dr. david s. p. dearborn lawrence livermore national...

Dr. David S. P. Dearborn Lawrence Livermore National Laboratory

UCRL-PRES-152247 and UCRL-PRES-202489This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory

Asteroid Crossing

Danger

Over 150 Recognized Terrestrial Impact Craters

Sudbury Crater1.8 billion200 km diameter 31,000 cubic kilometers of impact melt (Chicxulub has about 18,000 )

Tswaing CraterSouth Africa220,000 years old1.1 km diameter

(Data from Planetary and Space Science Center, University of New Brunswick)

Sierra Madera CraterFt. Stockton Texas<100 million years old13 km diameter

Map from UT Permian Basin

Risk Factors

SpeedMinimum ≈10 km/s inner solar system body overtaking the earth + Earth’s potential.

Maximum =72 km/s outer solar system body in retrograde orbit.

For 20 km/s, ε=47.8 Mega-Calories/kilogram = 50X TNT

Size and Density = MassChondrites 3.4 g/ccCarbonaceous chondrites 2.6 g/ccAverage 3.0 g/cc.

Rubble 1-2 g/cc.

metallic (Only 3 to 8% ) >7 g/cc

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LargeSmall

From NASA’s NEO Science Definition Team Report:Dead Slow <3 km/s

Future?LSST:

Large-aperture Synoptic Survey Telescope8 meter telescope capable of seeing the whole sky to 24th magnitude every 3 nights. Able to

detect asteroids >200 meters.

• High priority of National Academy Decadal Survey• Science: things that change

– Near Earth asteroids, Kuiper Belt comets, Supernovae, Gamma Ray Bursts, ...

• Technical challenges:– 2.3 gigapixel camera– Optical fabrication and testing– Giant data mining challenge (>5 terabytes/night)

PresentDiscovery teams using meter class telescopes with CCD’s

Lincoln Near-Earth Asteroid Research (LINEAR)Near-Earth Asteroid Tracking (NEAT)SpacewatchLowell Observatory Near-Earth Object Search (LONEOS)Catalina Sky Survey Japanese Spaceguard Association (JSGA) Asiago DLR Asteroid Survey (ADAS)

NEAR-EARTH OBJECT SEARCH PROGRAMS

The LINEAR GTS-2 1 meter telescope

Orbits Change: Precession

It is a 3D problem: Most NEO orbits do not actually intersect the earth’s orbit.

Orbit precession results in 4 intersections per cycle.(The orbits intersect along the line of Nodes)

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The frequency of intersections depend on the precession rate, (δΩ/dt), while the time pent at an intersection depends inversely on this rate. As a result, it cancels out.

Collision Probability

Low inclination orbits have increased probability of impact.

Earth Crossing Orbits lie between the blue lines.

Rate(per / year) ≈1.66 ×10−9 1+Sin2(i)

(e2 −1) + 2a − 1

a2

⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

1− P 2

P 2Tan(i)

- Primarily from ground-based optical searches (some radar)- Size range 10 meters and 30 kilometer- Estimated population about one million (>50 meters)

>2,225 Near-Earth Objects (NEO’s) Are Known.

> There are currently no large (>10 Km) asteroids that threaten the earth.

> The survey is incomplete for moderate (1 km) sized bodies - wait until 2008.

Averaging over the observed orbital properties of 1172 NEO’s:

Collisions/yr ≈ Ntot 6X10-9

Ntot > D (meters)3X107 105X105 100

103 1000

The collision probability per century for the 1172earth crossing NEO’s using NASA data.

The Flux of Small Near-Earth Objects Colliding With the Earth

More than 300 optical flashes Over the last 8 years (DOD satellites ).

The energy-frequency relationship agrees with infrasonic measurements.

Rates extrapolate to the expected values from NEO’s (but everything fits on 14 cycle log graphs)

Brown et al. Nature 420: 294-296 (21 November 2002)

Impact Rates Brown et al.,

“The Flux of Small Near-Earth Objects Colliding With the Earth”Nature 420: 294-296 21, November 2002

Duration of Planetary Defense

Conference


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Error Ellipsoids

δR = VδP ≈32

Vδaa

P

Position Uncertainty

The accuracy necessary to predict a probable impact one century in the future

requires observations over many orbits.

Let there be Light

M=mass of bodyr = radiusd = distance from sunAl= albedo

e = eccentricityρ = density (g/cc)M15 = mass in units of 1015 grams

Light absorption or reflection produces an acceleration that reduces the central force:

Acceleration =(1+ Al )

4 MLsun

crd

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

τ (centuries) =145Al(1−e)(1+ e)

ρ2 / 3M151/ 3

τ M D Paint

46.0 1015 1.0 2504.6 1012 0.1 80

centuries grams km tons

For a body of density 2 g/cc and e=0.5:

To change the path of a body on an impacting orbit enough to miss, you must begin early. The time required to miss by an earth radius is:

We have ignored the more important Yarkovsky effect associated with re-radiating the energy. Depends on many unknowns:

Nature Does Not Stop There!Not currently possible to know an asteroid orbit well enough to predict an impact in 4 centuries (much less 40).

Over a few centuries, uncertainty in the asteroid position from this source far exceeds other error sources.

Painting it white and waiting is as likely to cause a hit as a miss.

Asteroid shapeSurface Composition (Iron, olivine, …)Surface structure (solid, rubble)Rotation speed and DirectionFull inertia tensor

DA 1950Giorgini et al, 2002, Science, Apr 2002 v296, p132-136

A slightly asymmetrical spheroid with a mean diameter of 1.1 km,rotating once every 2.1 hours (requiring a density > 2.9 g/cc - not rubble).

First discovered on 23 Feb 1950 then lost.

Serendipitously rediscovered at Aricebo (radar) in March of 2001, when the body passed within 0.05 AU of earth (S Ostro - JPL).

Along-track effect Distance (Rearth) Time---------------------------------------------------------------------------------------------

Galactic tide -1.3 -10 minNumerical integration error -1.6 -12 minSolar mass loss +2.1 +16 minSolar oblateness (J2) +6.5 to +2.8 +49 to +21 min61 additional asteroids -235 -1.2 daysPlanetary mass uncertainty +215 to -240 +1.1 to -1.3 daysSolar radiation pressure -1,750 -9.1 daysCombined above -1,725 to -2,760 -9.0 to -14.0 daysYarkovsky effect only +1,870 to -11,000 +9.6 to -57.0 days

The collision probability on Saturday 16 March 2880 AD is in the range 0.33%.

Error Ellipsoids



MitigationAvoidance of being in the wrong place at the wrong time

Which way do I push (δV)?T: aligned with direction of motion (speed).

Changes the magnitude of the angular momentum vector but not orientation.Period increased or decreased (lose phase) - miss distance increases with time.

W: orthogonal to direction of motion but in the plane of orbit (yaw).Precess’s orbit

N: orthogonal to the direction of motion and the orbital plane (pitch).Changes eccentricity and rotates orbit

Phase MattersFor a fixed velocity perturbation, δV, in the speed (T direction), the magnitude of the period change depends on the phase at which it was applied.

δPPerihelion

δ PAphelion

=1 + e1 − e

Dmiss ≈VearthTδPP

= 3VearthTδVVast

The magnitude of the miss (where T is the time to impact) is well approximated by:

For a given δV:

Changing the orbit orientation or shape:

The miss distance does not improve with time.

N direction

W direction

For this orbit: Near passages with the Earth de-magnifies the miss distance

Early Is Not Necessarily Better

Rubble must be held together by gravity, setting a minimum rotation period of approximately 2 hours (��ρ1/2).

1999 TY2 0.119 80 meters1998 KY26 0.178 30 meters1998 WB2 0.317 60 meters1995 HM 1.62 120 meters2001 OE84 0.50 900 meters

Pravec et al Submitted to Icarus, 1999 December 13Ostro et al Radar and Optical Observations of Asteroid 1998 KY26 Science 1999 285: 557-559

ExceptionsObject P(hours) Diameter

g≈ few X 10-5g≈ few X 10-5

Rock or Rubble?Amalthea

a moon of Jupiter

Stone with ρ≈1 : Rubble!(John Anderson’s JPL analysis of Galileo fly)

Almost all asteroids larger than 200 meters are observed to rotate with periods > 2 hours.

Working Near An AsteroidIda: Density?

58Km long and 23 Km widetaken by Galileo 1993



Complex shape/motion: RigiditySlow Rotation Period: Rubble?

With a 4.6 hour period,there are no close stable orbits, and someone standing on Ida would see

”gravitational” shifts

The Changing Direction of

Up.

Changing Weight.Even a monster like Ida has a

gravity of only a few hundred μg’s

Asteroid �� Reaction Time to Impact δV Energy Energy Mass perihelion aphelion

m� tons Kt Tons days days 0.01 0.01 1. 104 2507 1290000.1 1.0 10. 105 250 12931.0 100.0 100. 106 25 129

10.0 10,000.0 1000. 107 3 12

Newton Says: let there be momentum conservationMinimum energy and mass necessary to change the velocity(δV) of an object of mass 1015 grams

(typical of a 1 Km diameter object).

Velocity of the ejecta, Vejecta is taken to be 1 km/s

Ignoring rotation of the asteroid, anchoring the rocket engine, and difficulties of pushing an asymmetric object:

The main engine of a Saturn V can divert a 1015 gram asteroid if it burns continuously for 35 days with a 2.5 million ton fuel supply.

Early action definitely saves on the fuel bill!

δV ≈Thrust ×Time

2M

Rockets

Reaction MassCan be reduced with higher propellant velocities

Limits on Rockets:Chemical propellants are limited by the energy available in the atomic bonds, and material properties of engine components.

≈2.1 km/s fpr kerosene and hydrogen peroxide≈7.0 km/s for Hydrogen and oxygen

Ion Drives (smarter not bigger):Use electricity to accelerate ionized propellant

NASA’s DS1accelerates Xenon to 30 km/sUses 2.5 KW of power for 92 mN thrust

Scale up factor 800 to divert 1015 gram asteroid 2 MW of power (nuclear reactor)55 years200 tons fuel

The CHALLENGE remains of how you push on a rubble object that is

rotating, yet bound by only μg’s



Ablative ProposalsUse directed energy device (Lasers, particle beams, mirrors orbiting in

space...) to heat the asteroid’s own material for reaction mass.

Must still satisfy Newton’s lawsTo divert a 1015 g Asteroid providing δV = 0.01 m/s

requires vaporizing 104 tons of material and giving it 1 Kt of kinetic energy.

1)To vaporize enough surface material requires >5 Kt of energy.

2) The energy must be delivered as intense pulses to avoid self-shielding (and defocusing).

3) The beam must have the high spectral purity required for precise focus (outside of the atmosphere)

3) The National Ignition Facility (NIF) can deliver this energy in 5 million pulses.

4) At the designed shot rate, require >6000 years.

21st Century Steam*:The Hollywood Approach

As part of the Plowshare Program, LLNL conducted the nuclear excavation experiment "Sedan" on 6 July 1962.

It utilized >3% of the available energy to move an amount of mass comparable to that of a 200 meter asteroid.

Nuclear reactions are nearly a million-times more energetic than chemical.

The material was impulsively accelerated to many 10’s of meters per second (>45 m/s)

*Medwin's Conversations of Lord Byron 1820’s: “… when a comet shall approach this globe to destroy it, as it often has been and will be destroyed, men will not tear rocks from their foundations by means of steam, and hurl mountains...”

A 104 kt device lifted about 1013 grams of alluvium to created a crater 390 meters in diameter and 100 meters deep.

Asteroid Management with Extreme Prejudice

Energy input from sunlight 43 Megatons/second

*A detailed analysis of coupling by Simonenko, Nogin, Petrov, Shubin, and Solem, 1993

One megaton at the center of a small, 400 meter diameter, asteroidapproximately 1000 days before impact.

Impact Actual Durationenergy Intercepted Energy of Impacts

orbit Megatons Fraction Kilotons Minutes1 4200 2.3X10-4 960 522 3200 4.0X10-5 128 803 1800 3.3X10-5 59 624 2900 7.8X10-6 37 85

If only 0.5% of the energy can be coupled into the material*, it will carry an RMS velocity of 25 m/s.

10 150 kilotons 25 Bad locally - probably won’t hit ground100 150 megatons 7000 Bad idea regionally - Km’s scale crater

1000 150 gigatons 3.4 million Global problem

D(meters) E(TNT) T(years) Note

1) 50,000 Megatons (about 700 m) = 20 cal/cm2

over a hemisphere. Sufficient to cause wide spread fires - BAD

2) 150 megatons <1 cal/cm2 when spread evenly over 3000 km square. To do this must an object must be engaged at about 5 lunar distances and dispersed >20 m/s)

The Miss must be Significant ε=47.8 Mega-Calories per kilogram

(Mc/kg) for typical speed of 20 km/s.

TNT = 1.0 Mc/kg

Gravity Binds Even RubbleThe escape velocity of a 1 km body is typically

near 30 cm/s.

Just a TapWith a one to a few decades notice, δV≈1to 10 cm/s can assure a miss.

��δV ≈ 1 to 10 cm/s << Escape Velocity the bulk of the object will remain bound (Solem, JBIS, V53, p180,2000).

The viscous nature of Rubble actually helps reduce velocity gradients and maintain cohesion.

A More Elegant ApproachThe Nuclear Nudge

δVperi =NRearth

3TVearth

GMsun

a1− e1+ e

⎛ ⎝ ⎜

⎞ ⎠ ⎟

12

Tyrant Newton

δM ejecta

M asteroid

=δV

Vejecta

≈ 10-5 for δV of 1 cm/s or 10-4 for 10 cm/s

Detonation well above the surface will result in heating of a hemisphere, and a broad, even push to the asteroid.

How to Tap with a Nuclear Device

1) For a 1015 gram body, one still must heat 10,000 to 100,000 tons to about 1ev.

2) For a specific heat of 0.2 cal/gm/k (basalt) and a latent heat of vaporization near1000 cal/g, it takes 1300 calories to begin to convert to a gas.

3) To raise the temperature to 1ev (sound speed about 2.4 km/s requires about 2500 Calories/gram.

4) Heating the ejecta mass requires 10 to 100 Kt coupled into the surface (not total yield).

Flux per unit yield

Flux distribution for a fixed GZ value

The Trade-OffDetonation above the surface:Broadens the impulse (more even push)Reduces the penetration requirement

but Increases Yield requirements.

Height of Burst EnergyAsteroid radii Yield/Coupled δV = 1 to 10 cm/s

0.3 6 0.06 to 0.6 Mt1.0 15 0.15 to 1.5 Mt

Nλ =2RδMejecta

3Masteroid[(1+ x)Cos(θ) −1]Sin(θ)dθ

[1+ (1+ x)2 −2(1+ x)Cos(θ)]1

20

θ max

∫

A lower height of burst requires less yield but must penetrate more deeply.

For a 1 km diameter body:

Height of burst Penetration (cm)(Asteroid radii) (δv = 1 and 10)

0.3 4.7 to 47.1.0 1.7 to 17.

To heat enough mass (δMejecta) Radiation must penetrate at least 2 to 5 cm for a 1 cm/s push and much deeper for 10 cm/s push.

In space, the nuclear output is mainly X-rays, γ-rays, and neutrons. There is too little material to form a blast wave.

Coupling to the Asteroid

How deeply must the radiation penetrate to heat enough mass?

Penetration to eject mass for 1 cm/s velocity change

Output:Neutrons, γ’s, or X-rays

1) The mean free path of Kev X-rays in silicate is 10’s of microns (at best). To penetrate centimeters requires burning in (high albedo very inefficient). Alternatively may try to use high energy tail of X-ray spectrum (still sensitive to composition) .

2) Neutrons or gamma rays have a much larger penetration depth than X-rays.

3) High energy(> Mev) neutrons are easy to generate and have an advantage of being only weakly dependant on composition.

λ =16.6 gcm3 ≈ 5.5cm in solid olivine.

Above 2 Mev, the precise composition is irrelevant. The neutron cross-section on oxygen, silicon, and magnesium is about 2 barns, and about 3 barns for iron.

Monte Carlo Simulationof an isotropic neutron flux incident on Granite

Includes all reactions (n,n’) (n,γ) (n,p) ( n,α) (n,nα), …

By 10 cm (28 g/cm2), >30 % of incident neutron energy is absorbed, and by 17 cm (48 g/cm2) >50% is absorbed

Only about 30% of the incident energy is reflected.

Accounting for albedo, velocity changes in the 1 to 10 cm/s range can be generated with 15 to 150 kt of incident neutron energy, or 0.1 to 1 Mt total neutron yield for a detonation 300 m above 1 km object.

δT (θ) =δTmax

1+ (1+ x)2 − (2 + 2x)Cos(θ)degrees δTmax =

Yield4πR2NλρCp

degrees

The Temperature Profile

Includes: albedo (i.e. 2/3rd of the neutron energy incident on the surface acts to heat it)

For a normal penetration depth of 10 cm, the requisite 4X1010 g heats to a vapor.

Where

for 0.95 Megatons of fusion neutrons detonated 300 meters above a 1 Km asteroid of density 2.

δV =2πR2NλρvδTmax

12

Mass(1+ x)α 2 −α

1+ (1+ x)2 −2(1+ x)α11+x

1

∫ dα

A total yield of 1.5 Mt delivers enough energy to provide an impulse changing the velocity of a 1 km diameter (density = 2 g/cm3)object >6.5 cm/s.

The velocity change(From the impulse component in the direction parallel to

the vector from GZ to the burst.)

There is an optimal height of burst:1) Below that height insufficient mass is heated. 2) Above that height too much energy is lost.

The Comet Threat?

Parent population appears to be large (1 to 10 km) - Bad!

Wider variety of orbits :a) Typically 2.5X higher velocity (Bad)

b) Larger inclination range (Good).

c) Difficult to discover with more than a year or two of warning (Bad).

d) Less time in inner solar system or fewer node crossings per year (Good).

e) Non-gravitational forces make orbit prediction very poor (Very Bad).

Halley’s Comet from Giotto

“Edmond Halley made clear (after 1705) that comets like that bearing his name could strike our planet and cause tremendous environmental upsets” (Duncan Steel and Alan Harris Astronomy & Geophysics December 2002)

When I was walking up the stairs, I passed a man who wasn’t there. He wasn’t there again today. O how I wish he’d go away.

Sudbury Crater: Recent work by Kieffer and Pope (Geological Society of America Paper No. 178-14, 2002) provides evidence that this 200 km crater resulted from a cometary impact

Based on discoveries the flux of comets was estimated to be a few percent of Asteroids (Everhart, E, Astr J Vol 72, 1002-1011, 1967, Chapman, C.R. & Morrison, D. Nature, 367 , 33-40,1994 )

“it is important to know whether comets represent 10% of the potential large impacts on Earth (as is commonly thought) or a much larger fraction.”(MICHAEL F. A'HEARN Nature 405, 285 - 287 2000)

Since 1997 22 new comets were discovered:9 were discovered by the survey’s. 7 were discovered by amateurs 6 were discovered by satellites.



Porthos Debris Ellipsoid A long period comet in a high inclination orbit that is aimed at the town of Brookfield, Missouri, USA.

It is discovered on 22Feb, 2003, and if un-deflected, it will approach the town from the southeast striking on 18 June, 2010 with a speed of 62 km/s.

Assume detonation of 260 days before impact (Beyond orbit of Mars).

Monte Carlo calculation in which the original body is split into 10,000 pieces with an RMS velocity distribution of 20m/s that is randomly oriented.

Energetically consistent with coupling 5% of the energy of a 1 Megaton explosion into a 1 km asteroid.

Result earth impacts only 10-4 of the debris.

Passage Through the Debris Ellipsoid Formed 260 days before impact.

Result earth impacts only 10-4 of the debris.



Conclusions1) Its only Natural - There will be another large impact resulting in global catastrophe any mega-year now.

Both impact structures are about 35 million years old, with diameters near 100 km. These crater events could have been responsible for theextinctions found near the Eocene-Oligocene boundary layer when 20% of the subgenera became extinct (compared to 80% at KT boundary).

Popigai crater in Siberia

Chesapeake Bay Crater, US

Don’t Panic2) A million years is a really long time.

Homo Heidelbergensis or "Archaic Homo Sapiens” from Africa 125,000-300,000 BPThe Riachao Ring in Brazil is

4.5 km in diameter and <200,000 years old.

A) Confirm its threat potential and reduce error ellipsoid.

B) Learn about the structure of the threatening object (solid or rubble).

3) Survey projects reduce the likelihood of very unpleasant surprises, and provide an abundant source of data for broad astrophysical research.

4) With decades to centuries of warning , there is time for reasoned action.

You Have Insurance:

STARFISH PRIME, July 9, 1962, 400-kilometer altitude, 1.4 megaton

5) Current technology can handle most possible threats, and it is more than presumptuous to speculate on future technology.

A) Even the nuclear option will require some years of preparation (device construction, fuse development, …).

B) Time is also necessary to manufacture boosters capable of quickly delivering even modest payloads to the optimal perturbation point.

Finally:

50

40

30

20

10

10 102 103 104

Meters

Nuclear TechnologiesYears

to Impact

Nuclear orAggressive

Development ofNew

Technologies

PartialMitigation

Terminado

dr. david s. p. dearborn lawrence livermore national...

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