying the YE, and this requires that the asteroid be sufficiently characterized a priori.

Solar concentrators are designed to work by flying a parabolic mirror in formation with the asteroid and using the mirror to focus an intense beam of reflected sunlight onto the asteroid’s surface. This focused beam will then vaporize the asteroid surface material touched by the beam, causing a jet of vaporized material to be expelled from the asteroid’s surface, which results in a small force imparted to the asteroid. While there are problems to be solved with the manufacture of such a device and with maintaining its position and orientation relative to the asteroid for a long period of time, the chief problem with this system is that the vaporized material coming off the asteroid’s surface would likely foul the mirror within a short period of time (Kahle et al., 2006), rendering the technique ineffective. In any case, a thorough understanding of the asteroid’s physical properties would be necessary in order to predict the performance of this system.

The GT is perhaps the most practical gradual deflection mechanism in terms of required technology. The GT performs a rendezvous with the asteroid and then maintains its relative position with the asteroid over a long period of time, during which the gravitational force due to the GT spacecraft’s mass pulls on the asteroid, imparting a very small force on the asteroid over time. To design an effective GT, the asteroid’s mass must be known because the GT spacecraft must carry enough fuel to negate the pull of the asteroid’s gravity on the spacecraft for the entire duration of the deflection activity. Also, the asteroid’s spin state and mass distribution must be known so that the guidance and control system of the GT can be properly designed for stability. All proposed gradual deflection systems depend on accurate knowledge of at least some of the asteroid’s physical properties, and each of them has unique advantages and disadvantages. One common disadvantage is that none of them are powerful enough to deflect an asteroid unless gravitational keyhole dynamics are present (as happens to be the case for Apophis) or the asteroid is discovered, and its orbit determined well enough to confirm impending impact, far in advance of the time of collision. Another common disadvantage is that they depend upon correct, continuous, and long term operation of equipment in the space environment near an asteroid, creating a real possibility of something going awry and ruining the mission.

A small series of studies was performed to quantify the amount of time required for a gradual system to deflect an asteroid. The GT was used as a representative system and its application to asteroids of various size was modeled. The orbit parameters of Apophis were utilized in all cases. The GT was assumed to be able to control itself perfectly and the amount of fuel required to maintain its position relative to the asteroid was not modeled. Clearly, this would be a significant limitation for situations in which the duration is particularly long. Larger GT spacecraft mass and larger asteroid mass will also drive up the fuel requirements. The purpose of these studies was simply to characterize by how much a GT can deflect a given asteroid under ideal conditions.

GT masses of 1000, 4000, 20,000, and 400,000 kg were used. Each of these was applied to asteroids with diameters of 140 m, 300 m, 650 m, 1 km, 3 km, 5 km, and 10 km. For reference, 1000 - 4000 kg is commensurate with the amount of mass that our current launch vehicles can deliver to rendezvous with an asteroid, 20,000 kg is the size suggested for the GT when it was first proposed (Lu and Love, 2005), and 400,000 kg is the mass of the International Space Station (ISS) upon completion. A 20,000 kg GT would require multiple launches followed by on–orbit assembly, and sending a 400,000 kg GT to rendezvous with an asteroid is completely impractical. Nevertheless, the 400,000 kg GT case is included to demonstrate how much mass would be necessary to achieve deflections quickly enough to compete with impulsive deflection methods. An asteroid size of 140 m is the smallest that NASA is required to detect and track under the current congressional mandate (and is also approximately equal to the minimum size for a PHA), 300 m is about the size of Apophis, 650 m was selected as an intermediate sub–kilometer size, 1 km is considered the minimum size for causing global effects upon impact, 3 and 5 km size asteroids are certain to cause global effects, including mass extinctions, and 10 km is the lower size estimate for the asteroid that caused the extinction of the dinosaurs. In all cases, the GT is assumed to maintain its position at a distance from the asteroid’s center of mass equal to 1.5 times the radius of the asteroid (Wie, 2008). This allows the spacecraft thrusters (thrusting against the asteroid’s gravity and hence pointing in the general direction of the asteroid) to be canted at angle that will prevent their exhaust from impinging upon the asteroid while still providing a net thrust vector that opposes the pull of the asteroid’s gravity.

Figure 12: Time required for various GTs to achieve a one Earth radius deflection within 10 years.

Figure 12 shows the amount of time required, in years, for GTs of various masses to deflect an asteroid’s orbit by 1 Earth radius (6378) km within 10 years. The two smaller GTs are shown to be incapable of achieving this, while the 20,000 kg GT can handle the 140 m asteroid but not the larger ones. The 400,000 kg GT can handle all the asteroids up to and including 1 km, but none larger than that within 10 years.

Figure 13: Achieved deflection of various GTs after 10 years of tractoring.

Figure 13 shows how much deflection each GT was able to achieve for each asteroid within 10 years. The small deflection values shown clearly indicate that gradual deflection systems are not practical unless the warning time is very long.

Figure 14: Time required for a 400,000 kg GT to achieve a one Earth radius deflection.

Figure 14 shows how much time would be required for the 400,000 kg GT to achieve a deflection of 1 Earth radius for each of the asteroid sizes considered. The inverse square nature of the gravitational force imparted on the asteroid by the spacecraft is clear when observing that the time required jumps from 9.55 years for a 1 km asteroid to 29.86 years for a 3 km asteroid.

4.2.2 Impulsive Asteroid Deflection

In an impulsive asteroid deflection, momentum is imparted to the asteroid virtually instantaneously. The goal is to cause a change, in the asteroid’s inertial velocity vector which will place the asteroid onto a new orbit that will go on to miss Earth rather than collide. The associated vector geometry is shown in Fig. 15.

Figure 15: Impulsive deflection vector geometry.

As stated before, previous research has shown that the optimal orientation for is generally along the asteroid’s inertial velocity vector and that should be applied when the asteroid is at its perihelion for maximum effect. (Note that Fig. 15 is meant to illustrate the concept of an impulsive velocity change and does not show the vectors in their realistic orientations.)

Systems that might be able to accomplish this are Nuclear Explosive Devices (NEDs) or Kinetic Energy Impactors (KEIs). In the case of NEDs, there are several ways in which they might be employed against an asteroid, but perhaps the most controllable method (and least likely to cause unwanted fragmentation) is standoff nuclear detonation, in which the NED is detonated at some standoff distance from the asteroid’s surface. Figure 16 shows an artistic rendering of a NED detonating in proximity to an asteroid, created by Peter A. Wilkins in November of 2005.

Figure 16: Artistic rendering of standoff nuclear detonation.

The NED is brought to rendezvous with the asteroid aboard a carrier spacecraft, and then gently positioned at the proper coordinates in space relative to the asteroid’s center of mass. This ensures that the resultant is oriented correctly and of the correct magnitude. Then the NED is detonated. The radiation released by the NED (primarily neutrons and x–rays) penetrates the asteroid regolith to a depth of 10–20 cm within the portion of the asteroid’s surface area that is struck by the radiation. The neutron component of the NED yield is thought to be the most effective in this regard. The thin shell of irradiated surface material is superheated and blows off, imparting momentum to the asteroid (Ahrens and Harris, 1994). There is currently no consensus in the modeling community with regard to optimal standoff distance or the magnitude of the resulting change in the asteroid’s velocity, Δv. However, there is agreement that the Δv imparted to the asteroid is very sensitive to standoff distance (too close or too far away greatly reduces Δv). Additionally, most models show that the achievable Δv is on the order of 1 - 10 cm/s. Some models have indicated that a 1 Mt NED can impart a Δv of 1 cm/s to an asteroid that is 1 km in mean diameter (Holsapple, 2004). A 1 Mt NED will likely have a mass of around 1000 kg, and this (plus the associated carrier spacecraft) is readily deliverable to rendezvous with a NEO using current launch vehicle and propulsion technology (Barbee and Fowler, 2007).

However, these results are all based on models that make significant assumptions about the composition and structure of the asteroid, the behavior of a NED in the space environment, and the coupling of a NED’s yield to an asteroid. Therefore, an incoming asteroid would have to be scientifically characterized before a NED could be sized and assembled for deployment against the asteroid. Additionally, NEDs will have to be tested on real harmless asteroids so that models can be calibrated and so that we can have assurance that deflection by standoff nuclear detonation really works as we believe it will before relying on it during a true emergency. While such testing may prove to be politically complicated, it is a scientific and engineering necessity, especially for a system upon whose correct operation we would depend for the survival of our species. We’ve never tested a NED on an asteroid before, and we certainly don’t want to be doing it for the very first time in a true emergency. As the great physicist Richard Feynman said, "For a successful technology, reality must take precedence over public relations, for nature cannot be fooled."

In the case of a KEI, an inert spacecraft mass is launched from Earth and placed onto a trajectory that will collide with the NEO. This impact alone will alter the asteroid’s momentum, and even more change in the asteroid’s momentum can be achieved if significant ejecta is thrown out of the resulting crater on the asteroid’s surface. Given our current launch vehicle and propulsion technology limitations, the maximum Δv that can be imparted to an asteroid by a KEI is generally on the order of millimeters per second, though in some cases it can be somewhat higher (Schaffer et al., 2007). One aspect of KEIs that is currently being researched is momentum scaling. The goal is to be able to predict the additional momentum imparted to the asteroid by the ejecta that may be thrown from the impact crater. The modeling for this is not yet fully understood. Additionally, this effect is strongly dependent on the asteroid’s composition and structure. Therefore, it will be important to scientifically characterize an incoming asteroid before constructing a KEI system to be deployed against it.

Additionally, for KEIs the design of the intercept trajectory must constrain the angle of incidence to produce a resultant in the correct direction while choosing the intercept trajectory to maximize imparted momentum by optimally balancing relative velocity at impact versus the delivered payload mass such that the momentum imparted to the asteroid is maximized. The constraints must also include striking the asteroid at its perihelion for maximum deflection efficacy.

Some basic simulations were performed to demonstrate the relative effectiveness of impulsive deflections with various Δv magnitudes. Δv values of 0.1 and 0.5 cm/s are representative of KEI performance, while Δv values of 1, 5, and 10 cm/s are representative of NED performance. As with the GT results shown previously, the orbit of the asteroid Apophis is used here, and deflections are applied at perihelion.

Figure 17: Achieved asteroid deflection as a function of impulsive velocity change magnitude.

Figure 17 shows the achieved deflection in Earth radii for each Δv magnitude over various durations. The 0.1 and 0.5 cm/s deflections are clearly only viable when there are at least several decades of warning. However, the 1 to 10 cm/s deflections are able to readily handle deflections with warning times ranging from 10 years to less than 1 year.

Figure 18: Time required for 1 Earth radius deflection for various impulsive velocity changes.

Figure 18 shows how many years each deflection Δv magnitude requires in order to achieve 1 Earth radius of deflection. The 0.1 cm/s deflection is rather impractical, but the 0.5 cm/s deflection is able to handle it in about 12 years, which is reasonable. The 1 cm/s deflection only requires about 6.6 years, which is encouraging, while the 5 cm/s deflection is capable of a one Earth radius deflection in just over a 1 year and the 10 cm/s Δv achieves a 1 Earth radius deflection in just over half a year.

Clearly, impulsive deflections are able to handle short warning time cases that gradual deflections cannot, provided that the incoming asteroid can be characterized quickly enough. Furthermore, the efficacy of impulsive deflections can be enhanced by applying multiple deflections to the asteroid while it is near its perihelion, assuming that the asteroid has sufficient structural integrity to withstand multiple impulses. Assessing the asteroid’s structural integrity with sufficient accuracy to determine whether it can withstand even a single impulse of a given magnitude cannot currently be achieved with ground observations.

4.3 Hazardous Asteroid Response

Understanding the sequence of events during a hazardous NEO situation highlights the importance of rapid response. Figure 19 shows the hazardous NEO response timeline, with the major events time ordered from left to right. The seven major time intervals are colored red, orange, yellow, green, blue, indigo, and violet.

Figure 19: Hazardous NEO response timeline.

The timeline begins with the detection of the NEO by observational assets. Then there is some time interval (red) during which the observations are collected and processed, improving the accuracy of the orbit determination for the NEO until the impending collision is confirmed or at least the probability of a collision becomes high enough to warrant action. One of the unanswered questions in planetary defense currently is what the probability of collision threshold for action should be.

Assuming the NEO is determined to be a threat, the next event is the beginning of mission planning for the deflection of the NEO, which takes place during the orange time interval. It is during this interval that the NEO must be scientifically characterized. At present this would require a precursor scientific characterization mission be sent to the NEO, which would require substantial time. If there is not sufficient time between when the NEO is first detected and the time of undeflected Earth impact, then the precursor science mission might have to be omitted and a deflection mission designed and launched based only on our best guesses of the asteroid’s physical properties, a highly undesirable situation where the likelihood of mission failure is high. The proposed advancements in NEO science presented in a subsequent section herein would be of tremendous aid here.

Once enough data has been collected and preliminary mission planning is complete, then the next interval begins (yellow) during which the spacecraft carrying the deflection system and the launch vehicle are constructed and made ready for deployment. Based on actual experience with this process, it can be lengthy. Every effort would be made to hasten this process during a NEO emergency, but rushing it too much might cause mistakes that would lead to fatal mission failure.

After the deflection spacecraft launches, it will require time to rendezvous with the NEO (green) and position the deflection system appropriately (blue). While advancements in spacecraft propulsion technology can reduce the flight time to rendezvous with the NEO, the natural orbital mechanics (which we cannot change) is often the limiting factor. This is why early detection and characterization are so important. Finally, once the deflection system is positioned and ready it can be deployed on the NEO, imparting a deflection. The effects of the deflection have time to accumulate during the interval between when the deflection is applied and the time of undeflected Earth impact (indigo). Clearly the goal is to maximize this time interval (by pushing all the other events as far backwards along the timeline as possible in order to stretch out the indigo segment by compressing the preceding intervals). This provides the best chance for causing the incoming asteroid to miss the Earth.

The final time interval (violet), shown at the end of the timeline, begins at the point in time past which no deflection could possibly avert the impending collision and ends at the time of undeflected Earth impact, when the asteroid would collide with Earth absent any intervention.

Advancements in interplanetary orbit determination techniques and improvements to our observing infrastructure (new and better ground–based telescopic and radar survey systems and/or orbiting observatories) can dramatically increase warning time by virtue of detecting asteroids sooner (making the entire timeline longer), and can also dramatically reduce the amount of time required to determine that the probability of collision is high enough to warrant a response by virtue of increased quantity and quality of observations. Advancements in asteroid scientific characterization techniques, such as those proposed in a subsequent section herein, would serve to the reduce the amount of time required to design and construct the deflection system by providing the necessary physical data on the asteroid more rapidly, not requiring a precursor science mission to the asteroid.

Advancements in propulsion technology, such as the VASIMR thruster (and new spacecraft systems to supply it with adequate power), could reduce the amount of time required to complete an intercept or rendezvous with an asteroid in certain cases, thereby maximizing the amount of time available subsequent to the deflection for it to take effect prior to the time of undeflected impact.

In combination, these advancements would provide us with a longer time interval overall and a shorter time interval between when the threat is first detected and when the deflection system arrives at the asteroid and deploys. That serves to maximize the amount of time available for the deflection to take effect, which in turn serves to maximize the achieved deflection or allow a given deflection margin to be achieved for less energy.

Additionally, more research is required to identify and fully characterize asteroid deflection system payloads in combination with current launch vehicle and propulsion technology in order to determine the limits of applicability of the various potential NEO deflection techniques in terms of NEO mass (size) and warning time. Figure 20 illustrates this concept.

Figure 20: Notional lead–time vs. NEO mass applicability envelopes for selected deflection methods.

There are some cases in which the NEO is too large and the warning time too small to allow us to successfully deflect it with current technology. In the other areas of the space, each proposed technique should be able to handle various combinations of NEO mass and warning time. Clearly, the gradual techniques will be more limited in the sizes of NEO that they can handle, and they will require more lead time in any case. The impulsive techniques can handle larger NEOs, and with less warning time. This analysis can be made more accurate by repeating it for all the conceivable types of NEO orbits. For instance, the eccentricity of a NEO orbit determines how much additional deflection is possible through exploitation of the property that deflecting at perihelion maximizes achieved deflection due to the higher inertial velocity of NEO at that point on its orbit. The semi–major axis of a NEO’s orbit determines its period, which in turns determines how many perihelion passes it will make prior to an Earth collision. Also, NEOs with higher orbit plane inclinations require more fuel to rendezvous with, which decreases available spacecraft payload mass capacity for deflection systems. These analyses will show what can be done with current technology and help define requirements for new technology development that will expand our capabilities. In all cases, developing the ability to rapidly characterize asteroids will greatly enhance the ability of any proposed deflection technique to deal effectively with an incoming asteroid.

5 The DIOGENES A Mission: Advancements in Asteroid Science

Some NASA researchers have been studying a mission known as DIOGENES A, an acronym for DIagnostic Observations of the GEology of Near Earth, Spectrally–classified Asteroids. The goal of the DIOGENES A Mission is to turn the squiggly lines of the present asteroid spectral classification scheme into a solid understanding of the chemical composition and physical structure of the underlying body. Chemical composition is only one of several factors likely to affect the way an asteroid reflects sunlight. The impact of micrometeorites, the chemical sputtering of the solar wind and even coating the surface in a varnish made by photolysis of organic compounds and water slowly leaking from the interior of the asteroid over time can all change the spectral signature of a material. In addition, a solid piece of rock or metal will reflect more light than will a jumbled collection of rocks, boulders, sand, and dust that is just barely held together by its own gravitational attraction. It is possible that asteroids of many different spectral types start with nearly identical chemical compositions, but that exposure to different processes over time changes their spectral signatures. DIOGENES A will visit a number of asteroids of different spectral types and analyze both the chemical composition of the reflecting outer surface as well as the composition of the material up to a meter below the surface, in order to provide ground truth for the spectral classification system. The more asteroids visited the better we will understand the processes that convert the spectral properties of the bulk material to the myriad signatures observed in the asteroid population.

DIOGENES A will measure the chemical composition of representative members of each major asteroid spectral class, and as many of the sub–classes as possible, in order to base the current spectral classification system on a strong analytical foundation. It will map the surface of each asteroid from 400 nm to 4000 nm at 10 meter spatial resolution in order to compare the spectral signatures of typical asteroid surfaces with much lower spatial resolution measurements made from ground–based or space–based instruments (e.g. Spitzer). Such maps will be used to choose appropriate locations for in–situ measurements. If possible, the mission will also use Ground Penetrating Radar and Radio Sounding techniques to determine the interior structure of each asteroid encountered. In order to accomplish all of the goals of the mission, DIOGENES A requires two spacecraft.

The first is a bus, shown in Fig. 21, that uses Solar Electric Propulsion (SEP) to efficiently travel from asteroid to asteroid and carries a camera, spectrometer and radio sounding experiment as well as the second spacecraft. The massive solar arrays required to power the highly efficient electric engines make landing the bus on an asteroid’s rocky surface quite risky if the ultimate goal of the mission is to visit more than a single target.

Figure 21: Conceptual design of the proposed DIOGENES A spacecraft bus.

The second spacecraft is a probe, shown in Fig. 22, optimized for surface operations that uses a new Advanced Sterling–cycle Radio–isotope Generator (ASRG) to power the avionics and the instruments. This compact probe would only need to travel from the bus to the asteroid surface and return to the bus, though it might also “hop" from place to place on the surface.

Figure 22: Conceptual design of the proposed DIOGENES A probe spacecraft.

The probe will measure the composition of the thin surface layer responsible for the spectral reflectance signature we use to classify the object using x–ray spectroscopy stimulated by an electron gun. The probe will measure the composition of a one meter cubic volume below the surface of the asteroid using pulsed neutron, gamma ray spectroscopy. It will also determine the nature of volatiles released by progressively heating the surface and analyzing any released gases using a Gas Chromatograph Mass Spectrometer. Once all measurements at one site are completed, the probe may move to another site of interest and perform an identical suite of measurements. The probe can also serve as a mobile receiver for the Radio Sounding experiment that will map the density and structure of the interior by measuring the intensity of radio waves transmitted through the asteroid from the carrier to the probe. When the chemistry of each unique spectral site has been determined, and the mission has obtained as much information on the interior structure of the asteroid as is practical, the probe will return to the carrier spacecraft and the pair will use SEP to move to the next NEO in the target sequence. In the ideal mission at least 10 separate asteroids will be targeted for exploration. Each will be thoroughly mapped from orbit, or while flying in formation, as appropriate. We plan to analyze at least three surface sites on each target with in–situ instruments, and will use each landing site as a base for interior measurements using radio sounding techniques. We will plan to spend six months at each rendezvous, though complex asteroids may require more time to achieve our measurement goals and simple bodies could easily require less. Therefore to more efficiently use our spacecraft resources and because of the flexibility provided both by SEP and by the very large number of NEOs, we plan to re–target our mission as we go. In other words, if a body displays a very homogeneous surface and appears to be a uniform block of material, we may not need to do a large number of measurements at different sites. Such bodies might require only a 3–month mapping and analysis phase. Rather than waste three months waiting for the launch window to our next target we can calculate a new trajectory either to the next asteroid in our original sequence, to a completely new and interesting target, or to an asteroid that we had planned to visit later in the mission. Similarly, if we encounter a very complex asteroid that requires more than 6 months of analysis to understand the relationship between its chemical properties and spectral class, we can take the time needed to do a proper analysis of each different spectral component that we observe without fear of jeopardizing our mission objectives. We will simply re– target the spacecraft to another interesting asteroid once our analysis is finished. We may be able to visit our original target later in the mission or we might choose to visit another asteroid of similar spectral type instead. The primary objective of the DIOGENES A mission is to obtain the ground truth required to transform the present asteroid spectral classification system into a definitive measurement of the physical and chemical properties of the target. This will permit us to geologically characterize any asteroid with confidence based upon a few hours (or days) of remote sensing data. It will also identify the measurements that prove to be the most diagnostic in revealing both the chemical and physical properties of an unknown small body in space with a specific spectral signature. In order to keep the mission lifetime reasonable (less than 20 years) we will restrict our targets to the NEO population. In order to unravel as many of the important factors that control the spectral signature of a given asteroid type as possible, we may choose to target more than one representative asteroid of a given type, especially if our initial target, upon close examination, proves to be a highly complex object. Finally, in order to ensure confidence in and to provide validation for our in–situ measurements, we will attempt to target one or more of the asteroids that are prime targets for asteroid sample return missions such as RQ36 or JU3.

6 Spacecraft Trajectory and Mission Design for DIOGENES A

Algorithms are currently under development to facilitate the design of spacecraft trajectories that will allow a significant number of NEAs to be visited during a single mission. These algorithms will incorporate all relevant aspects of the spacecraft mission design, including launch vehicle capabilities, propulsion capabilities, and spacecraft payload mass requirements.

6.1 DIOGENES A Mission Profile

The notional range of launch years for the DIOGENES A mission is 2017 to 2027 and the mission duration will be limited to 10 years following launch. The objective is to rendezvous with 6 to 10 asteroids (ideally 10) and stay at each asteroid for 3 to 6 months. Each asteroid visited should be well–classified spectrally and be of a different spectral type. The asteroids should have an estimated mean diameter (based on observed absolute magnitude and assumed albedo) on the order of 1 km. The preference is for each of the asteroids to be a PHA, but the entire NEA population may be considered in order to maximize the number of viable candidate mission solutions found.

6.2 Problem Characterization

As described previously, prior spacecraft missions to NEAs have only visited one or two objects per mission. The trajectory design for such missions, while challenging, is generally relatively straightforward and well understood. The problem posed by the DIOGENES A mission concept is far more daunting. An ordered set of asteroids (itinerary) is to be selected out of the general NEA population such that a spacecraft with a given payload mass can rendezvous with each asteroid in the itinerary while respecting launch vehicle and propulsion system constraints. This problem bears similarity to the famous “Traveling Salesman" problem, in which the goal is to find the shortest cyclical itinerary for a set of N cities such that each is visited in turn, followed by a return to the city of origin. The challenge lies in choosing the order in which the cities are visited such that the total path distance traveled is minimized (Press et al., 1992). In the case of the asteroid tour problem posed here, the goal is not only to order the asteroids, but also to select them from a large population, and do so in a manner that makes the rendezvous trajectories connecting them sufficiently efficient to be achievable by current spacecraft launch vehicle and propulsion technology.

Additionally, the algorithm should be flexible enough to permit “Just–In–Time–Mission–Design", allowing the itinerary to be revised at any point during the mission due to changing circumstances. That is, if the spacecraft needs to spend more or less than its allotted time at any given asteroid, the remainder of the mission can be re–targeted in a manner that preserves or enhances the overall scientific value of the mission. Exhaustively sampling all possible permutations of ordered asteroid sets to identify the globally optimal solution is not an option because the number of permutations quickly grows to levels that are impossible to handle. For example, choosing an ordered set of 3 asteroids out of a population of 5 yields only 60 permutations, but we wish to consider much larger populations. Choosing an ordered set of 6 asteroids out of a population of 60 yields 36,045, 979,200 permutations, which is a huge number to sample, but even a population of 60 is still not useful given the size of the NEA population. If we attempt to select a set of 10 asteroids out of the entire NEA population (approx. 6000), the number of permutations is so large that it is practically incalculable.

6.3 Asteroid Tour Algorithm Design

This problem brings to mind computer chess program algorithms, which ideally look many moves ahead, considering as many moves as possible before selecting the next move. Unfortunately, the computational cost of looking more than one move ahead for a useful number of moves in this problem is not tolerable. However, it is computationally tractable to look one move ahead, sampling all possible moves, and choose the best next move, albeit without consideration of subsequent moves. In this fashion an asteroid itinerary can be constructed one asteroid at a time, in series, and thus the Series Method algorithm was born. This algorithm was dubbed the Series Method since it constructs the asteroid itineraries in a serial fashion, utilizing Lambert targeting to calculate ballistic rendezvous trajectories between asteroids with impulsive maneuver modeling for computational speed. The algorithm operates by starting at each asteroid in the population under consideration and determining the minimum fuel rendezvous trajectory to each other member of the population. The destination asteroid that offers the overall minimum fuel consumption is then selected as the next asteroid in the itinerary. The algorithm continues in this fashion until the desired number of asteroids has been added to the itinerary. In the beginning, the possibilities for the first asteroid in the itinerary are limited according to the ability of the launch vehicle and propulsion system to reach the asteroid from Earth. A prototype of the Series Method program was written early in the development of the DIOGENES A mission concept in an effort to assess the feasibility of computing the desired spacecraft trajectories. The prototype performed well, laying the foundation for ongoing research and development work.

6.4 Prototype Algorithm Results

A case study was performed with the first Series Method prototype algorithm in which the goal was to generate an itinerary of 6 asteroids out of the 949 PHAs known when this case study was performed. The year of Earth departure was allowed to vary between 2012 and 2017, the allowable flight time between asteroids was allowed to vary between 10 and 400 days, and the loiter time at each asteroid was allowed to vary between 60 and 240 days. Flight time and loiter time were each scanned at a resolution of 0.5 days. For the Series Method, this produced 4,583, 606,995 trajectory grid points to sample.

The algorithm generated a 6 asteroid itinerary with an Earth departure C₃ of 10.6 km²/s² and a mission duration of 7 years. The orbits of the 6 asteroids, the spacecraft rendezvous trajectories between them, and the segments of the asteroid orbits during which the spacecraft is loitering in the vicinity of each asteroid are all shown in Fig. 23 (Barbee et al., 2009).

Figure 23: Rendezvous with 6 asteroids.

At this stage of development the algorithm contained no logic to ensure that each asteroid visited was of different spectral type, and no research on the asteroid population had been performed to eliminate asteroids that are not well–classified spectrally. Therefore none of the 6 asteroids selected by the algorithm has a known spectral classification. Additionally, no means existed to convert the impulsive trajectory maneuvers into low–thrust maneuvers. This is important because the DIOGENES A mission will utilize low–thrust propulsion throughout (solar electric propulsion). These aspects of the problem are still being researched. Nevertheless, the asteroid itinerary was subjected to parametric mission analysis using a range of launch vehicles, propulsion system specific impulse values, and spacecraft dry mass values. The results of this analysis showed that the mission design was indeed feasible for certain combinations of these parameters (Barbee et al., 2009).

6.5 Global Trajectory Optimisation Competition

The Series Method code was then enhanced (new features, code optimization) for use in the 4th annual Global Trajectory Optimisation Competition (GTOC4). In this case the constraints of the problem were different: the spacecraft was to fly–by (intercept) each asteroid in the itinerary rather than rendezvous, the number of asteroids visited was to be maximized rather than chosen a priori, launch vehicle constraints were specified a priori, and the spacecraft dry mass, thruster specific impulse, and maximum thrust magnitude were all specified a priori. Additionally, the spacecraft was to perform a rendezvous with a final asteroid after performing all the fly–bys.

This competition was taken as an opportunity to refine and expand the Series Method algorithm code, and it performed well under these new constraints, finding a total of 149,040 trajectory solutions with the number of achieved spacecraft fly–bys ranging from 7 to 39 (Barbee et al., 2009). The distribution of the number of achieved fly–bys for the 149,040 trajectory solutions is shown in Fig. 24 (Barbee et al., 2009). Note that the number of achieved fly–bys was the performance index in the GTOC4 problem and was denoted as J.

Figure 24: Distribution of the number of achieved asteroid fly–bys for 149,040 trajectories.

A total of 58 trajectory solutions were found in which the spacecraft could intercept 39 asteroids. One of these solutions is presented in Fig. 25 (Barbee et al., 2009), which shows the spacecraft trajectory amidst the orbits of all the intercepted asteroids, along with the spacecraft trajectory by itself for clarity (with asteroid flyby locations marked).

Figure 25: GTOC4 trajectory design results for a 39 asteroid fly–by mission.

While substantial improvements were made to the Series Method code, the competition only lasted 4 weeks and so there was not sufficient time to complete the low–thrust portion of the problem solution. Even with optimized code, a computer programming language that produces fast executables (C), an operating system geared for scientific computing (Linux), and efficient underlying algorithms (Lambert targeting), the Series Method requires substantial time to compute solutions when the size of the candidate asteroid population is large (thousands of candidate asteroids), as is typically the case. This is addressed by employing distributed computing. For the GTOC4 problem, a small cluster of 6 CPUs was utilized, and a moderately– sized Beowulf computing cluster is currently under construction for ongoing work. The use of a computing cluster reduces the required processing time to manageable levels, allowing efficient mission design prior to launch as well as responsive re–targeting as needed throughout the course of the mission.

6.6 Continuing Work

Software, algorithms, and methodologies are still being studied that will facilitate the conversion of impulsive trajectory design results from the Series Method into low–thrust results in order to satisfy the DIOGENES A mission requirements. Some modifications to the Series Method algorithm itself will be necessary to achieve this. Additionally, logic is being developed to ensure that each asteroid in the itinerary is of a different spectral type. The Beowulf cluster should be brought online soon and the Series Method code will be further modified to take full advantage of this new computing resource. Finally, the known asteroid population is being researched to identify all spectrally classified asteroids in order to provide a proper candidate population for the Series Method to operate on.

After these tasks are accomplished, we anticipate that the Series Method will generate an array of feasible notional mission designs for DIOGENES A that will demonstrate the viability of the mission.

7 Conclusion

Asteroids and comets have always been, and will continue to be, crucial to the evolution of life on Earth. The impact that made the dinosaurs extinct also paved the way for humans to become the dominant species on the planet. Despite the enormous importance of this singular event in shaping the course of life on Earth, mankind remained blissfully ignorant of even the existence of asteroids until relatively recently in our scientific history. Such celestial events happen on a regular basis, and it is clear that a deadly impact could come at any time and almost completely without warning. This despite the tremendous strides made by our detection and tracking teams, whose successes are all the more impressive for being achieved on a relatively tiny budget. A variety of research efforts have aimed to develop methods and systems for deflecting incoming asteroids, leading to an array of possible solutions. While the testing and development of these systems is crucial if we are ever to rely upon them in a true emergency, equally critical is the ability to design, construct, and deploy these systems rapidly since there is no guarantee of substantial warning time.

There is no silver–bullet solution to the asteroid threat. Asteroids are physically unique in virtually every respect and therefore deflection systems must be designed according to the parameters of a particular asteroid in order to be effective and reliable. This requires the characterization of an incoming asteroid prior to the design, construction, and deployment of a deflection system. Typically this characterization can only be achieved with a precursor science mission, which requires a great deal of valuable time. The DIOGENES A mission might offer us a far more expeditious alternative, and ongoing advances in spacecraft propulsion systems, trajectory design algorithms, and scientific instrumentation make a mission of such ambitious scope truly possible.

The ultimate goal of the DIOGENES A mission is to gain sufficient knowledge of the correlation of the spectral signature of an asteroid and its physical properties (chemical composition, interior structure) that we can use telescopic observations to survey all of the small bodies in the solar system. Understanding the chemical composition and physical characteristics of this population of asteroids would be essential if the need ever arises to avoid a collision with one.

If an asteroid is ever observed to be on a collision course with the Earth, one set of ground–based observations could then potentially reveal all that we need to know about the impactor to decide on an appropriate course of action. The observations would obtain the spectral type of the asteroid and therefore enable us to derive its composition, physical structure and mass.

Apart from the crucial goal of rapidly informing an asteroid deflection mission, the telescopic surveys facilitated by DIOGENES A will develop a quantitative picture of the compositional gradients and gradual evolution of the small bodies in the solar system. This leap in understanding will make tremendous contributions to solar system science. Additionally, understanding the composition and physical characteristics of these bodies could also provide critical data on an important resource base for use in the future exploration of the solar system. Once DIOGENES A completes its mission, we will know where to find the resources needed for mankind to transition from a planet–bound species to one that truly inhabits our solar system. What happens next is up to us. Will humans follow the dinosaurs into extinction or learn to mitigate, and then utilize, one of the most severe threats to life on Earth?