36
LLNL-PRES-659183 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and was partially funded by the Laboratory Directed Research and Development Program at LLNL under tracking code 12-ERD-005. Lawrence Livermore National Security, LLC. 13 January 2016 Future In-Space Operations (FISO) Telecon

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Page 1: 13 January 2016 Future In-Space Operations (FISO) Telecon · 13 January 2016 Future In-Space Operations (FISO) Telecon . ... Cody Raskin Jared Rovny (summer) William Schill (summer)

LLNL-PRES-659183 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and was partially funded by the Laboratory Directed Research and Development Program at LLNL under tracking code 12-ERD-005. Lawrence Livermore National Security, LLC.

13 January 2016 Future In-Space Operations (FISO) Telecon

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Lawrence Livermore National Laboratory LLNL-PRES-659183 2

§  Background on the threat •  Historical events •  Governmental interest

§  Options •  Emergency response •  Deflection

—  Kinetic Impactor

—  Nuclear Ablation

•  Disruption & Dispersal

§  Research drivers

Overview

Asteroid impacts are a national-security threat requiring advanced science and technology solutions.

“Blue Marble” image from NASA

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Lawrence Livermore National Laboratory LLNL-PRES-659183 3

Peter Anninos

Tarabay Antoun

Laura Chen (grad student)

David Dearborn

Deborah Dennison

James Elliott

Souheil Ezzedine

Seran Gibbard

Eric Herbold

Kirsten Howley

Brian Kaplinger (summer)

Patrick King (summer)

Ilya Lomov

Robert Managan

Aaron Miles

Paul Miller (Project Lead)

Michael Owen

Cody Raskin

Jared Rovny (summer)

William Schill (summer)

Megan Syal (postdoc)

Damian Swift

Joseph Wasem

Sean Whitney (summer)

Participants

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Lawrence Livermore National Laboratory LLNL-PRES-659183 4

§  A Near-Earth Asteroid (NEA) has a perihelion less than 1.3 AU (1.3 times the Earth-Sun distance)

Background

12,748 known NEAs (June 2015)

872 NEAs larger than 1 km (global catastrophe-sized)

Figures: Alan B. Chamberlin (JPL)

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Lawrence Livermore National Laboratory LLNL-PRES-659183 5

Size: ~20 m diameter Yield: about 0.5 Mt Approx. 1500 injuries

Background

Images from Wikipedia

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Lawrence Livermore National Laboratory LLNL-PRES-659183 6

~90% 1 km or larger NEAs discovered Surveys much less complete for smaller sizes

Background

NEA data: Harris and D’Abramo (2015)

K-T melted/

vaporized region

Reproduced with permission from Stephen Nelson

Fallen trees, Tunguska

Image source: Wikipedia

Che

lyab

insk

Tung

uska

K-T

Bou

ndar

y

Threshold of Global Catastrophe

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Lawrence Livermore National Laboratory LLNL-PRES-659183 7

§  1992: U.S. Congress tasks NASA with locating NEOs larger than 1 km

§  2007: NASA “Near-Earth Object Survey and Deflection Analysis of Alternatives” Report to Congress

§  2008: NASA Authorization Act — NASA lead agency for NEO detection and deflection mission

§  2010: OSTP Letter (John Holdren) to Congress

§  2010: NRC (National Academies) report to Congress, identifies nuclear as only option for larger objects (≥ 1 km)

§  2013: NASA-FEMA TTX at FEMA HQ

§  2014: NASA-FEMA TTX2; NASA-DARPA meeting

§  2015: NASA-NNSA Interagency Agreement Signed, Planetary Defense Coordination Office (PDCO) set up

U.S. Government Interest

Image from Wikimedia

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Lawrence Livermore National Laboratory LLNL-PRES-659183 8

NNSA capabilities

We have the capabilities to address this problem

Castle Bravo explosion

§  High Performance Computing and 3-D simulations

§  Multi-physics modeling

§  Nuclear-explosive physics and function

§  Algorithmic development

§  Hydrodynamic simulation

§  Equation of State and opacity modeling

§  Material strength, damage, and failure

§  Validation & Verification and Uncertainty Quantification

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Lawrence Livermore National Laboratory LLNL-PRES-659183 9

Interactions include: §  Support to other agencies

§  University collaborations

§  Postdocs

§  Summer students

§  National and international conferences

Benefits Interactions

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Lawrence Livermore National Laboratory LLNL-PRES-659183 10

ISAS/JAXA

Option 1: Take the hit — Emergency Response Option 2: Deflection (push it off course)

a. Kinetic Impactor b. Nuclear Ablation

Option 3: Disruption (break it up and disperse it)

Options

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Lawrence Livermore National Laboratory LLNL-PRES-659183 11

Option 1: Emergency Response

50m Fe-Ni, 39 deg, 10 Mt

The evolution of the probability-of-impact is one of the greatest challenges, particularly for short-warning impacts

Uncertainty ellipse at three weeks

Two weeks

Eight days

Images: Paul Chodas (JPL)

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Lawrence Livermore National Laboratory LLNL-PRES-659183 12

50m Fe-Ni, 39 deg, 10 Mt

Credit: S. Ezzedine (GEODYN and SWWP codes)

Air

Ocean Water rims

50m Fe-Ni, 39o, 10Mt

time

Impact

USA

Mexico

±3m wave heights

Cuba

T=+0hr T=+1hr T=+2hr

T=+3hr T=+4hr T=+5hr

Coupling between GEODYN and SWWP enables bridging the spatio-temporal scale disparities between non-linear near-field and the linear far-field physics.

Option 1: Emergency Response

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Lawrence Livermore National Laboratory LLNL-PRES-659183 13

Option 2: Deflection

Details will depend on individual asteroid’s orbit (Ahrens and Harris, 1992)

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Lawrence Livermore National Laboratory LLNL-PRES-659183 14

What To Do?!

Start with Newton: !

Push in direction of motion (T). Changes the Period. Miss distance increases with time.!

Speed Change!(Conservation of momentum)!

Deflection !Speed!

=!

What To Do?!

Start with Newton: !

Push in direction of motion (T). Changes the Period. Miss distance increases with time.!

Speed Change!(Conservation of momentum)!

Deflection !Speed!

=!

Options include pushing: •  Along orbit (T) •  Out of plane (W) •  In plane, normal to orbit (N)

Pushing along the orbit • Changes the period • Deflection increases with time • Usually most effective direction

Option 2: Deflection

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Lawrence Livermore National Laboratory LLNL-PRES-659183 15

Deflection by Kinetic Impact: Sensitivity of Response to Asteroid Properties

Megan Bruck Syala,⇤, J. Michael Owena, Cody D. Raskina, Paul L. Millera

a

Lawrence Livermore National Laboratory, Livermore, CA 94551, USA

Abstract

Keywords: Asteroids, Impact processes, Cratering, Asteroids, dynamics, Asteroids, rotation

1. Introduction

Asteroids which pose a threat to Earth may be deflectedo↵ of an Earth-impacting trajectory by stando↵ nuclear bursts(Bruck Syal et al., 2013; Howley et al., 2014) or kinetic im-pactors (Holsapple and Housen, 2012; Jutzi and Michel, 2014).Among the range of proposed concepts for asteroid mitiga-tion, these two methods are considered to be the most tech-nologically mature, as discussed in the report by the NationalResearch Council (2010). Nuclear devices represent the onlyviable option to prevent Earth impacts for large asteroids orthose detected with little warning time (Dearborn and Miller,2014); however, under conditions where a kinetic impactor willbe e↵ective, it is the preferred strategy. Hence, studies whichquantify the e↵ectiveness, risks, and uncertainties for the ki-netic impactor method, under a range of initial conditions, arenecessary. Planetary-scale experiments to test the e�cacy ofkinetic impactors are rare; these valuable opportunities must becomplemented by extensive numerical treatment of the prob-lem. The Deep Impact mission successfully deployed a 370 kgimpactor to remotely excavate the surface of Comet Tempel 1in 2005 (A’Hearn et al., 2005; Schultz et al., 2007), providingthe first demonstration of kinetic impact technology on a smallbody. While the large size of Tempel 1 precluded a measure-ment of the body’s change in velocity, future asteroid defense-focused missions will aim to directly measure the momentumtransfer imparted by kinetic impactors. In particular, the AIDAmission, a joint ESA and NASA venture, will seek to providethe first quantitative test of asteroid deflection, using the DARTspacecraft to impact the secondary of asteroid Didymos (Chenget al., 2015).

A spacecraft impacting along an asteroid’s center of masswill transfer all of its momentum, p

i

= m

i

v

i

, to the body, chang-ing the asteroid’s translational velocity by �v = m

i

v

i

/ma

. Anadditional transfer of momentum is achieved through the crater-ing process, as material is ejected above escape speed, oppositeto the direction of impact. This additive e↵ect to the momentumtransfer can be expressed as:

�vm

a

= m

i

v

i

+ m

e j

v

e j

= �mi

v

i

(1)

⇤Corresponding author, 1-925-423-0435Email address: [email protected] (Megan Bruck Syal)

where � denotes the multiplication factor applied to the im-pactor’s momentum by crater ejecta. The value of � is oneof the primary uncertainties associated with the use of kineticimpactors. It is known to be dependent on both the asteroid’smaterial properties and the impactor velocity (Holsapple andHousen, 2012; Jutzi and Michel, 2014; Stickle et al., 2015);thus, it may vary substantially between di↵erent deflection sce-narios. The AIDA mission will provide a critical first measure-ment of � for an actual asteroid deflection event.

Owing to the diversity of near-Earth asteroids which maythreaten Earth in the future, numerical study of kinetic impactdeflection, including variability in details such as composition,porosity, strength, internal structure, shape, and rotation, canprovide guidelines for kinetic impactor mission design, includ-ing pre-impact reconnaissance of the asteroid. Additionally, nu-merical calculations, performed for a range of conditions, helpdefine the current limitations of the kinetic impact approach.Advance knowledge of scenarios where other mitigation meth-ods would be necessary (or present lower cumulative risk) canspeed the response of international decision makers in the eventof an emergency.

Prior numerical study of kinetic impact deflection has fo-cused on planar target geometries (Jutzi and Michel, 2014), ora limited number of cases to simulate the relatively low-speed(⇠6 km/s) AIDA mission impact (Stickle et al., 2015). Both ofthese studies used modest impactor masses (300 kg), similar tothe planned mass to be delivered by the DART impactor duringthe AIDA event. The present paper, in contrast, seeks to re-solve the limitations and sensitivities of the kinetic impactor ap-proach within a somewhat broader context, by modeling entireasteroid bodies, using larger impactor masses (1000 - 10,000kg, representative of the limits posed by current launch vehi-cle technology), and probing response sensitivity to a range ofasteroid characteristics. Specific asteroid-dependent parame-ters explored in this work include: equation of state, porosity,strength/damage, and rotational state. In addition, we considerthe e↵ects of varying impactor velocity, numerical resolution,and the volume of asteroid that is modeled. Our results are in-tended to serve as a guide for future calculations incorporatingthe details of specific asteroids or including additional varia-tions in shape, composition, and internal structure, for both theasteroid and impactor.

Preprint submitted to Icarus June 22, 2015

Credit: Megan Bruck Syal, Spheral ASPH code

β =1+pejectapimpactor

Option 2: Deflection

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Lawrence Livermore National Laboratory LLNL-PRES-659183 16

Option 2: Deflection

Constraints on Kinetic Impactor Approach:

§  Transportable mass may not be sufficient (given current launch vehicle capabilities)

§  Surface ablation: more mass-efficient

§  Risk of unintentional disruption for smaller bodies with short warning times

§  Could create poorly-dispersed debris field

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Lawrence Livermore National Laboratory LLNL-PRES-659183 17

Option 2: Deflection

Credit: Ilya Lomov, GEODYN code

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Lawrence Livermore National Laboratory LLNL-PRES-659183 18

Option 3: Disruption

Credit: J. Michael Owen, Spheral ASPH code

From the 2013 NASA-FEMA TTX: •  50-m iron-nickel asteroid

•  High density

•  Moderate porosity •  Megaton proximity explosion

Strategy: •  Rapid dispersal

•  Small pieces (atmosphere

protects against < 10 meters)

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Lawrence Livermore National Laboratory LLNL-PRES-659183 19 Figure: Bruck Syal et al., (2013)

fragmented. In the porous body, more than 65% of thematerial is nominally bound and is expected to coalesce.The momentum in this bound material provides a speedchange of several centimeters per second. Propagating thebound piece and individual fragments from these modelsalong an orbit (a!2 AU, e!0.5), shows that the porosityactually provided a superior result (Fig. 8).

The fragmented (non-porous) model was weakly dis-persed, and, even after 100 days, most of the materialwould still impact the Earth. The speed increment asso-ciated with the bound portion of the porous modelresulted in a successful miss by this material after only60 days. With earlier dispersal, the debris field of theejected material expands at about the same rate as thenon-porous model, but as the mass fraction of the debrisis smaller, the cumulative impacting material is belowthat of Tunguska after only 200 days (Fig. 8). This pair ofsimulations shows that a 70 kt yield is too high for thisheight of burst (HOB) on a 270 m body and demonstratesthat we can recover the weakly fragmented case thatshould be avoided. It also provides the interesting resultthat, in an energy rich environment, porosity can actuallyimprove the odds of a successful deflection. In the absence

of a characterization mission, and with the need for astrong push, assuming non-porous is the conservativechoice.

This next pair of models reduced the source yield to7.0 kt at the same 60 m HOB, such that 1.70 kt irradiatesthe surface of the asteroid (1.19 kt of total absorbedenergy). By maintaining the burst height, the energyheated the same azimuthal region as the previous calcu-lation. The amount of material that was still nominallybound was between 60 and 65% in both the porous andnon-porous models (Fig. 9). The coalesced pieces of thenon-porous model had higher speed, missing Earth afteronly 20 days of flight, but even the large piece of theporous model missed by 60 days (Fig. 10). Here the timefor the cumulative volume of the threatening fragmentsto drop below a Tunguska-sized event is about 300 days.

For a simple deflection, the 7.0 kt yield is still too high(or, alternatively, the HOB too low). Stepping down againin yield, models were run for a 0.5 kt burst detonated at a60 m HOB (0.0852 kt of total absorbed energy). Most ofthe material (499.7% of the body) remained bound inthis case (Fig. 11). The speed change imparted to thebound portion was !3 mm/s for the nonporous case andjust !1 mm/s for the porous case. While these deflectionvelocities may be appropriate for situations involvingrelatively large warning times (decades), the factor ofthree difference in asteroid response between the non-porous and porous cases illustrates the importance ofquantifying a body0s material properties prior to deploy-ing an impulsive deflection method. In addition, it shouldbe noted that the porosities of many asteroids greatlyexceed the modest value of F¼0.16 used in this study[19], which was limited by the availability of experimen-tal crush curve data.

For this last 0.5 kt yield case, it is instructive tocompare the calculated velocity change (du) with anestimate derived from an analytical approach to theproblem. An approximate expression for a standoffburst-delivered velocity change is du¼0.1Ay/D3, where yis total neutron yield in kt (here, 0.35 kt), A represents adimensionless efficiency factor (here, !0.3), D is asteroiddiameter in km (0.27 km), and du is deflection velocity incm/s [20]. For these parameters, du!5.33 mm/s, a slightlylarger impulse than the numerical results obtained inthis study for the nonporous asteroid (du!3 mm/s). The

Fig. 7. Kinetic to potential energy ratios for the non-porous (left) and porous (right) asteroid models, plotted 6 s after a 70 kt standoff burst (HOB¼60 m).Material with speeds above escape velocity appears purple; green through red material has insufficient kinetic energy to escape the gravitationalpotential. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. The percentage of the asteroid0s total mass that will impact Earthfor both the porous (red) and non-porous (blue) cases is plotted as afunction of days until impact (70 kt burst). (For interpretation of thereferences to color in this figure legend, the reader is referred to the webversion of this article.)

M. Bruck Syal et al. / Acta Astronautica 90 (2013) 103–111108

Cumulative Volume: Tunguska Size

Porous

Non-porous

Per

cent

age

Impa

ctin

g

Days to Impact 101 102 103 104

100

10

1

0.1

0.01

0.001

Option 3: Disruption

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Lawrence Livermore National Laboratory LLNL-PRES-659183 20

Credit: David Dearborn

Mitigation Strategies

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Lawrence Livermore National Laboratory LLNL-PRES-659183 21

Credit: David Dearborn

Mitigation Strategies

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Lawrence Livermore National Laboratory LLNL-PRES-659183 22

Energy Deposition

Internal structure Porosity Shape

Rotation

Image Credits: Megan Bruck Syal, J. Michael Owen, Eric Herbold

b.

c.

Damage Trace

0.00

0.75

1.50

2.25

3.00 a.

Resolution Strength

Research drivers

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Lawrence Livermore National Laboratory LLNL-PRES-659183 23

AIDA (AIM+DART) Mission Concept

Image Credit: ESA

§  Prioritization of asteroid characteristics for deflection: input for small body characterization missions

§  May affect deflection strategy §  Critical for interpretation of

results from rare, full-scale impact experiments, e.g. AIDA

Research drivers

LLNL: contributor to DART Working Group 1, numerical modeling of deflection event

Didymos secondary: ~150 m

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Lawrence Livermore National Laboratory LLNL-PRES-659183 24

§  Equations-of-state for modeling (including melting/vaporization points) —  Essential for imparted-Δv estimates

§  Nuclear-generated x-ray deposition —  especially the thin layer at the surface

§  Sets density at the grain scale

In particular, the presence of high-Z (metals) or low-Z (volatiles) elements plays a big role

Composition

Table credit: Kirsten Howley and Rob Managan

X-ray penetration depths into four materials

Material Density (g/cm3)

1 keV depth (µm)

10 keV depth (µm)

Ice 1.0 2.4 1900

Quartz 2.65 1.2 200

Forsterite 3.25 1.1 190

Fe-Ni 7.5 0.14 8

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Lawrence Livermore National Laboratory LLNL-PRES-659183 25

!0 200 400 600 800 1000 aaaaaaa"Height of Burst (m)

0

5

10

15

20

25

Del

ta v

(cm

/s)

vescape

Ice

Wet Tuff

Granite

SiO2

Hydrated Forsterite

Composition

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Lawrence Livermore National Laboratory LLNL-PRES-659183 26

Strength/Damage

Y0 = 1 kPa

Y0 = 100 MPa

Damage t = 0.108 s

100 102 104 106 1081

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Cohesion (Pa)

β

Pressure-dependent strengthvon Mises strength

(no strength)

pile structures, remains a priority for later studies. A nominal spherical shape was used to110

model each asteroid, for straightforward comparison across a range of parameters. However,111

as discussed in Section 3.5, asteroid shape introduces non-trivial changes to the imparted112

deflection velocity and should be accounted for in uncertainty assessments.113

Most asteroids for which bulk-density information is available are believed to contain114

significant porosity, in the form of microporosity (at the grain level), macroporosity (larger115

voids between boulders and rubble-pile fragments), or some combination of the two (Britt116

and Consolmagno, 2000; Britt et al., 2002; Lindsay et al., 2015). Here we focus on microp-117

orosity; investigating the e↵ects of macroporous structures is reserved for future calculations.118

Spheral uses a strain-based approach, defined in Wunnemann et al. (2006), to include aster-119

oid microporosity. The strain-based porosity method, termed the ✏-alpha model, contains120

an elastic regime, an exponential-compaction regime, and a power-law compaction regime;121

only the initial porosity �, elastic-plastic transition strain ✏e, power law transition strain ✏X ,122

and exponential compaction rate need to be defined (Wunnemann et al., 2006). Values123

used for these parameters are listed in Table 1.124

Asteroid strength was included using either a von Mises yield criterion (constant strength)125

or a pressure-dependent model for strength:126

Yi = Y0 +µiP

1 + µiP/(YM � Y0)(2)

where Y0 is shear strength at zero pressure (cohesion), µi is the coe�cient of internal friction,127

and YM is the von Mises plastic limit of the material (Lundborg, 1968; Collins et al., 2004).128

Recent work highlights the importance of including pressure-dependent constitutive models129

when calculating the outcomes of asteroid collisions (Jutzi, 2015); hence, most simulations130

reported here used a pressure-dependent strength model. As direct measurements of asteroid131

strength are not yet available, a range of values for asteroid cohesion, Y0 (yield strength at132

zero pressure), were explored: Y0 = 1 kPa - 100 MPa. The lower end of this range corresponds133

to typical values for weak soils (e.g., lunar regolith), while the upper end is representative134

of strong, competent rock. In the absence of available yield-strength data on asteroidal135

materials at high pressures, a constant value of Ym = 1.5 GPa was assumed (Collins et al.,136

2004). A value of µi = 1.2, consistent with the 50� angle of internal friction determined for137

6

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Lawrence Livermore National Laboratory LLNL-PRES-659183 27

Porosity

Φ = 0.0

Φ = 0.5

Pressure t = 6 ms

0 0.1 0.2 0.3 0.4 0.51

1.5

2

2.5

3

3.5

4

4.5

5

Porosity (φ)

β

Y0 = 1 kPaY0 = 100 MPa

0 0.1 0.2 0.3 0.4 0.51

1.5

2

2.5

3

3.5

4

4.5

5

Porosity (φ)

β

Y0 = 1 kPaY0 = 100 MPa

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Lawrence Livermore National Laboratory LLNL-PRES-659183 28

Porosity

0 0.1 0.2 0.3 0.4 0.5

1

2

3

4

5

6

Porosity (φ)

∆v(cm/s)

Y0 = 1 kPaY0 = 100 MPaEscape Velocity

0 0.02 0.04 0.06 0.08 0.10

0.05

0.1

0.15

0.2

0.25

Time (s)

FractionDisru

pted

Φ = 0.0Φ = 0.1Φ = 0.2Φ = 0.3Φ = 0.4Φ = 0.5

Larger Δv at greater porosities, shown for 100 m asteroids

Even a little porosity protects against unintentional disruption

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Lawrence Livermore National Laboratory LLNL-PRES-659183 29

Rotating

Rotation

0 0.05 0.1 0.15 0.2 0.25 0.3 0.351

1.5

2

2.5

3

3.5

Time (s)

β

P = 100 s, StrengthlessNon-rotating, StrengthlessP = 100 s, StrengthNon-rotating, Strength

Non-rotating

Disrupted material

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Lawrence Livermore National Laboratory LLNL-PRES-659183 30

§  Ejecta momentum oriented normal to surface, not in direction of impactor §  Consistent with analytical models (Scheeres et al., 2015) §  Local slope of impact point may be difficult to control/predict §  Detailed look at shape effects in Feldhacker et al. (2016)

Damage Trace

0.00

0.75

1.50

2.25

3.00

Asteroid Golevka

Shape

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Shape

Angle between ejecta momentum vector and impact direction, for impacts along Golevka’s principal axes

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Shape

Credit: J. Michael Owen, Spheral ASPH code

1 Mt source of 2 keV X-rays.•  350 m from center of Bennu (88 m HOB) •  65% reradiation yields 51.1 kt deposited.

Deflec%on(velocity(

Deflec%on(angle(

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Velocity

1 100.1

1

10

Velocity (km/s)

β-1

Y0 = 1 kPa, φ = 0.4µ = 0.44 power-law

asteroid’s principal axes, the final direction of push is not through the asteroid’s center of287

mass, as the ejecta momentum vector is directed 7 degrees o↵ axis. Variations associated288

with local topography can thereby degrade the e�cacy of the kinetic-impactor approach,289

leading to a smaller e↵ective � (where � is defined as the momentum multiplication along290

the impact trajectory). In this case, the final � calculated is 2.33, which corresponds to a291

modest change in velocity of �v ⇠ 1 mm/s.292

3.6. Velocity Scaling293

While a nominal impact velocity of 10 km/s was employed for most simulations in this294

study, we investigated the velocity scaling for momentum transfer, for comparison with ana-295

lytical models and available experimental data (Holsapple and Housen, 2012). Experiments296

are necessarily limited to smaller impact sizes and lower velocity regimes (< 6 km/s). Nu-297

merical modeling allows the full range of likely encounter velocities to be investigated at the298

impact-size regime of interest for asteroid deflection.299

Based upon point-source scaling relations, the velocity scaling for the momentum of300

escaping ejecta, P , relative to impactor momentum, mU , should follow a power law:301

P

mU= � � 1 ⇠ U3µ�1 (3)

where µ is the velocity-scaling exponent of the impact coupling parameter from point-source302

solutions (Holsapple and Schmidt, 1987; Holsapple and Housen, 2012). The value of µ is303

material dependent and may vary between the limits imposed by pure momentum scaling304

(µ = 1/3) and pure energy scaling (µ = 2/3). Experiments using geological materials find305

that µ generally ranges from 0.4 to 0.55 (Holsapple, 1993; Holsapple and Housen, 2012).306

Results from impact velocities ranging from 1 km/s to 30 km/s are plotted in Figure307

10. This set of simulations used low-cohesion (Y0 = 1 kPa) and 40% porous material. A308

power-law fit to the data yields µ = 0.44, intermediate between experimentally determined309

values of µ for sand and competent rock (Holsapple, 1993). Although prior numerical study310

by Jutzi and Michel (2014) found impacts 5-15 km/s to be described by µ = 0.62, closer to311

pure energy scaling, this di↵erence can be attributed to the higher value of cohesion used in312

that study, Y0 = 100 MPa, representative of relatively strong rock.313

18

§  Power-law slope depends on geological material properties

§  Experiments: v < 6 km/s §  Simulations extend this to

mission-relevant velocities (1-30 km/s)

§  µ = 0.44: between sand (µ=0.41) and rock (µ=0.55)

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Resolution

10 15 20 25 30 35 40 45 50

1

1.05

1.1

1.15

Spatial Resolution (cm)

β/β

hi−

res

b.

c.

Damage Trace

0.00

0.75

1.50

2.25

3.00 a.

Increasing resolution

Resolution studies define where numerical convergence occurs

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Lawrence Livermore National Laboratory LLNL-PRES-659183 35

§  Less frequent but more dangerous; potential global catastrophe

§  Large, high-speed, short warning

§  Both intercept and deflection/disruption are difficult

§  Jetting can cause perturbations in trajectories

Comets

Credits: ESA/Rosetta/NAVCAM – CC BY-SA IGO 3.0. Edit by Jason Major.

§  Current discussion on asteroids; comets are not forgotten

§  As surveys find asteroids, comets represent a greater fraction of unknown risk

Comet Churyumov-Gerasimenko

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Lawrence Livermore National Laboratory LLNL-PRES-659183 36

§  Asteroid impacts present a range of threats, including rare but very high-consequence ones

§  Emergency response, deflection and/or disruption approaches may be employed, depending on the situation

§  The challenge derives from both difficult science problems and lack of knowledge of initial conditions

§  A scenario-based approach is needed, because every case is unique and it is an integrated problem

Summary

See also: Bruck Syal et al. 2016. Deflection by Kinetic Impact: Sensitivity to Asteroid Properties. Icarus, Accepted.