[extropy-chat] NEO deflection

[David Lubkin]

Long, but clearly an extropian concern. Past issues are in the archives 
(see end); this one isn't there yet.

>From: "David Morrison" <dmorrison at arc.nasa.gov>
>To: "David Morrison" <dmorrison at arc.nasa.gov>
>Sent: Tuesday, August 09, 2005 2:44 PM
>Subject: NEO News (08/08/05) Deflection Scenarios for Apophis
>
>
>NEO News (08/08/05) 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 at 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 at aiaa.org.)
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