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Original Message
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Posted By: Kaspel
Date: Wednesday, 10 August 2005, 4:17 p.m.
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.
Donald B. Gennery
[email protected]
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.
continued:
[link to www.spaceref.com]
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