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Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Received: December 21, 2011 / Accepted: January 10, 2012 / Published: February 15, 2012.
Abstract: This paper shows 2D and 3D simulations from a validated hydrocode (RAGE) of the effects of a strong explosion on the surface of a porous non-spherical asteroid like object. The composition of the simulated asteroid is made more realistic than previous work by using a random distribution of rocks constrained by a non-spherical outer surface. These simulations can be categorized as explosion effects on “rubble pile” asteroids. The main goal of this work is to apply realistic hydrodynamics to 2D and 3D rubble pile models and examine the results to see if sufficient momentum is transferred to the porous object so as to mitigate the hazard posed by the initially Earth crossing orbit.
Key words: Asteroid mitigation, nuclear explosions, potentially hazardous objects (PHOs).
1. Introduction
The authors have performed detailed hydrodynamic simulations of the shock interaction from a strong surface or subsurface explosion with sample asteroid objects. The purpose of these simulations is to apply modern hydrodynamic codes that have been well verified and validated (V&V) to the problem of mitigating the hazard from a potentially hazardous object (PHO), an asteroid or comet that is on an Earth crossing orbit [1]. The cod used for these simulations is the RAGE code from Los Alamos National Laboratory[2-6]. Ref. [2] contains many of the V&V reports for the code which were completed prior to publication. It should be noted for those not familiar with the RAGE code that it has been extensively V&V’d for shock physics and shock interactions with multiple materials. It is confident that the shock physics simulations presented here represent realistic hydrodynamics of the complex shock interactions, including the effect of the shock on the rocks themselves (assumed to be spherically shaped objects).
Initial runs were performed using a spherical object. We next ran simulations using the shape form from a known asteroid: 25143 Itokawa [7, 8]. This particular asteroid is not a PHO but we use its shape to consider the consequences of non-spherical objects. The initial work was performed using 2D cylindrically symmetric simulations and simple geometries (solid non-spherical objects). Next we progressed to Itokawa shaped models filled with uniform size “rocks”composed of granite and a solid background material(alluvium). These models had no porosity and were mainly done as a test of the code hydrodynamics. The first runs used a spherical energy source at the center of the object (typically 1 Mt), both with and without a“drill hole” which would be necessary to emplace an explosive at this location. Since the escape velocity of this object is very low, the disruption and bulk velocities indicated from these simulations is sufficient completely mitigate a PHO threat. That is to say, the velocities calculated were so large as to preclude re-assembly of the fragments and moreover ensure that with even modest lead times that all fragments would be pushed well beyond an Earth crossing orbit if the parent body was a PHO.
2. Methods
All of the simulations presented in this paper were performed with the RAGE hydrodynamic code from Los Alamos National Laboratory [2]. This code features a well verified and validated continuous adaptive mesh refinement (CAMR) described in Ref.[2] as well as the extensive validation done prior to the publication of that paper. We ran 2D cylindrically symmetric and 3D models of the shock interaction of a strong explosion with the asteroid material. Most of the results shown here are 2D simulations for ease of parametric studies and savings on computer time. Models were done for several parametric studies, including the effect of solid (no-porous) models, the effect of non-spherical models, the effect of similar strength explosions at various depths from the asteroid surface to the center of the object, long-side versus short side surface explosions as finally full 3D models. These models used source energies from 500 kt to 1 Mt, with most models run at 500 kt. The main physics employed in the multi-physics, multi-material RAGE code were the detailed CAMR Eulerian hydrodynamics and the material strength package, the Steinburg-Guinan (SG) model for the“rock” strength. Radiation is available in the code but was not used for these simulations. For simulations with radiation transport included, the effect of momentum transfer from the energy source to the asteroid will only increased, so these results represent lower limits to the momentum transferred to the model objects.
3. Models
The models used for these studies transitioned from simple to more complex. The models shown in this paper are:
(1) A non-spherical asteroid 25143 Itokawa shape with a uniform iron composition and a central explosion site. This model was done first to test the code for reasonable results and assess the effects of non-spherical models;
(2) Next we wrote a simple program to fill the non-spherical outer shape of the asteroid with a random distribution of rocks. These rocks could be of arbitrary size between size 1 and size 2 and were spherical in shape with the centroids within the asteroid surface. These models represent what we call“rubble pile” compositions, which is considered to be more realistic on average than uniform or spherical compositions;
(3) The first runs of this type were done with single size “rocks” (really torus’s in 2D) composed of granite material equation-of-state (EOS) with an alluvium background material. Thus these first runs had no porosity. It is generally believed that typical asteroids have porosities of 30%-40% due to multiple collisions and subsequent re-aggregation;
(4) Next we simulated porosity by removing the background alluvium and leaving the granite rocks. This resulted in porosities of 25%-40% (in 3D). The main effect of the high porosity is to significantly degrade the shock strength and therefore impart less momentum to the asteroid;
(5) We then modeled the effect of the depth-of-burial of the explosion from the center of the object to the surface and also the effect of short-side versus long-side surface bursts;
(6) Our final model in this series is running now and is a full 3D porous object filled with three different size rocks from 5m to 50m.
4. 2D Results
Work done previously to this meeting included the non-spherical uniform composition central explosion simulation with an energy of 1 Mt. The resulting images from the 2D RAGE simulation are shown in Fig. 1. This initial model indicated the importance of non-spherical geometry. The shock from the central explosion clearly reaches the surface of the asteroid along the shortest chord and ultimately ejects the two large end caps at a velocity of ~ 50 m/s due to the enormous pressure inside the explosion cavity at breakout time.
Next we used a program to fill the shape object with a distribution of rocks. This first simulation was done with a background material of alluvium and rocks composed of granite with SG strength. Thus this run had no porosity. Again dispersion velocities of all the asteroid material and “rocks” were calculated to be~1 m/s, significantly above the escape velocity. These results are shown in Fig. 2.
Next we explored the asteroid mitigation for various depths-of-burial of the explosion from the center to the surface. These results are shown in Fig. 3. Significant velocities (much greater than escape velocity) were imparted to all the asteroid material for each depth-of-burial from a surface burst to the centroid position. Given these results, the easiest mission to proceed with is a surface/contact burst mode. This mission could easily be un-manned and no“hollywood style” equipment would be necessary. The main focus from here forward will thus be on surface burst scenarios.
This initial set of RAGE simulations was meant to explore the parameter space of using this type of surface/subsurface explosion to totally disrupt an asteroid of ~500 m size. However, these simulations all had no porosity, which we then addressed in a fashion that is well suited to the RAGE code. Not knowing the exact internal composition of such an asteroid, but knowing it’s porosity is likely to be 30%-40% and it composition to be made of a distribution of rock materials, we started a new set of simulations. These simulations had two main advances that moved towards more realistic scenarios:(1) we used a distribution of rocks size: typically in a range from ~5 m spherical rocks to ~50 m spherical rocks randomly distributed in the outer shape of the asteroid; and (2) we added porosity to the simulations be removing the background alluvium. This left the initial geometry to be comprised of the rocks separated by porous void regions. This gave a total porosity of the simulated asteroid of ~20%-40% depending on the random distribution of rocks and on their size distribution. The result of these random size rock distributions with porosity gave the expected result of a weaking of the shock wave that translated into smaller velocities imparted to the asteroid materials. The typical reduction was about a factor of 5-10. Specifically for a surface burst (easiest mission), a 25% porous non-spherical 2D object was given a bulk velocity of ~6 m/s at 10 seconds after a 500 kt explosion (Fig. 4).
Fig. 1 The initial non-spherical uniform composition simulation with the RAGE hydrocode.
Fig. 2 The next RAGE simulation had “rubble pile” for a composition with uniform 5 m rocks and an alluvium background material. The velocity imparted to the asteroid material from the central 1 Mt explosion was again > 10m/s at 0.1 sec.
Fig. 3 The effects of the depth-of-burial of the explosion from a central location to the surface along both major directions. This study showed that explosions along the short side of this non-spherical object resulted in the greatest velocities (at 1 sec after explosion). These simulations had no porosity.
Fig. 4 The next set of simulations by removing the background alluvium material, leaving voids between the rocks. The depth-of-burial study was redone from both the long and short side of the asteroid. At this point we also varied the size distribution of the internal random rocks from ~5m to ~50m radius spheres. Although the bulk velocities were down ~5 times the explosion was still more than adequate to totally disrupt the asteroid.
Fig. 5 The first 3D simulation analogous to the 2D porous surface burst shown in Fig. 4 but with a 1 Mt source energy. The shock seems to dissipate more strongly in 3D than 2D. However, final conclusions require the 3D run to complete.
In summary the effect of the porosity as modeled in 2D here with the RAGE code indicate that even for at 500 kt explosion (modest energy) and significant porosity (~20%) the asteroid material was given a bulk velocity of ~>5 m/s at 10 seconds, sufficient to mitigate the PHO hazard. Thus for short notice PHO’s one should not consider the nuclear explosive option as “off the table”. There are clearly significant international issues to be resolved:
which nuclear country will be given the lead on such a mission?
which international organization will be in charge of such a mission?
should multiple missions be undertaken (at the same time) to ensure mitigation?
The answers to these questions should be addressed in an international forum best suited for the salvation of the Earth. The authors do not make light of the fact that these issues are outstanding and of major concern.
5. 3D Models
The previous results were based on 2D cylindrically symmetrical simulations ultimately with porosity and credible internal compositions for an actual asteroid. We have recently started full 3D simulations similar to those shown in Fig. 4. These runs are quite expensive with a courant limited shock physics code. However, the initial runs have progressed to ~25 ms and show interesting differences to the 2D results.
The 3D simulation included porosity as described above and had random rock size distributions from 5m to 50 m within the outer shape of asteroid Itokawa. The initial results show that the shock seems to be significantly degraded compared to the 2D results at~25 ms. Realize that the 3D run needs to run to about 1-10 seconds to make a fair comparison. However, it appears that the 2D symmetry for a surface burst subtends a much larger solid angle (2D Torus’s) than the 3D simulation resulting in the significant reduction of shock strength in 3D. These 2D to 3D results are very preliminary and should wait for the 3D run to finish. The initial time sequence from the 3D run is shown in Fig. 5.
6. Conclusions
These initial full hydrocode simulations of non-spherical objects including porosity seem to show promise for a late time discovery of a PHO. The 2D bulk velocity imparted to the asteroid material is sufficient to mitigate the PHO hazard. The 3D runs are still in progress and thus the results of the simulations await their completion. The bottom line to these authors is that nuclear explosion options for recently discovered PHOs should not be eliminated and scientific hydrocode results tend to support this option. Radiation effects were not included in these results and will ultimately add to any effect simulated here.
References
[1] W.F. Huebner, The engagement space for countermeasures against potentially hazardous objects(PHOs), in: International Conference in Asteroid and Comet Hazards, the Russian Acamedy of Sciences, St. Petersburg, 2009.
[2] M. Gittings, R. Weaver, The RAGE radiation-hydrodynamics code, Comp. Sci. Disc. 1 (2008) 015005.
[3] R. Weaver, M. Clover, M. Gittings, The parallel implementation of RAGE: A 3D continuous adaptive mesh refinement radiation-hydrodynamics code, in: Proceedings of the 22st International Symposium on Shock Waves (ISSW22), London, 1999, paper 3560.
[4] G. Gisler, R. Weaver, Mader, Gittings, Two and three dimensional simulations of asteroid ocean impacts, Science of Tsunami Hazards 21 (2003) 119.
[5] G. Gisler, R. Weaver, C. Mader, M. Gittings, Two- and three-dimensional asteroid ocean impact simulations, International Journal of Impact Engineering 29 (2003) 283.
[6] G. Gisler, R. Weaver, C. Mader, M. Gittings, Two and three dimensional asteroid impact simulations, Computing in Science and Engineering 6 (2004) 38.
[7] NASA geometry courtesy of S.J. Osto et al. (2002) in Asteroids Book 3.
[8] Itokawa image courtesy of JAXA, http://www. isas.jaxa.jp/e/snews/2005/1102.shtml#pic001.
Received: December 21, 2011 / Accepted: January 10, 2012 / Published: February 15, 2012.
Abstract: This paper shows 2D and 3D simulations from a validated hydrocode (RAGE) of the effects of a strong explosion on the surface of a porous non-spherical asteroid like object. The composition of the simulated asteroid is made more realistic than previous work by using a random distribution of rocks constrained by a non-spherical outer surface. These simulations can be categorized as explosion effects on “rubble pile” asteroids. The main goal of this work is to apply realistic hydrodynamics to 2D and 3D rubble pile models and examine the results to see if sufficient momentum is transferred to the porous object so as to mitigate the hazard posed by the initially Earth crossing orbit.
Key words: Asteroid mitigation, nuclear explosions, potentially hazardous objects (PHOs).
1. Introduction
The authors have performed detailed hydrodynamic simulations of the shock interaction from a strong surface or subsurface explosion with sample asteroid objects. The purpose of these simulations is to apply modern hydrodynamic codes that have been well verified and validated (V&V) to the problem of mitigating the hazard from a potentially hazardous object (PHO), an asteroid or comet that is on an Earth crossing orbit [1]. The cod used for these simulations is the RAGE code from Los Alamos National Laboratory[2-6]. Ref. [2] contains many of the V&V reports for the code which were completed prior to publication. It should be noted for those not familiar with the RAGE code that it has been extensively V&V’d for shock physics and shock interactions with multiple materials. It is confident that the shock physics simulations presented here represent realistic hydrodynamics of the complex shock interactions, including the effect of the shock on the rocks themselves (assumed to be spherically shaped objects).
Initial runs were performed using a spherical object. We next ran simulations using the shape form from a known asteroid: 25143 Itokawa [7, 8]. This particular asteroid is not a PHO but we use its shape to consider the consequences of non-spherical objects. The initial work was performed using 2D cylindrically symmetric simulations and simple geometries (solid non-spherical objects). Next we progressed to Itokawa shaped models filled with uniform size “rocks”composed of granite and a solid background material(alluvium). These models had no porosity and were mainly done as a test of the code hydrodynamics. The first runs used a spherical energy source at the center of the object (typically 1 Mt), both with and without a“drill hole” which would be necessary to emplace an explosive at this location. Since the escape velocity of this object is very low, the disruption and bulk velocities indicated from these simulations is sufficient completely mitigate a PHO threat. That is to say, the velocities calculated were so large as to preclude re-assembly of the fragments and moreover ensure that with even modest lead times that all fragments would be pushed well beyond an Earth crossing orbit if the parent body was a PHO.
2. Methods
All of the simulations presented in this paper were performed with the RAGE hydrodynamic code from Los Alamos National Laboratory [2]. This code features a well verified and validated continuous adaptive mesh refinement (CAMR) described in Ref.[2] as well as the extensive validation done prior to the publication of that paper. We ran 2D cylindrically symmetric and 3D models of the shock interaction of a strong explosion with the asteroid material. Most of the results shown here are 2D simulations for ease of parametric studies and savings on computer time. Models were done for several parametric studies, including the effect of solid (no-porous) models, the effect of non-spherical models, the effect of similar strength explosions at various depths from the asteroid surface to the center of the object, long-side versus short side surface explosions as finally full 3D models. These models used source energies from 500 kt to 1 Mt, with most models run at 500 kt. The main physics employed in the multi-physics, multi-material RAGE code were the detailed CAMR Eulerian hydrodynamics and the material strength package, the Steinburg-Guinan (SG) model for the“rock” strength. Radiation is available in the code but was not used for these simulations. For simulations with radiation transport included, the effect of momentum transfer from the energy source to the asteroid will only increased, so these results represent lower limits to the momentum transferred to the model objects.
3. Models
The models used for these studies transitioned from simple to more complex. The models shown in this paper are:
(1) A non-spherical asteroid 25143 Itokawa shape with a uniform iron composition and a central explosion site. This model was done first to test the code for reasonable results and assess the effects of non-spherical models;
(2) Next we wrote a simple program to fill the non-spherical outer shape of the asteroid with a random distribution of rocks. These rocks could be of arbitrary size between size 1 and size 2 and were spherical in shape with the centroids within the asteroid surface. These models represent what we call“rubble pile” compositions, which is considered to be more realistic on average than uniform or spherical compositions;
(3) The first runs of this type were done with single size “rocks” (really torus’s in 2D) composed of granite material equation-of-state (EOS) with an alluvium background material. Thus these first runs had no porosity. It is generally believed that typical asteroids have porosities of 30%-40% due to multiple collisions and subsequent re-aggregation;
(4) Next we simulated porosity by removing the background alluvium and leaving the granite rocks. This resulted in porosities of 25%-40% (in 3D). The main effect of the high porosity is to significantly degrade the shock strength and therefore impart less momentum to the asteroid;
(5) We then modeled the effect of the depth-of-burial of the explosion from the center of the object to the surface and also the effect of short-side versus long-side surface bursts;
(6) Our final model in this series is running now and is a full 3D porous object filled with three different size rocks from 5m to 50m.
4. 2D Results
Work done previously to this meeting included the non-spherical uniform composition central explosion simulation with an energy of 1 Mt. The resulting images from the 2D RAGE simulation are shown in Fig. 1. This initial model indicated the importance of non-spherical geometry. The shock from the central explosion clearly reaches the surface of the asteroid along the shortest chord and ultimately ejects the two large end caps at a velocity of ~ 50 m/s due to the enormous pressure inside the explosion cavity at breakout time.
Next we used a program to fill the shape object with a distribution of rocks. This first simulation was done with a background material of alluvium and rocks composed of granite with SG strength. Thus this run had no porosity. Again dispersion velocities of all the asteroid material and “rocks” were calculated to be~1 m/s, significantly above the escape velocity. These results are shown in Fig. 2.
Next we explored the asteroid mitigation for various depths-of-burial of the explosion from the center to the surface. These results are shown in Fig. 3. Significant velocities (much greater than escape velocity) were imparted to all the asteroid material for each depth-of-burial from a surface burst to the centroid position. Given these results, the easiest mission to proceed with is a surface/contact burst mode. This mission could easily be un-manned and no“hollywood style” equipment would be necessary. The main focus from here forward will thus be on surface burst scenarios.
This initial set of RAGE simulations was meant to explore the parameter space of using this type of surface/subsurface explosion to totally disrupt an asteroid of ~500 m size. However, these simulations all had no porosity, which we then addressed in a fashion that is well suited to the RAGE code. Not knowing the exact internal composition of such an asteroid, but knowing it’s porosity is likely to be 30%-40% and it composition to be made of a distribution of rock materials, we started a new set of simulations. These simulations had two main advances that moved towards more realistic scenarios:(1) we used a distribution of rocks size: typically in a range from ~5 m spherical rocks to ~50 m spherical rocks randomly distributed in the outer shape of the asteroid; and (2) we added porosity to the simulations be removing the background alluvium. This left the initial geometry to be comprised of the rocks separated by porous void regions. This gave a total porosity of the simulated asteroid of ~20%-40% depending on the random distribution of rocks and on their size distribution. The result of these random size rock distributions with porosity gave the expected result of a weaking of the shock wave that translated into smaller velocities imparted to the asteroid materials. The typical reduction was about a factor of 5-10. Specifically for a surface burst (easiest mission), a 25% porous non-spherical 2D object was given a bulk velocity of ~6 m/s at 10 seconds after a 500 kt explosion (Fig. 4).
Fig. 1 The initial non-spherical uniform composition simulation with the RAGE hydrocode.
Fig. 2 The next RAGE simulation had “rubble pile” for a composition with uniform 5 m rocks and an alluvium background material. The velocity imparted to the asteroid material from the central 1 Mt explosion was again > 10m/s at 0.1 sec.
Fig. 3 The effects of the depth-of-burial of the explosion from a central location to the surface along both major directions. This study showed that explosions along the short side of this non-spherical object resulted in the greatest velocities (at 1 sec after explosion). These simulations had no porosity.
Fig. 4 The next set of simulations by removing the background alluvium material, leaving voids between the rocks. The depth-of-burial study was redone from both the long and short side of the asteroid. At this point we also varied the size distribution of the internal random rocks from ~5m to ~50m radius spheres. Although the bulk velocities were down ~5 times the explosion was still more than adequate to totally disrupt the asteroid.
Fig. 5 The first 3D simulation analogous to the 2D porous surface burst shown in Fig. 4 but with a 1 Mt source energy. The shock seems to dissipate more strongly in 3D than 2D. However, final conclusions require the 3D run to complete.
In summary the effect of the porosity as modeled in 2D here with the RAGE code indicate that even for at 500 kt explosion (modest energy) and significant porosity (~20%) the asteroid material was given a bulk velocity of ~>5 m/s at 10 seconds, sufficient to mitigate the PHO hazard. Thus for short notice PHO’s one should not consider the nuclear explosive option as “off the table”. There are clearly significant international issues to be resolved:
which nuclear country will be given the lead on such a mission?
which international organization will be in charge of such a mission?
should multiple missions be undertaken (at the same time) to ensure mitigation?
The answers to these questions should be addressed in an international forum best suited for the salvation of the Earth. The authors do not make light of the fact that these issues are outstanding and of major concern.
5. 3D Models
The previous results were based on 2D cylindrically symmetrical simulations ultimately with porosity and credible internal compositions for an actual asteroid. We have recently started full 3D simulations similar to those shown in Fig. 4. These runs are quite expensive with a courant limited shock physics code. However, the initial runs have progressed to ~25 ms and show interesting differences to the 2D results.
The 3D simulation included porosity as described above and had random rock size distributions from 5m to 50 m within the outer shape of asteroid Itokawa. The initial results show that the shock seems to be significantly degraded compared to the 2D results at~25 ms. Realize that the 3D run needs to run to about 1-10 seconds to make a fair comparison. However, it appears that the 2D symmetry for a surface burst subtends a much larger solid angle (2D Torus’s) than the 3D simulation resulting in the significant reduction of shock strength in 3D. These 2D to 3D results are very preliminary and should wait for the 3D run to finish. The initial time sequence from the 3D run is shown in Fig. 5.
6. Conclusions
These initial full hydrocode simulations of non-spherical objects including porosity seem to show promise for a late time discovery of a PHO. The 2D bulk velocity imparted to the asteroid material is sufficient to mitigate the PHO hazard. The 3D runs are still in progress and thus the results of the simulations await their completion. The bottom line to these authors is that nuclear explosion options for recently discovered PHOs should not be eliminated and scientific hydrocode results tend to support this option. Radiation effects were not included in these results and will ultimately add to any effect simulated here.
References
[1] W.F. Huebner, The engagement space for countermeasures against potentially hazardous objects(PHOs), in: International Conference in Asteroid and Comet Hazards, the Russian Acamedy of Sciences, St. Petersburg, 2009.
[2] M. Gittings, R. Weaver, The RAGE radiation-hydrodynamics code, Comp. Sci. Disc. 1 (2008) 015005.
[3] R. Weaver, M. Clover, M. Gittings, The parallel implementation of RAGE: A 3D continuous adaptive mesh refinement radiation-hydrodynamics code, in: Proceedings of the 22st International Symposium on Shock Waves (ISSW22), London, 1999, paper 3560.
[4] G. Gisler, R. Weaver, Mader, Gittings, Two and three dimensional simulations of asteroid ocean impacts, Science of Tsunami Hazards 21 (2003) 119.
[5] G. Gisler, R. Weaver, C. Mader, M. Gittings, Two- and three-dimensional asteroid ocean impact simulations, International Journal of Impact Engineering 29 (2003) 283.
[6] G. Gisler, R. Weaver, C. Mader, M. Gittings, Two and three dimensional asteroid impact simulations, Computing in Science and Engineering 6 (2004) 38.
[7] NASA geometry courtesy of S.J. Osto et al. (2002) in Asteroids Book 3.
[8] Itokawa image courtesy of JAXA, http://www. isas.jaxa.jp/e/snews/2005/1102.shtml#pic001.