Deflection of Fictitious Asteroid 2017 PDC: Ion Beam vs. Kinetic Impactor

Transcription

1 5 th IAA Planetary Defense Conference PDC May 2017, Tokyo, Japan IAA-PDC Deflection of Fictitious Asteroid 2017 PDC: Ion Beam vs. Kinetic Impactor Claudio Bombardelli a,1,, Emilio Jose Calero a,2, Juan Luis Gonzalo a,3 a Technical University of Madrid, Pl. Cardenal Cisneros 3, 28040, Madrid, Spain, ph: Abstract Mission scenarios for the deflection of fictitious asteroid 2017 PDC are investigated. Two deflection options, kinetic impactor (KI) and ion beam shepherd (IBS), are studied and compared on the basis of deflection performance, safety, as well as mission schedule and political aspects. Firstly, we propose the launch of a medium-size rendevous spacecraft equipped with at least two ionic thrusters that can serve as propulsion means for the interplanetary trajectory up to rendezvous with the asteroid and as contactless actuators for a possible follow-up deflection mission. The asteroid, whose uncertainty ellipsoid is initially too large to establish whether (and how) it should be deflected, is reached by the rendezvous spacecraft after a low-thrust interplanetary trajectory of reasonable duration. Following rendezvous the spacecraft is placed in an orbit around the asteroid to estimate its mass, study its structure and composition and, crucially, reduce its uncertainty ellipsoid by ground tracking to confirm or rule out an impact. Assuming that an impact is confirmed two main deflection scenarios are considered based on the actual asteroid size. Ion beam deflection is considered with the possibility of full deflection (the asteroid misses the Earth by a safe margin) or impact location adjustment (the impact footprint is diplaced to the nearest unpopulated region) depending on the asteroid size. The launch of a kinetic impactor mission is also considered with the employment of the rendezvous spacecraft to measure the deflection outcome and possibly to refine the deflection in case it is needed. The deflection performance of the two methods is compared. Corresponding author address: claudio.bombardelli@upm.es (Claudio Bombardelli) 1 Research Associate, Space Dynamics Group 2 Graduate Student, Space Dynamics Group 3 PhD Candidate, Space Dynamics Group 1

2 1. Introduction Following a similar scheme to the 2015 edition [1], the organizers of the 2017 planetary defense conference (PDC) released a hypothetical asteroid impact scenario to be used as a basis for an emergency response exercise to be conducted at the conference site. The fictitious m diameter asteroid, discovered on March 6, 2017 (MJD= ) and named 2017 PDC, was found to have several potential impacts with the Earth, the earliest and most likely on July 21, The impact probability estimation for that event would reach 1% in mid-may 2017 and would continue to rise with the rest of the scenario to be played out at the conference. Starting from ephemeris data provided by the conference organizers and propagating forward until impact with the Earth one finds a nominal impact point in the little populated Kalamaili Nature Reserve in the Xinjiang Uyghur Autonomous Region of Northwest China, roughly 60 km north of the town of Jimsar and about 150 km off of the Mongolia border. The impact would take place around 08:17:12 UT, corresponding to the local time 16:17:12, with an impact velocity of around 14 km/s. Adding orbit determination uncertainties along the asteroid line of variations (LOVs) one can obtain a path of risk stretching from the middle of the North Pacific Ocean (roughly half way between Japan and Hawaii) and the middle of the North Atlantic (more than 700 km west of Ireland) and passing through heavily populated areas in Northern Europe and Northern Asia, and through, or near, major cities like Tokyo, Seul, Beijing, Karamay (Northwest China), Minsk, Kaliningrad, Newcastle, and Belfast. Owing to the asteroid orbit geometry with respect to the Earth, the asteroid will be observable only until December 2017 with no further opportunities to increase the accuracy of the asteroid orbit by future ground-based observations. This paper deals with two worst case scenarios in which the asteroid is predicted to impact in the vicinity of Tokyo and Beijing. Two mitigation strategies are investigated and compared in this article: a slow-push deflection using an ion beam shepherd (IBS) spacecraft and an impulsive deflection produced by a kinetic impactor (KI). Technical and political aspects are discussed in details. 2. Impact Scenario The reference orbital elements of fictitious asteroid 2017 PDC on the discovery date March 6, 2017 at 0:00:00 UT are provided in Table 1. The elements are referred to a heliocentric J2000 ecliptic reference system. The asteroid orbit is propagated up to the instant of intersection with the Earth ellipsoid using a simplified solar system model including gravitational perturbations from the solar system planets, the Moon (through JPL DE405 ephemerides) and the three largest asteroids (Ceres, Vesta and Pallas) as well as first order relativistic corrections. While the propagation of the nominal asteroid ephemerides would lead to an impact in Northwest China (89.3E, 44.9N) a preliminary path of risk estimate can be obtained after propagating the asteroid orbit starting from a set of slightly modified reference epochs. This would approximate a line of variations (LOVs) sampling of the asteroid close to the direction of the greatest orbit determination uncertainty. The path of risk obtained following the above procedure is plotted in Fig. 1 and stretches from the middle of the North Atlantic (-26.43E 52.86N) and the middle of the North Pacific Ocean 2

3 Table 1: Nominal ephemerides of fictitious asteroid 2017 PDC reference epoch (MJD) semi-major axis (AU) eccentricity inclination (deg) argument of pericenter (deg) longitude of ascending node (deg) mean anomaly (deg) Figure 1: Path of risk of fictitious asteroid 2017 PDC (175.79E 31.51N). A number of large cities lay on or near to this path. Eight of them are listed in Table 2 together with the modified reference epoch resulting in an impact. One crucial aspect to be pointed out here is the way the asteroid impact point moves along the path of risk. Because the asteroid approaches the Earth coming from the inner Solar System any action delaying its arrival will result in the impact point moving eastwards. A deflection action pushing the asteroid in the same direction as its orbital velocity, thereby increasing its semimajor axis and orbital period, would give rise to such delay and eastward shifting of the impact point. The direction at which the asteroid is hit by a KI is constrained by the optimized interplanetary trajectory. In particular, we will show that for 2017 PDC a KI always results in a deflection opposite to the asteroid velocity, meaning a KI would always shift the impact point westwards. 3

4 Table 2: Modified reference epoch of Table1 leading to worst case impacts reference epoch (MJD) Impact coordinates nearest city country impact time (UTC) E N Belfast UK 08:14: E N Newcastle UK 08:14: E N Kaliningrad Russia 08:13: E N Minsk Belarus 08:13: E N Karamay China 08:16: E N Beijing China 08:21: E N Seul South Korea 08:22: E N Tokyo Japan 08:25:07 3. Rendezvous and Orbit Refinement Based on observations through may , the size of the propagated uncertainty region of the asteroid up to the possible impact epoch largely exceeds the size of the Earth. It is therefore not possible to predict whether or not an impact will occurr and, if it will, where it is expected to take place. Nevertheless, one can be quite sure that if an impact is going to take place it will be sufficiently near to the path of risk depicted in figure 1, which poses a threat for the densely inhabited areas along this path. In such uncertain, yet potentially devastating scenario the most urgent action is to attempt reducing orbit uncertainties in order to be able to either rule out an impact or to predict its geographical location with the highest possible accuracy. In the absence of future groundbased observation opportunities the only option left is to send a spacecraft to rendezvous with the asteroid and drastically reduce the uncertainty of its orbit by collaborative orbit determination using the spacecraft radio links. Following a similar analysis to the one conducted in a previous paper ([1]) one can see that a reduction of the size of the 1-sigma impact ellipse to a few tens of km is possible for 2017 PDC, which can answer the key question of whether or not an impact would take place and, if yes, where. If an impact is confirmed a deflection action will be planned using two possible technological solutions: a kinetic impactor [2] and an ion beam shepherd (IBS) spacecraft [3, 4] Interplanetary trajectory optimization One crucial aspect that affects the design of a rendezvous trajectory for an asteroid tracking and deflection mission is the stringent time constraint. One would need to arrive to the asteroid as early as possible to leave a large enough margin period for an effective deflection. Assuming, as a quite convenient design solution, that the spacecraft is already equipped with an IBS deflection capability it will be possible to make use of one (or more) of its high-specific-impulse ionic thrusters to efficiently rendezvous with the asteroid. With this in mind, a preliminary estimate for the total spacecraft mass at interplanetary orbit insertion is of 1200 kg including 400 kg of Xenon to be distribute between the trajectory and the deflection (a similar figure to the total wet mass of the Dawn mission). Regarding the propulsion subsystem, a preliminary design proposes two sets of 4

5 ionic thrusters mounted at a relative orientation of 180 to provide ion beam shepherding capability with a 3500 s specific impulse and a mn maximum thrust at 1 AU. Note that it is assumed that the available power depends on the distance to the Sun with an inverse exponent of 1.7 (not purely 2 as solar cells gain performance at lower temperatures), which is reflected on the thrust capability. The role of the launch vehicle is paramount in the trajectory design. The hyperbolic excess velocity of the spacecraft after launch (related to the launcher s C 3 ) does not only affect the time up to reach the target orbit, but also the character of the solution. In any case, it is considered that such excess velocity always provides a favorable effect upon the optimization as long as the outgoing asymptote direction is appropriate. Thus, a C 3 of 60 km 2 /s 2 is used, which can be easily achieved for that initial mass with an Atlas V 551. At this point, different trajectories can be found depending on the departure epoch. In order to guarantee enough development time as well as enough deflection time the launch window considered was set between three and five years after discovery. As for the transfer time, an attempt has been made to keep it as short as possible (to maximize the post-rendezvous deflection) compatibly with a reasonable fuel mass consumption. In this regard, in order to allow for a successful deflection the trajectory should not exceed a single revolution. This was probably the reason why no solution was found at a departure epoch around three years after discovery. Nevertheless, the one obtained around four years after discovery, besides meeting the time requirements, provides a very high performance relative to the propellant consumption. Figure2 depicts the Pareto s front in relation with this local solution, comparing the improvement in propellant consumption, m p = 1 1 m f 1 m f, against the deterioration in transfer time duration, t f = t f t f t, with respect to the minimum time problem, where m f and t f represent f the final S/C mass and the final transfer time, respectively, and the superscript denotes the same values for the case of minimum time optimization. As can be seen, an increment of about 10% in the final time leads to an enhancement of more than 50% in the propellant consumption, being this the baseline solution chosen in this study. The nominal solution is characterized by a total transfer time of about 886 days and a total propellant consumption of 93.4 kg, with departure epoch on Jun 27, 2021 and arrival epoch on Nov 30, It consists of a coast-thrust-coast-thrust structure of 236 days, 177 days, 309 days and 164 days, respectively, in which the first thrust stage consumes 33 kg of propellant and the second one about 60 kg. Regarding the resulting outgoing asymptote, its declination is about 13º and its right ascension is -23.4º. The latter does not involve any restriction as it is always attainable choosing the launch time in a proper way, but the former is constrained by the latitude of the launch site. In this case it is achievable launching from Cape Canaveral. Figure 3 shows the Ecliptic projection of the trajectory where the thrust arcs are represented with a thicker line. Figure 4 provides the S/C distances to the main bodies. The maximum distance to the Sun is below 3 AU whereas the maximum Earth distance is 3.75 AU. The distance to the Sun at arrival is 1.25 AU, and to the Earth 1.7 AU. The same figure plots the S/C angles with respect to the Sun and Earth reveals that the superior conjunctions occur far enough from the arrival epoch, allowing a good radiometric link to the S/C from the Earth and thus a proper orbit determination solution. Figure 5 represents the mass evolution along the trajectory and the thrust magnitude. 5

6 Figure 2: Pareto s front of the optimization problem: improvement in propellant consumption vs. increment of transfer time S/C Earth 2017-PDC Figure 3: Ecliptic projection of the low-thrust transfer trajectory from Earth to 2017 PDC. 6

7 Angle Sun-S/C-Earth Angle Sun-Earth-S/C 0.5 Distance to Sun Distance to EARTH Distance to 2017-PDC Figure 4: Time evolution of the S/C distances to the Sun, the Earth and 2017 PDC and of the S/C angles to the Sun, and the Earth Figure 5: Time evolution of the S/C mass and thrust magnitude 4. Deflection Let us assume that, following the rendezvous and a tracking campaign, the asteroid has been confirmed to strike the Earth and needs to be deflected. Two scenarios will be considered here: 1. Impact in Tokyo 2. Impact in Beijing In addition, let us assume the asteroid average diameter has been estimated to 150 m and its average density to 2.0 kg/cm 3. The results can be easily scaled to asteroids of different sizes as the final achievable deflection simply scales with the cube of the asteroid diamter Deflection by Kinetic Impact The kinetic impactor (KI) is, currently, the asteroid deflection method that is most favored by the space science and technology community. This is mainly because of the 7

8 high level of momentum that can be delivered to the asteroid and the immediacy of the effect. One of the most important aspect of the KI, and its main drawback, is the uncertainty in the quantity of effectively delivered momentum, strongly related to the well known beta factor which takes into account the effect of ejecta on the net deflecting momentum eventually transmitted to the asteroid. Because this effect is not always properly accounted for in the literature we have devoted the following section to discuss it Beta factor vs. deflection magnification Conservation of linear momentum of the spacecraft+asteroid system during the impact is the key law of physics that allows one to estimate the net impulse transmitted to the asteroid and the corresponding deflection V. Let us consider a frame with its center at the center of mass of the asteroid and parallel to an inertial frame. Let U denote the relative velocity of the KI spacecraft with respect to that frame. Let M ast and M sc indicate, respectively, the asteroid and spacecraft mass at impact. Finally, let ˆn be the local normal unit vector of the asteroid surface at the impact location. Let us assume, as reasonable, that the spacecraft mass will collapse entirely into the asteroid body and that the overall momentum of the asteroid material ejected from the collision location will be parallel to ˆn. Then, the asteroid will have its linear momentum varying from zero (before the impact) to the post-impact value p which obeys [5]: p = M sc U ( 1)(U ˆn) ˆn. (1) In the above equation the coefficient quantifies the role played by the ejecta in determining the final linear momentum of the asteroid. A value of = 1 implies no ejecta contribution to the transferred momentum. Having <1 is extremely unlikely as it would mean the ejecta are expelled along the inward normal direction, which is only possible if some asteroid material is expelled from a different location than the one of the impact. Neglecting the mass of the ejecta and of the spacecraft compared to the asteroid mass, the resulting V imparted to the asteroid yields: V p M ast. (2) Contrarily to what often believed, a beta factor coefficient greater than one does not always imply a better deflection performance. As a matter of fact there are cases where a large beta can reduce the achievable deflection. This is due to impact point uncertainties and appears when the direction of the relative impact velocity U differs from the direction of the absolute asteroid velocity V, i.e. for a non-tangential impact, as can be easily understood by looking at Fig. 6. Depending on the impact point location, the ejecta momentum can play in favor or against the deflection. Note that, as in most of the cases, the impact is assumed to occur sufficiently early in time so that any nontangential momentum component transmitted to the asteroid plays a negligible role in the b-plane impact point displacement. 8

9 Figure 6: Ejecta influence on the achievable deflection depending on the impact point. It is assumed that any transmitted momentum component orthogonal to the asteroid velocity has a negligible effect on the final deflection Deflection map A KI deflection map employing an V 551 launcher is shown in Figure 7. The latter Figure has been obtained by solving Lambert s problem for a grid of departure dates and transfer durations assuming Keplerian orbits for the Earth, the asteroid and the S/C and starting from an impact right in the Earth center. A more refined analysis accounting for perturbations and starting from an accurate collision configuration would probably not change the results considerably. Note that in order to compute the achievable deflection we have employed the maximum mass that can be launched by Atlas V for the particular C 3 corresponding to Lambert s problem solution. The achievable deflection for each Lambert s problem solution has been computed starting from a delta-v provided by Eqs. (1,2) with a beta factor set equal to one and using the formulation described in [6, 7, 8] to compute the b-plane displacement with the Earth gravitational focusing effect properly taken into account. A deflection of more than three Earth radii can be achieved with an early launch in june A late launch at the end of may 2023 can still provide a deflection of more than one Earth radius. Figure 8 provides another very important piece of information: the angle betweem the absolute asteroid velocity V and the relative S/C-asteroid velocity U. This angle, which is plotted only for the launch dates and time of flight corresponding to a deflection of more than one asteroid radius, lays between about 130 and 240 degrees which means that a KI deflection always decreases the asteroid semimajor axis hence anticipating its arrival. For this particular asteroid, that is equivalent to shifting its impact point westwards as discussed in a previous section. In the case of an impact in Tokyo, for instance, this could have important consequences, as an unexpected deflection outcome would put other large populated regions in danger and create political instability. Note that the likelihood of a KI deflection to go wrong can be significant owing precisely to the uncertainty in the ejecta contribution to the final deflection, as the impact relative velocity is highly non-tangential for the great majority of deflection solutions found. 9

10 Figure 7: Deflection map for a kinetic impactor spacecraft intercepting asteroid 2017 PDC. The influence of the asteroid surface ejecta is not taken into account here Ion Beam Deflection An interesting alternative to KI deflection is ion beam shepherding, which, unlike the former, can be carried out with the rendezvous spacecraft previously sent to the asteroid to reduce its orbit uncertainty. One crucial advantage of employing an IBS as deflection solution is the capability for accurate impact point retargeting: the asteroid impact footprint can be shifted along the path of risk in both directions according to specific needs [1]. This is particularly relevant for larger asteroids that cannot be deflected by a large amount (a few Earth radii) unless nuclear detonation is employed. Furthermore, an unexpected deflection outcome may result in the asteroid impacting a densely populated region along the path of risk with potentially disastrous consequences. The IBS deflection capability of asteroid 2017 PDC following the two worst case scenarios previously outlined has been investigated numerically using the same highfidelity numerical propagator employed to study the asteroid path of risk. A continuous low-thrust deflection force is transmitted to the asteroid along or opposite to the instantaneous velocity vector. The thrust is applied starting on January 1st 2024 (one month after rendezvous) and for a duration between one and 20 months obtaining a series of displaced impact points according to the duration of the deflection. The 150 m diameter asteroid has been perturbed with a 185 mn deflection force at 1 AU (to account for ion beam momentum transfer efficiency losses with a 200 mn thruster), with a varying magnitude inversely proportional to the distance from the Sun raised to the 1.7 power. 10

11 Figure 8: Angle between the absolute asteroid velocity (V) and the KI velocity relative to the asteroid at impact (U) Tokyo impact A predicted impact of 2017 PDC in Tokyo would prompt to an immediate action to plan a deflection maneuver. The most reasonable solution appears to move the asteroid eastwards to either have it impacting in the open sea or avoiding the Earth completely if the deflection action is sufficient to make the asteroid fly by the Earth above the North Pacific Ocean. This solution seems to be completely acceptable from a political point of view as no other countries would be intercepted by the asteroid impact footprint as the deflection is being executed. Letting the asteroid striking the open sea might be acceptable for the considered asteroid size, which is too small to generate tsunami-like waves [9]. On the other hand, an impact to within about 100 km from the coast can have disastrous consequences and needs to be avoided at all costs by making the deflection mission design highly redundant. The shift of the impact point during a deflection with the ion beam pushing the asteroid in the direction of its orbital velocity is shown in Fig 9. A full deflection is achievable after 15 months Beijing impact An impact in Beijing would be more complicated to deal with using an IBS spacecraft. Moving the impact point westwards to let the asteroid strike in the Yellow Sea is risky as the impact could end up too close to the coastline. A longer westward deflection would have the impact footprint passing over Seul, the Japan Sea and Tokyo to finally 11

12 50 45 Latitude (deg) Longitude (deg) Figure 9: IBS eastward deflection track starting from a predicted impact in Tokyo. reach the North Pacific Ocean after about 20 months of deflection. This solution is feasible but would require solving important political issues before its implementation. An eastward deflection, on the other hand, could be employed to shift the impact point in a deserted area in Northern China. This last solution would be much easier to handle politically as the impact footprint would be confined within Chinese territory except for a small part transiting through the (almost unpolulated) southern Mongolia border with China. The results of an easward and westward deflection are shown in Figs.10 and 11, respectively. 5. Conclusions A comparison has been performed cosidering two deflection strategies for dealing with an impact of the fictitious asteroid 2017 PDC. Employing a kinetic impactor and considering launch mass limits compatible with an Atlas V 551 launcher would allow one to reach a maximum deflection of up to 3.5 Earth radii for a 150 m spherical asteroid of 2.0 kg/cm 3 average density and neglecting any contribution from ejected asteroid material (i.e. assuming a beta factor equal to one). However, it has been observed that a larger beta factor does not always increase the achievable deflection, owing to the particular impact geometry. Because a KI can only displace a geographical impact point westwards, this fact poses important risks that need to be accounted for especially when an impact is predicted to occur in the eastern part of the asteroid impact corridor. A deflection by means of an ion beam shepherd spacecraft cannot reach a deflection of a few Earth radii for this asteroid. However, it offers important advantages that need 12

13 45 Latitude (deg) Longitude (deg) Figure 10: IBS eastward deflection track starting from a predicted impact in Beijing. 55 Latitude (deg) Longitude (deg) Figure 11: IBS westtward deflection track starting from a predicted impact in Beijing. 13

14 to be considered. The first is the accuracy of the achievable deflection, which minimizes the risk of having the asteroid striking at a highly populated region in case of deflection errors. This advantage can be exploited to shift the asteroid impact point towards deserted areas at a much lower cost in terms of required propellant and thrusting time. The second is the compatibility of the method with a rendezvous mission that is required to accurately track the asteroid before the deflection (to confirm the asteroid impact) as well as to accurately measure the outcome of any deflection method (including, possibly, a KI). Acknowledgments The research leading to these results is funded by the Spanish Ministry of Economy and Competitiveness within the framework of the research project Dynamical Analysis, Advanced Orbital Propagation, and Simulation of Complex Space Systems (ESP P). Juan L. Gonzalo thanks the Spanish Ministry of Education, Culture and Sport for his doctoral fellowship under the FPU Program (reference number FPU13/05910). The authors would like to thank the organizers of the 2017 Planetary Defense Conference for proposing this very interesting and stimulating problem. References [1] C. Bombardelli, D. Amato, J. L. Cano, Mission analysis for the ion beam deflection of fictitious asteroid 2015 pdc, Acta Astronautica 118 (2016) [2] T. J. Ahrens, A. W. Harris, Deflection and fragmentation of near-earth asteroids, Nature 360 (1992) [3] C. Bombardelli, J. Peláez, Ion beam shepherd for asteroid deflection, Journal of Guidance, Control, and Dynamics 34 (2011) [4] C. Bombardelli, H. Urrutxua, M. Merino, J. Pelaez, E. Ahedo, The ion beam shepherd: A new concept for asteroid deflection, Acta Astronautica 90 (2013) [5] D. J. Scheeres, J. W. McMahon, B. A. Jones, A. Doostan, Variation of delivered impulse as a function of asteroid shape, in: Aerospace Conference, 2015 IEEE, IEEE, pp [6] C. Bombardelli, G. Baù, Accurate analytical approximation of asteroid deflection with constant tangential thrust, Celestial Mechanics and Dynamical Astronomy 114 (2012) [7] C. Bombardelli, Analytical formulation of impulsive collision avoidance dynamics, Celestial Mechanics and Dynamical Astronomy 118 (2014) [8] C. Bombardelli, J. Hernando-Ayuso, Optimal impulsive collision avoidance in low earth orbit, Journal of Guidance, Control, and Dynamics 38 (2015) [9] G. Gisler, R. Weaver, M. Gittings, Calculations of asteroid impacts into deep and shallow water, Pure and applied geophysics 168 (2011)