NASA NEO News: Deflection Scenarios for Apophis
Following is an unusually long and technical edition of NEO News. The subject is the deflection options for Apophis (MN4) as described in a new analysis by Donald Gennery, who has kindly made this draft available to NEO News. Future editions will revert to the usual format.
David Morrison
WHAT SHOULD BE DONE ABOUT ASTEROID APOPHIS (2004 MN4)?
Donald B. Gennery
dgennery@earthlink.net
August 7, 2005
1. Introduction
In a recent paper [1] and letter [2], Rusty Schweickart made some recommendations on dealing with the threat of a possible impact in 2036, and he called on further analysis to be done. This is my input to that analysis. Comments are welcome.
The most important thing that I propose is that deflection by the impact of a spacecraft is practical in this case. Such a mission could be done fairly quickly at a reasonable cost.
The asteroid under discussion, with the provisional designation 2004 MN4, has now been assigned the number 99942 and the name Apophis. (Apophis was the Greek name of the Egyptian god Apep, “the destroyer.”) Therefore, I use this name below.
2. Background Review
Apophis will make a very close pass by Earth (roughly 37,000 km) on April 13, 2029. The deflection of its trajectory by Earth’s gravity at that time will greatly magnify the uncertainty in its orbit, making predictions of a possible future collision with Earth difficult at this time. There are several dates that (as of July 31) have a slight chance of impact. Especially, April 13, 2036, has a probability of impact equal to 0.00012, with lesser probabilities for April 14, 2035, and April 13, 2037 [3]. Since the diameter of Apophis is 320 m, it could cause destruction over a large local area. Apophis will make fairly close passes by Earth (roughly 0.1 AU) in 2013 and 2021 that will allow accurate measurements of its orbit, and easier trajectories to it are available around those times.
Because of the above facts, Schweickart called for immediate consideration of a plan to start work very soon on a mission to Apophis that would place a radio transponder on the asteroid, so that the knowledge of its orbit can be improved enough to make a decision by 2014 as to whether or not to start work on a mission to deflect Apophis. He said that any later start date than 2014 on a deflection mission might not allow enough time to deflect Apophis before the close pass in 2029, after which deflection will become much more difficult, especially for a possible impact only about 7 years thereafter. He considered the possibility that 6 years might be enough for the deflection mission, but he considered it more likely that a deflection mission might require as long as 12 years and a transponder mission 7-8 years.
In deciding how much deflection might be needed, there are three components to consider. One is the width of the “keyhole” through which the center of mass of Apophis would have to pass in 2029 in order to hit Earth in 2036. According to Schweickart, this is only 641 m. Therefore, to move out of the keyhole might take as much as half of this, or 0.32 km. Another, much larger, component is the uncertainty in the orbit due to measurement errors. At present, as extrapolated to 2029, this has a standard deviation (sigma) of 1800 km. Using a 5-sigma tolerance for safety thus could require a deflection of 9000 km. However, this large uncertainty results from data having only a short time span. As more measurements are taken around 2013 and 2021 this value will greatly decrease, probably to much less than 100 km. The third component is the fact that the orbit is changing because of the Yarkovsky effect, as Schweickart pointed out in his July letter.
The Yarkovsky effect is the phenomenon in which the orbital energy of an object changes due to a nonradial force caused by the fact that the absorption and reradiation of energy from the Sun are in different directions, depending on the rotation of the object. This causes the object to either accelerate or decelerate in its orbit, depending on whether energy is being subtracted or added. If the rotation, shape, and thermal properties of the object are known, the direction and magnitude of this effect can be calculated. However, at present these are largely unknown for Apophis, so extrapolating from the present to 2029 could produce an uncertainty from this cause of a few thousand kilometers. Future measurements will reduce this uncertainty also; some possibilities are mentioned in Section 4.
3. General Discussion
I claim that 6 years is more than enough time for a deflection mission (not counting the travel time to Apophis), because deflecting Apophis before 2029 is easier than Schweickart implies. As he says, the amplification that occurs at that time because of Earth’s gravity means that only a small change in Apophis’s velocity would be needed. (Estimated values are given in Section 4.) Because both the needed velocity change and the mass of Apophis are small, the needed impulse (change in momentum) is so small that deflection can be done simply by ramming the asteroid with the spacecraft, and such a deflection by impact is the easiest deflection method. The rendezvous and docking that Schweickart mentions are not needed, and the actual deflection would take place in a less than a second, instead of during lengthy operations at Apophis.
If deflection can be done by the impact method, only a few years preparation would be needed. The Deep Impact project [4] took less than 6 years. (NASA decided to do it on July 7, 1999, work started on Nov. 1, 1999, launch occurred on Jan. 12, 2005, and impact occurred on July 4, 2005.) Deep Impact was a slightly more involved mission than the deflection mission would need to be, since it had both an impactor and a flyby vehicle for observing. (Of course, a flyby vehicle would be desirable here also, for scientific and verification purposes, but it could be launched separately if that is more convenient.) Its target was larger, but so was its approach velocity, so the difficulty of guidance wasn’t all that much different. The experience gained from Deep Impact, and possibly much of the hardware design, would be applicable. Therefore, the deflection mission, from approval to launch, probably could be done in less than the 5.5 years of Deep Impact. A rush project would need even less time, but at a higher cost.
It is sometimes said that, if the hit is well off center, the impact method of deflection method would not be very effective, with the main result being rotation induced in the asteroid instead of a change in its trajectory. However, that is a fallacy. Momentum is conserved, so any energy going into rotation is not subtracted from the energy going into translation, but instead is subtracted from the energy going into kinetic energy of blasted-out fragments and heat, which is where most of the energy goes. An off-center hit reduces the deflection only in three situations: when there is reliance on the gain produced by the kinetic energy blasting out material, which I do not use here; when the hit is so close to the edge of the object that either it merely knocks off a chunk of material, leaving the main part of the object practically undisturbed, or the spacecraft merely grazes the asteroid and bounces off without much change in direction; or when the relative approach velocity vector is not roughly aligned with the orbital velocity vector of the asteroid, in which case a hit well off center that causes a significant momentum of blowoff material due to kinetic energy from the impact could cause the impulse to be applied in the wrong direction.
A concern with any method of sudden deflection is dispersal of the object. If the danger from this cannot be made extremely small, the impact method would have to be ruled out in this case. This problem and ways of dealing with it are discussed in Section 5.
4. Deflection Scenarios
In order to demonstrate that deflecting Apophis by impact is practical, I present the results of my calculations below for a few situations. There are many possibilities, depending on what measurements can be taken at what times. I consider here two main scenarios, which seem to be reasonable. In these, I have assumed certain values for uncertainty in the orbit, which I have derived by some approximations from information in Schweickart’s paper and other references [5, 6], and which for the most part I assume can be achieved without a transponder. (How a transponder can help is described primarily in Sections 5 and 6.) These values should be checked by others who are more familiar with those particular issues. If it turns out that my values are too large, the task would be even easier than I estimate, and a smaller, cheaper launch vehicle could be used. If it turns out that the values should be twice as large as my estimates, more than one launch with separate space vehicles could be used where I have called for one, which would cause only a modest increase in the total cost. If it turns out that the values should be many times my estimates, a precursor transponder mission would be necessary in order to reduce the uncertainty, or perhaps deflection by impact could turn out to be completely impractical, but I think that the latter is very unlikely.
In what follows, I have made several conservative assumptions. In computing the amount of deflection, I have used only the momentum of the impacting vehicle, and I have ignored the momentum of material blasted out by the kinetic energy of the impact. (In some cases, this effect can increase the momentum by a large factor, but it might be small for a rubble pile, as Holsapple has pointed out [7].) I have assumed that the trajectory of the vehicle to Apophis, after escaping from Earth, is a single Keplerian orbit with no midcourse maneuvers other than small course corrections. For these trajectories, I have used launch dates and intercept dates that are fairly efficient, but I have not done thorough searches to find absolutely optimum dates. I have assumed that the space vehicle detaches from the upper stage of the launch vehicle. (If it could be kept attached, the mass delivered to the asteroid would be increased, but controlling this combination in order to make course corrections might be unwieldy. An integrated device could be developed, but this would require more time and money.) I have assumed the use of present launch vehicles. No doubt, in the coming years the performance of launch vehicles will increase. However, this gain might be canceled by the fact that I have used the estimated value of the mass of Apophis in the calculations, whereas the actual mass might be greater. (Of course, it might be less.)
In Scenario 1, I assume that by 2014 the rotation of Apophis will be known, either by Earth-based measurements or by means of a precursor mission, so that the Yarkovsky effect can be roughly estimated by considering the expected range of surface properties for asteroids, without knowing the particular surface properties of Apophis. I further assume that the total uncertainty in the position of Apophis as it approaches Earth in 2029, as estimated in 2014, including both the unknown portion of the Yarkovsky effect and measurement errors, is 150 km to either side of a nominal position. This (strictly speaking, plus the 0.32-km semiwidth of the keyhole, which is negligible in comparison) is the maximum amount that we might need to deflect the trajectory, if the keyhole is centered exactly on the region of uncertainty. I also assume that in 2014 the estimated probability of an impact in 2036 is high enough to justify starting work on a deflection mission, to be launched around the close approach of 2020-2021.
In Scenario 2, I assume that the rotation of Apophis is still unknown in 2014, but that by mid-2021 radar and optical measurements of its orbit have greatly constrained how it is perturbed by the Yarkovsky effect. This possibility arises from the fact the close approaches around 2005, 2013, and 2021 in effect provide three accurately determined points that allow the acceleration of the longitude of Apophis to be determined, even if nothing is known about its surface properties or rotation. As a result, I assume that the the total uncertainty in the position of Apophis as it approaches Earth in 2029, as estimated in 2021, is 50 km. I also assume that preliminary work on a deflection mission is started after 2014, and that in 2021 the probability of an impact in 2036 is high enough to go ahead with completing the project for a launch 2023.
I also include Scenario 3, which is a perhaps optimistic possibility of what a transponder placed a few years before 2020 might allow. It is discussed in Section 5 as one way of reducing the risk of dispersion.
For each scenario there are two cases (A and B), depending on whether we want to add or subtract orbital energy in order to move Apophis away from the keyhole. These cases use different trajectories for the spacecraft, since in the impact method of deflection the asteroid must be approached in the approximate direction in which we want to deflect it.
The following table summarizes the results of my calculations for the above scenarios. In Scenario 1, cases A and B have different launch dates. In Scenario 2, the two cases have the same launch dates, but the launch directions are different, resulting in either 3 or 6 revolutions of the spacecraft around the Sun during the trip. The quantities in the table are defined as follows: DeltaX is the maximum shift needed in the approach trajectory to Earth in 2029, as determined by the above assumptions; Vinf is the hyperbolic excess velocity after escape from Earth; Vapp is the approach velocity relative to Apophis; Vpar is the component of Vapp parallel to the orbital velocity vector of Apophis, which is the useful component under the approximation used here; DeltaV is the change in velocity of Apophis needed to produce the stated value of DeltaX; and Mass is the mass that must be impacted to produce this result, based on an Apophis mass of 4.6e10 kg [3]. In computing DeltaV, I have used the approximation that, for a given orbit and Earth approach point, it is only the change in orbital energy and the time between the DeltaV deflection and the DeltaX result at the approach that matter. (This assumption is strictly true only for an infinite time interval, but it is fairly accurate a few revolutions in advance.) I have taken into account how the point in the orbit at which the deflection takes place affects the orbital energy.
Sce- DeltaX Launch Intercept Vinf Vapp Vpar DeltaV Mass
nario km date date km/s km/s km/s mm/s kg
1A 150 Sept. 1, Jan. 1, 4.73 3.53 +3.02 0.242 3690
2020 2021
1B 150 Mar. 15, May 20, 5.40 3.51 -3.05 0.220 3320
2021 2021
2A 57 Apr. 13, July 10, 5.17 4.78 +4.07 0.407 4600
2023 2027
2B 43 Apr. 13, July 10, 5.34 3.30 -2.96 0.307 4770
2023 2027
3A 10 Apr. 14, Jan. 15, 5.62 0.595 +0.583 0.0203 1600
2020 2023
3B 10 Apr. 13, Dec. 1, 5.43 0.407 -0.360 0.0291 3720
2022 2024
The reason for using different values of DeltaX in the two cases of Scenario 2 is to balance the task better between the two cases, so that only one launch vehicle is needed, as described below. If it is desired to deflect always in the shortest direction, the use of differing values could be eliminated by in some cases adding another launch with a smaller rocket. However, launch vehicles probably will improve so much in the next 18 years that neither of these approaches would be necessary.
If a 10% allowance for propellant for course corrections is added, the above table shows that for Scenario 1 we need to launch either about 4100 kg at 4.73 km/s or about 3700 at 5.40 km/s. Both of these situations are within the capability of the Atlas V 551, which can launch a payload of 4300 kg or 3800 kg for these two values of Vinf [8]. However, we might want to change our minds just before the first launch date about which way to deflect, in case new data is obtained in time to refine the orbit significantly. Therefore, we might fix the mass ahead of time and want to be able to launch 4100 kg at 5.40 km/s. This is beyond the ability of the Atlas V 551, but the Delta IV Heavy can launch a payload of 5300 kg with Vinf = 5.40 km/s [8]. (Once launch occurs, the direction of deflection by impact cannot be changed. However, the deflection can be canceled by commanding the spacecraft to miss the asteroid.)
For Scenario 2 as done in the table, the hardest case to launch (B) has a mass of about 5200 kg (including propellant for course corrections) with Vinf = 5.34 km/s. This matches the Delta IV Heavy payload of 5300 kg at that velocity, which is why the two cases in the table were partitioned in that way. (The Delta IV Heavy has the largest payload capability for escape trajectories of any launch vehicle that now exists.)
The cost of the Delta IV Heavy is roughly $160M, and the cost of the Atlas V 551 is probably somewhere around $120M. The cost of the Deep Impact project was about $330M which includes the Delta II 7925 launch vehicle, which costs about $60M. That leaves $270M development cost. Because of the similarity to Deep Impact, Scenario 1 probably could be developed for less, so adding the cost of the Atlas V 551 produces a total less than $390M. This is within the range of what Schweickart estimated for the transponder mission. Using a Delta IV Heavy instead of an Atlas V 551 would bring the cost to slightly more than $400M. Because Scenario 2 uses a Delta IV Heavy and might involve a rush project (if not much is done before 2021), its cost could be greater, perhaps around $600M.
If nothing is done until 2029 and it then turns out that Apophis is going to hit Earth in 2036 or one of the nearby years, deflection becomes much more difficult. The DeltaV needed is too large to use deflection by impact, and the amount of time available probably is not sufficient for the preparation and execution of one of the methods of gradual deflection, unless there is a considerable improvement in technology. I have calculated that deflection by one or more nuclear explosions could do the job, based on some previously presented information about buried explosions [9] and standoff explosions [10]. However, there are several technical difficulties involved, related to the mass of Apophis, the short time available, and the uncertainty about what the capability for such things will be in 2029, that make the practical feasibility of using explosions doubtful in this case, and it also has political problems. Deflection before 2029 would be greatly preferred.
5. The Danger of Dispersal and What to Do about It
The kinetic energy of the impacts used in Scenario 1 is 2.30e10 J and 2.05e10 J for the two cases. For Scenario 2 it is 5.26e10 J or 2.60e10 J. Based on its estimated mass of 4.6e10 kg and its diameter of 320 m, the gravitational binding energy of Apophis is 5.3e8 J. Therefore, the kinetic energy of the impacts in Scenarios 1 and 2 range from 39 to 99 times the gravitational binding energy, so a dispersal of the object is possible in principle. However, the escape velocity of Apophis is 0.20 m/s, which is 490 times the largest of the deflection velocities used in the scenarios. There are two effects of this large ratio.
First, the large value of the escape velocity relative to the deflection velocity means that, if the asteroid disperses, the fragments will scatter by a large amount around their center of mass, which is deflected by the same amount whether or not dispersal occurs. (Such considerations have been discussed in detail for the general problem [10].) Therefore, only a very small fraction of the fragments would hit Earth in the target year (e.g. 2036). However, as the fragments pass Earth in 2029 (before they are further dispersed by Earth’s gravity), a much larger fraction would hit. Therefore, it is important that dispersal not occur.
Second, the large ratio of escape velocity to deflection velocity makes it very unlikely that dispersion would occur. This can be verified with the help of some information [11, 12] that indicates that in this case there is not enough energy in the impacts to break up a monolith, and a rubble pile would absorb the energy so well that it could not be distributed to cause a large-scale dispersal.
Of course, some pieces could be ejected locally at at the impact site, but they probably would have sufficient velocity to miss Earth, and they probably would be so small that the atmosphere would protect us, anyway. In case there is any worry about the possibility of dispersal, however small, there are some steps that could be taken to reduce the danger even further.
If a transponder is placed on Apophis, the uncertainty in its orbit as extrapolated to 2029 would be reduced, and this could reduce the amount of deflection needed compared to that in Scenario 1 or 2, which would reduce the energy of each impact. Another possibility is to use Several vehicles instead of one, each delivering a smaller impact. Different trajectories could be used, instead of the ones in the table, that would make the velocity of each impact less. (Since momentum is proportional to velocity whereas energy is proportional to velocity squared, the energy of each impact can be reduced by the square of the number of vehicles, while keeping the total impulse constant. As a byproduct, this method also makes the guidance of the vehicle towards impact easier.)
Scenario 3 in the above table shows how a launch in 2020 or 2022, depending on which way we want to deflect, could arrive almost 3 years later with a small relative approach velocity. If a transponder could reduce the total uncertainty enough so that DeltaX = 10 km, a mass of 1600 kg or 3720 kg would have sufficient momentum to do the job. Then only one launch with Delta IV Heavy would be needed (for case A, a Delta IV Medium+(5,4) would suffice), and the impact energy of 2.8e8 J or 3.1e8 J would be less than the gravitational binding energy, so that total dispersal would be completely impossible.
In Scenario 3 it is likely that the uncertainty in 2022 would be less than that in 2020. However, we might not be able to take full advantage of that fact because the new data might move the center of the error ellipse to the other side of the keyhole, so that conceivably we would have to deflect in the long direction in case B. Therefore, the same value of DeltaX is used here for both cases of Scenario 3.
Consider an extreme case of the last situation for Scenario 3B. In the unlikely case in which the error ellipse is off center in the changed direction by 2 or 3 standard deviations, an interesting situation would arise that is somewhat similar to what Schweickart called “The Real Deflection Dilemma” [13], although there he was concerned with a small error ellipse that is slowly moved across Earth, whereas here we are concerned with a large error ellipse that suddenly jumps (we hope) completely across Earth. The same situation could occur in either case of Scenario 3 if, during the almost 3 years of flight time, new data from the transponder moves the reduced error ellipse to the other side of the keyhole. An argument could ensue about whether to proceed with the deflection or to cancel it.
Whether or not any of the above things are done to reduce the jolt to Apophis, it is possible to spread out the impact in both space and time by exploding the vehicle just before it hits. The debris hits the asteroid, but the fact that it is spread out over a considerable portion of the surface instead of being concentrated at one point makes dispersal less likely. Also, since it hits over an appreciable interval of time, it applies a more gentle push to the asteroid instead of creating a shock wave in its material. For example, spreading the debris over about 200 m would still enable almost all of it to hit within the 320-m diameter of Apophis if the guidance is sufficiently accurate. At the highest approach velocity in Scenarios 1 and 2 of 4.78 km/s, the impact of a 200-m cloud of debris would be spread out over 0.042 s. If the speed of sound in the material is 2000 m/s, a disturbance will travel 84 m in this time, which is 26% of the diameter of Apophis. By shaping the vehicle and the explosive charge appropriately, it should be possible to spread out the cloud considerably more in the direction of approach than transversely, so as to increase this time even more and to make the push even more gentle. (Unless we are using several very small vehicles, most of the material is there just for its mass, so it can be anything that is dispersed easily, such as sand.)
6. Transponder Mission
As discussed above, a transponder on Apophis would reduce the orbital uncertainty that results from both measurement errors and the Yarkovsky effect. With less uncertainty, less deflection is needed, and thus there would be less chance of dispersing the asteroid. Depending on the accuracies that can be achieved without a transponder, having one could even make the difference between deflection by impact being practical or not. There is also the fact that a transponder could show that a deflection mission is unnecessary. Although a deflection mission might not cost any more than a transponder mission, it would be wise to avoid deflection if we could, in case there is some slight chance that it could disperse Apophis.
However, it is difficult to justify committing to a transponder mission at this time on a purely monetary basis. Schweickart estimates that the monetary value of the damage that would be done by an impact in 2036 is around 400 billion dollars. If this is multiplied by 0.00015, which is the current total probability of impact before the year 2046 [3], the result is $60,000,000 for the amount that would be reasonable to spend at this time on mitigating the threat. It is unlikely that a useful mission to Apophis could be done for that amount of money. Schweickart’s own estimate for a mission to place a transponder is at least $300M. Future observations of Apophis can make the probability either increase or decrease; it is better to wait to see which it is. It would need to get to around 0.001 in order to justify the expenditure, based on the information in Schweickart’s paper. His data indicates that this value is likely to be reached no sooner than 2012 or 2013 even if an impact actually is going to occur, so that this might be the earliest date at which a commitment to such a mission would be well justified.
Still, peace of mind is worth something. If nothing is done until 2013 and it then turns out that action is needed, it might be 2020 or 2021 before a transponder could be placed on Apophis, which might be too late to provide the data needed. A transponder mission launched around 2013 might be very helpful.
A reasonable compromise might be to do preliminary work on the transponder mission, with less than the full expenditure of funds, until 2013. Then, if the probability of an Earth impact is high enough, work can proceed for, say, another 4 years to complete the project, for a launch in 2017 and an arrival in 2018. There would still be from 2 to 5 years of data before the launch of a deflection mission, depending on which scenario is used. Since preliminary work on the deflection mission could start in 2014, that should be sufficient time.
In addition to the uses of a transponder mission previously mentioned and its general scientific purposes, another use of a transponder might be to verify that the desired deflection has been produced. Therefore, even if it is decided that a precursor mission is not justified, it might be reasonable to launch a transponder mission at about the same time or shortly after a deflection mission is launched. The expense could be justified because, by that time, if the probability of impact has become high enough to justify a mission, very likely it would be high enough to justify the expense of two missions.
7. Summary
If the probability of an impact on Earth by Apophis in 2036 or one of the nearby years rises to around 0.001, action should be taken. Deflection after the very close pass by Earth in 2029, although possible in principle, is difficult.
If Apophis is deflected before 2029, the amount of deflection needed to prevent an Earth impact in 2036 or one of the nearby years is so small that it can be accomplished merely by hitting the asteroid with a spacecraft, provided that the influence of the Yarkovsky effect on Apophis can be approximately determined. If this determination cannot be done by observations from Earth by 2014, perhaps a transponder mission shortly after 2014 could do it, or radar and optical observations of Apophis around 2005, 2013, and 2021 should be able to determine it.
A spacecraft to perform the deflection by impact could be launched by an existing launch vehicle. Some reasonable launch dates are in the years 2020-2023. The total cost of such a mission, including development costs and the launch vehicle, could vary from less than $400M to around $600M , depending on how soon a decision is made, provided that only one launch vehicle is used. This is not much different from the cost of a transponder mission.
The danger of large fragments hitting Earth from a dispersal of Apophis caused by the impact of a space vehicle is very small, especially if a transponder is used to reduce the orbital uncertainty and thus the amount of deflection needed. There are several methods for making the danger even smaller, including hitting Apophis with several vehicles with less mass or less velocity instead of one, and exploding the space vehicle just before it hits Apophis.
Further analysis should be done to resolve some of the issues raised here, especially about the accuracies that are likely to be achieved at various times and how much a transponder would help.
References
[1] R. L. Schweickart, “A Call to (Considered) Action,” Presented at the National Space Society International Space Development Conference, Washington, DC, May 20, 2005 (available at http://www.b612foundation.org/papers/Call_for_Action.pdf).
[2] R. L. Schweickart, letter to David Morrison, July 20, 2005 (available in the News Archive at http://impact.arc.nasa.gov/).
[3] http://neo.jpl.nasa.gov/risk/a99942.html
[4] http://deepimpact.jpl.nasa.gov/
[5] S. J. Ostro, “The Role of Groundbased Radar in Near-Earth Object Hazard Identification and Mitigation,” in Hazards Due to Comets and Asteroids, T. Gehrels (ed.), University of Arizona Press, 1994, pp. 259-282.
[6] J. N. Spitale, “Asteroid Hazard Mitigation Using the Yarkovsky Effect,” Science 296, p. 77 (April 5, 2002).
[7] K. A. Holsapple, “An Assessment of Our Present Ability to Deflect Asteroids and Comets,” paper AIAA-2004-1413, from [14].
[8] S. J. Isakowitz, J. B. Hopkins, and J. P. Hopkins Jr., International Reference Guide to Space Launch Systems, Fourth Edition, American Institute of Aeronautics and Astronautics, 2004.
[9] B. P. Shafer, M. D. Garcia, R. J. Scammon, C. M. Snell, R. F. Stellingwerf, J. L. Remo, R. A. Managan, and C. E. Rosenkilde, “The Coupling of Energy to Asteroids and Comets,” in Hazards Due to Comets and Asteroids, T. Gehrels (ed.), University of Arizona Press, 1994, pp. 955-1012.
[10] D. B. Gennery, “Deflecting Asteroids by Means of Standoff Nuclear Explosions,” paper AIAA-2004-1439, from [14].
[11] K. Holsapple, I. Giblin, K. Housen, A. Nakamura, and E. Ryan, “Asteroid Impacts: Laboratory Experiments and Scaling Laws,” in Asteroids III, W. F. Bottke Jr., A. Cellino, P. Paolicchi, and R. P. Binzel (eds.), University of Arizona Press, 2002, pp. 443-462.
[12] E. Asphaug, S. J. Ostro, R. S. Hudson, D. J. Scheeres. and W. Benz, “Disruption of Kilometre-Sized Asteroids by Energetic Collisions,” Nature 393, pp. 437-440 (June 4, 1998).
[13] R. L. Schweickart, “The Real Deflection Dilemma,” paper AIAA-2004-1467, from [14].
[14] 2004 Planetary Defense Conference: Protecting Earth from Asteroids, sponsored by the American Institute of Aeronautics and Astronautics and The Aerospace Corporation, Garden Grove CA, Feb. 23-26, 2004. (The individual papers can be downloaded at http://www.aiaa.org/search, and the conference proceedings on CDROM containing all of the papers and the conference White Paper can be purchased by email at warehouse@aiaa.org.)
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