JOURNAL OF SPACECRAFT AND ROCKETS Vol. 30, No. 2, March-April 1993
Interception of Comets and Asteroids on Collision Course with Earth
Johndal . SolemeC * Los Alamos National Laboratory, Los Alamos, New Mexico 87545
I delineat utilitye eth , performance rangd an ,f applicabiliteo f rockeyo t interceptors designe disrupo dt t (deflect or pulverize) comets or asteroids on collision course with Earth. I discuss the relationship among several quantitie f practicaso l interes interceptioe th n ti n problem mose th , t importan mase th orbi f whicn ) sti o 1 e thar or initial mass of the interceptor, which will usually dominate the cost of the system, and 2) the blowoff fraction, the fractio assailane th f no t object's mass expelle imparo dt t transverse momentum, which also providesa measure of the probability that the object will fracture. I calculate optimum interception strategies for both kinetic-energy deflection and nuclear-explosive deflection, assuming a fairly general relationship between the energy deposited and the blowoff mass. In the nuclear-explosive case, I calculate the interceptor mass and cratering effect for detonations above and below the surface as well as directly on the surface of the assailant. Because different assailants could posses wida s e rang f densitieeo materiad san l properties principae th , l value of this work is to show the relationships among the salient parameters.
Nomenclature velocit _s~• 1f m ,abou yo k whic 5 2 t h would giva kineti t ei c diameter of assailant (comet or asteroid) energ abouf yo t 1000 Mton populatea n I . d area damage th , e g = Earth gravitational constant would be catastrophic. If it were a comet, the relative velocity specific impulse would be more like 50 km • s~ *, and the energy would quadru- ISp = 2 3 Ma - mas f assailanso t ple. The Tunguska event ' (1908) offers sobering evidence Me = mass of crater ejecta that such potentially catastrophic collisions are not so infre- final mass of interceptor quent that they can be ignored. That impact was about 10 initial mas f interceptoso orbin i r t Mton and could be expected every few hundred years. Recent Q = estimates4 indicate that a 20-kton (Hiroshima-size) event RI = range when assailant is intercepted should occur every year. This oughconspicuouse b o t t t bu , rang= RIe when intercepto launches i r d apparently object thif so s size ten breao dt whilp ku e penetrat- V = interceptor velocity ing the atmosphere,5 dissipating much of their energy as closin= vg spee f assailando t smaller fragments. That larger cataclysm t generallno e ar s y assailan= v ± t transverse velocity component recorde archivee th n di f naturaso l disasters seems somewhat a = crater constant o mysteryfa .attribute e Perhapb n face ca th t t si thato d t , until jS = crater exponent 20te th h century, ver yEarth'e littlth f eo s surfac popus ewa - At = time elapsed from launch to intercept lated.6 Nevertheless bees ha nt ,i asserted tha rise beinf tth ko g 6 = energy fraction, ______killed as a result of asteroid impact is somewhat greater than 7 V2 x ejecta kinetic energy /intercep kinetitor c energy the risk of being killed in an airplane crash. e = assailant deflection distance firse Th t serious stud defensa f yo e against asteroid colli- assailan= p t density sion8 was conducted as an interdepartmental student project in systems engineering at the Massachusetts Institute of Technol- ogy. Remarkably, the study was conducted in the spring of Introduction 1967 dozea , n years befor Alvaree eth z discovery hypothe .Th - 1 esis was a predicted 1968 collision with Icarus, a kilometer- INCE Alvarez et al. announced evidence for asteroid scale Apollo asteroid. The prognosis was deployment of six
Downloaded by UNIVERSITY OF NOTRE DAME on January 13, 2015 | http://arc.aiaa.org DOI: 10.2514/3.11531 S impact as the putative cause of the cretaceous-tertiary Satur rocketnV s carrying 100-Mton warhead defleco t s r o t extinction, ther bees eha n heightenea d awareness thafair rtou pulverize the asteroid. planet is and always has been in a state of merciless cosmic In 1981, NASA and the Jet Propulsion Laboratory (JPL) bombardment. Not all of this cannonade has been deleterious; sponsore dworkshopa evaluato 9t ratconsequencee d eth ean s for example evene th , t Alvarez suggest havy sma e clearee dth of collisions with both asteroid cometsd an s , whic hI collec - way for the rise of Homo sapiens. But being a selfish subspe- tively call astral assailant rise f creatinth ko t a s pathetiga c cies, we would rather hold on to our domination of the Earth fallacy. The workshop also considered requirements for a and deny a chance to any more well-adapted creature for as mission capable of deflecting an asteroid from Earth collision cane lonw . s gLesa s facetiou possibilite th s si strika f yo e from and concluded that it was probably within technological interplanetarn a y body witt i mh 0 f ordeI .radiue 10 th f n ro so means. It seems unlikely, however, that an object requiring were an asteroid, such an assailant would likely have a relative deflection woul detectee db d over a perio f tim do r whic efo h the technology was relevant. In 1984, Hyde10 further explored using nuclear explosives to counter astral assailants 1990n I . , Woo t al.de 11 showed that defense against small assailants could be accomplished with Received Feb. 20, 1992; revision received Aug. 24, 1992; accepted nonnuclear interceptors, largely using the kinetic energy of the for publication Sept , 19923 . . Copyrigh Americae th 199© t y 2b n Institut Aeronauticf eo Astronauticsd an s , U.SInce Th . Government assailant itself. has a royalty-free license to exercise all rights under the copyright The problem of preventing a collision with a comet or claimed herei r Governmentafo n l purposes l otheAl . r righte ar s asteroi consideree b n dca domainso dtw action) 1 take:e b o nst reserved by the copyright owner. if the collision can be predicted several orbital periods in *Coordinator for Advanced Concepts, P.O. Box 1663. advance and can be averted by imparting a small change in 222 SOLEM: INTERCEPTION OF COMETS AND ASTEROIDS 223
velocity (most effectively at perihelion); and 2) actions to be orders of magnitude higher than the kinetic energy of the taken whe objece nth less i t s tha astronomican na l unit .(AU) interceptor collision. away, collision is imminent, and deflection or disruption must be accomplishe objece th s da t close Earthn so calI .firse th l t Kinetic-Energy Deflection domai actionf no s remote interdictio secone th d dnan domain of actions terminal interception. The final velocity of an interceptor missile relative to the If all of the Earth-threatening asteroids were known, the Earth, or the orbit in which it is stationed, is given by the orbits coul calculatee db procese th d f deflectiodso an n could rocket equation, b ea leisurel carrien i t you d manner. Remote interdiction t optiobeee woul th ye hav n% t e f choicednb o 99 eno t Bu . discovered.12 Furthermore ,enormou n thera e ear s numbef o r 0) unknown long-period comet r whicsfo thorougha h searcs hi completely impractical. In general time th , e require reaco dt h this relative velocity will Asteroids in the 100-m size range are exceedingly difficult to be short compared with the total flight time. The time elapsed detect unless they are very close. Comets in this size range are from launc intercepo ht s i t more conspicuous owing to their coma, but they move a lot retrogradn i e b n fasteca eplane d e orbitth th an r f f eo o st orou ecliptic. In either case, it seems likely we will have little time to (2) respond to a potential collision. It therefore appears that V v+ terminal interception—disruption or deflection at relatively close range—i mose sth t important issue. So the range at which the assailant is intercepted will be given In this paper, I consider the dynamics of the terminal inter- by cept problem. I explore the possibility of using kinetic-energy deflection as well as nuclear explosives. Nuclear explosives can be employed in three different modes depending on their vV,+ (3) location at detonation: 1) buried below the assailant's surface by penetrating vehicle detonate) 2 , assailant'e th t da s surface, impace Ith f t give assailane sth transversa t e velocity compo- or 3) detonated some distance above the surface. nent v± , then the threatening assailant will miss its target poindistanca y b t e Interception and Deflection Scenario Figur show1 e interceptioe th s n scenarioe th Fig n , I . la . asteroid or comet is headed toward Earth at a velocity v. The (4) interceptor traveling at a diametric velocity V is about to engag assailane eth t object assailane Th mas.a s sha t Md ffan , wher ehavI e neglecte Earth' e effece th d th f o t s gravitational the interceptor, because it has long since exhausted its fuel, focusin used gan dlineaa r approximatio Kepleriao nt - nmo has its final mass Mf. We cannot hope to deflect the assailant tion. To obtain the transverse velocity component, we would like a billiard ball because Ma > Mf. So the interceptor must use the kinetic energy of the interceptor to blast a crater on the supply energ bloportioa o y t assailant' f e wth of f no s surface, assailante th sid f eo momentue Th . ejecte th f mao woule db as shown in Fig. Ib. The blowoff material is very massive balanced by the transverse momentum imparted to the as- 13 compared with the interceptor, Ma > Me > Mf. One might sailant. From Glasstone's empirical fits, mase th materiaf so l think that a conventional high explosive would suffice, but the cratee inth r produce larga y db e explosios ni energ t woulyi d supply woul relativele db y insignificant. Stan- 3 10 dard high explosive releases 10 calories = 4.184 x 10 erg per Me = (5) gram. An asteroid moving at 25 km • s'1 has a specific energy of 3.125 x 1012 erg per gram—about 75 times the specific wher e/d 3 a.depen an locatio e th explosione n th do f no soie ,th l energ f higyo h explosive interceptoe th f I . movins i re th t ga composition and density, gravity, and a myriad of other same speed in the opposite direction (V - v =25 km • s"1), parameters. Clearly the crater constant a. and the crater expo- interceptoe th r would impact wit hspecifia c energ time0 y30 s nent j8 will vary dependin whethen go considerine ar e w r n ga that of high explosive. There is a whole lot of kinetic energy assailant composed of nickel iron, stony nickel iron, stone, available; a chemical energy release would be in the noise. chondrite, ice, or dirty snow. For almost every situation, However, even this tremendous kinetic energy woul come db - however fine w ,d 0 =* 0.9.
Downloaded by UNIVERSITY OF NOTRE DAME on January 13, 2015 | http://arc.aiaa.org DOI: 10.2514/3.11531 pletely swampe nucleaa y db r explosive yield-to-weighe Th . t kinetie Th c energy available whe interceptoe nth r collides rati f nucleaoo r explosive generalls si y measure kilotonn di s with the astral assailant is per kilogram, that is, tons per gram. A typical specific energy is a million times that of chemical high explosive or about four (6) Onl yfractioa interceptor'e th f no s kinetic energ convertes yi d kinetio t c energejectee th f r blowofyo do f material t thiLe s. fractio equae nb o ViSt l r 2o , ejecta kinetic energy 6 = 'interceptor kinetic energy (7) The reason for this strange definition is that it greatly simpli- fiealgebrae sth wilI . l calparametee lth energe r dth y fraction. T !• The transverse nth e velocity imparte assailane th o dt s i t
a) b) Mc Fig. 1 Interception scenario: a) interceptor about to engage the as- sailant intercepto) b d an , r supplies energ portiobloo a yt e f wth of f no (8) assailant's surfac impartd ean transverssa e velocity. Ma 224 SOLEM: INTERCEPTIO COMETF NO ASTEROIDD SAN S
0 = 0.8, 0.9, and 1.0. It shows the increasing advantage to higher specific impulse derived from Eq. (14). A great deal of physical insight can be obtained just by studying the axis labels of the dimensionless plot. From the same ordinateth tha e r e se fo valu t e w f ,g/ eo sp/v, whics hi more or less fixed by interceptor design, the asteroid deflec- tion e is proportional to the range of the assailant at launch R{, inversely proportiona assailane mase th th f so o lt t Mfl, nearly proportiona lvelocit e tassailanoe th th f yo t relativ Earto et h V0 ~ vo.99 neariy proportional to the initial mass of the inter- ceptor M//2(/3 + 1} — Mf'95 , proportiona cratee th o t rl constant proportionad aan , square th o t e fractiol th roo f f o to n 10 interceptor kinetic energy converted to blowoff kinetic energy
Equatio rearrangee nb (14n )ca giv o drequiret e eth d initial Fig. 2 Dimensionless plot of kinetic-energy deflection. mas masr so interceptore orbin th si f o t , M ve 1 a (15) We can combine Eqs. (4), (5), and (8) to obtain mase Th s. (15 giveEq ) y wilnb l generall largese th e yb t single e = adRi (9) factor in the cost of a defensive system of this sort. To appre- Mav ciate the magnitude of the problem, it is now necessary to put numbersw fe ia ne bes Th .t chemical fuels might hava e Equation (9) reveals the importance of the intercept velocity specific impulse as high as 500 s, which I will use to make the V9 whic proportionas hi specifio lt c impuls
(14) 10- 2 id1 io IO3 Remarkably, whe t int. (14). (12resultinpu oe Eq n Eq s )th ,i g exceedingly comple dimensionlesn i x t expressiopu e b n nca s form. Figur 2 plot ee dimensionlesth s s parameter eMa/ Fig. 3 Initial masses of optimally designed interceptors using kinetic-
e dimensionlesth s v s parameterr glfo /v energy deflectio ocear nfo n diversio Mm)1 n( .
sp
) 1 SOLEM: INTERCEPTION OF COMETS AND ASTEROIDS 225
Figure 3 shows the initial mass of the interceptor required to deflect the astral assailant by 1 Mm, as a function.of the assailant' ss rang it diamete d e an whe d e assailanr th n s i t 0.14- launched Rh I have assumed an assailant density of p = 3.4 gm cm~• n assailan3 a s",• 1a cratem , k 5 t r2 velocit = v f yo 4 exponen f 0.9= fto a tcrate , 10~x r 2 constan= a f o t UOOO 3000 5000 gm1/2(1 ~0> • cm-*3 • s*3, and an energy fraction of d - 0.775. A 0.10 1-Mm deflectio typicas ni f tho l e course change requireo dt IIP (sec) diver e assailanth t t from impac a populate n i t d a are o t a nearby ocean interpreo T . figur e 10-Ma th tr efo m deflection, which would be conservative for missing the planet entirely 0.06 (Re = 6.378 Mm), multiply the masses by a factor of 10 (M/oce2/(?+1}, so a factor of 10 in e corresponds to a factor of 11.3 in MI). An ocean impac without no s ti t damage,15'16 but generaln ,i , Fig. 5 Asymptotic decrease of blowoff fraction with specific im- the damage will be far less than if the impact were in a pulse. populated area. Roughly speaking, the height of the wave and the distance from impact are jointly proportional to the square 17 damag appears ea havo st e bee case nth e with Tunguskat I . root of the energy deposited in the water. A 100-m diameter should be noted that the blast from a bomb does more damage chondrite might typically impact with 100 Mton of energy. 18 cita yo t whe detonatioe nth soms ni e altitude abov targee eth t Taking about 5% of that energy as coupled to the water, a than when the detonation is on the surface. To insure that no water wav heighn f aboui e o m t3 t woul encounteree db 0 d10 damag dones ei t wil i ,necessar e b l pulverizo yt assailante eth , km from the impact point. that is, break it into very small pieces that are sure to dissipate To interpret Fig. 3 for a 10-Mm deflection, which would be all of their energy in the atmosphere. conservative for missing the planet entirely (/?© = 6.378 Mm), To get a handle on the problem of whether the assailant will we nee multiplo dt massee yth abouy sb . [Frofactoa t 10 f mo r 2/(/3+1 be deflected, fragmented r pulverizedo , neee estimatw ,n da e Eq. (15), M/oce \ so a factor of 10 in e corresponds to a of what fractioe assailanth f o n e t th wil e blown i b l f nof facto f 11.o r M/.n 3i ] Figur makee3 cleasa r statement about collision combininy B . g Eqs. (1), (5), (11) (15)d fine an , w ,d e applicabilitth f kinetic-energyo y deflection. Kinetic-energy that the fraction of the assailant blown off is given by deflection is practical only for assailants considerably less than 100 m in diameter. To handle a 100-m assailant would require a 1000-ton interceptor even if launched when the assailant was still 1/10 AU away. The mass would go to 10,000 ton if the Ma assailant were deflecte miso dt planee sth t entirely rather than 2 diverted to an ocean. Thus, dealing with assailants larger than 0 1+ (16) 100 m requires another technology. where Qagais i n . (12) giveEq .y nSomb e qualitative features Kinetic-Energy Fragmentatio Pulverizatiod nan n blowofe oth f f fractio immediatele nar y apparent. Equation (15) gives the initial mass of an optimally designed blowofe 1Th ) f fractio nearls ni y independen f assailano t t interceptor for deflecting an astral assailant by blowing off its surface derives wa t I .d unde assumptioe rth n tha amoune tth t blowofe 2Th ) f fractio nearls ni y proportiona cratee th o rlt of mass bjown off is small compared with the assailant's mass. constant, a2/(1 + ® - a1-05. ejectee Ifth d largemaso to crate e s si ,th r will have dimensions 3) The blowoff fraction is nearly inversely proportional to a significant fraction of the assailant's dimension, and it is the energy coupling, d2^1 + ®~ 6°-947. more likely that the assailant will break up. If the fragments 4) The blowoff fraction decreases asymptotically with spe- are too large and are scattered at random, they may still be cific impulse. abl penetrato et Earth'e eth s atmospher damageo d d ean A . Using the aforementioned parameters, Fig. 4 shows the 2-m fragment of a nickel-iron asteroid has about the same blowoff fractio ocear nfo n diversio functioa s na assailanf no t e atmospheraveragth s a r ep e measured vertically froa mse diamete threr rfo e different range assailane th o st t intercepta - leve thud an ls will penetrat atmosphere eth e losing only about tor launch (p = 3.4 gin-cm'3, /3 = 0.9, a = 2 x 10~4 3 hal s energyit f 50-A . m chondrite, however, will probably gm'/2( 0is- • )~ . «* cm-*d m , k 0.775) 5 2 • = s*f mor I .v , e than
Downloaded by UNIVERSITY OF NOTRE DAME on January 13, 2015 | http://arc.aiaa.org DOI: 10.2514/3.11531 brea owindynamip e ku th o gt c stres traversinf so atmoe gth - 10% is blown off, the assailant will probably break up. What sphere. Shock fro energe s explosiomth it f y o stil y o d lnma we learn from Fig. 4 is that, if we cannot launch the intercep- about a r to bettertr o 1/3 cannoU e 0A ,w t deflec assailane th t t without fracturing it. Under those circumstances, it is better to 0.3- try to pulverize it with an array of masses, probably resem- bling spear r maximusfo m penetration. Equation (16) beasuggest o t fracture y th t wa sa e problem. blowofe Th f fractio reducee b n increasinnca y d b specifie gth c 0.2- impulse. Figure 5 shows the blowoff fraction as a function of specific impulse for a 100-m assailant with the mission launched at a range of 1/100 AU. With a specific impulse of 0.1 500, over 14% of the assailant mass is blown off, whereas at specifia c impuls f 5000eo , les sblows i tha % n4 off.
Nuclear-Explosive Deflection 10 Much more deflection can be obtained if a nuclear explosive 20 30 40 50 is used to provide the cratering energy. In this scenario, most weighe oth f t afte rockee th r t fue expendes i l d woule th e db d(m) nuclear explosive, which produces a yield of Fig. 4 Blowoff fraction for ocean diversion (1 Mm) using kinetic-en- ergy deflection. E = wher yield-to-weighe th e s yi t ratio. Again, d 2thif /2o s energy 10-i. goes intdire oth t ejected fro cratere transverse mth th o s , e velocity imparte assailane th o dt s i t V J- = - (18) 10- We can combine Eqs. (4), (5), and (18) to obtain (19) v + V Mav Optimum Mass Ratio for Nuclear-Explosive Deflection io-2 Substituting Eq. (1) into Eq. (19) and solving Eq. (10), we 101 102 103 finlogarithe dth mase th f sm o rati o that produce largese sth t value of e, Fig. 6 Initial masses of optimally designed interceptors ising nii- clear-explosive deflection for ocean diversion (1 Mm). Q=- + T (20) 2glsf In the limit of very high specific impulse, the optimum mass appropriate Th e dimensionles comparisose ratith r ofo s ni ratio is Rm^ (26) (21) M where the subscripts n refer to the parameters for nuclear-ex- plosive deflection and the subscripts k refer to the parameters limie I nth f ver o t y low specific impulse optimue th , m mass for kinetic-energy deflection. This is the actual ratio of initial ratio is interceptor weights for kinetic-energy vs nuclear-explosive de- flection. Figur showa e7 s this ratifunctioa s oa f assailanno t = exp (22) velocit specifir fo yv c impuls . Figurs 0 showb e50 e 7 I = spe sth i+ l same ratifunctioa s oa n of specific impuls er assailan Ifo sp t velocity v = 25 km • s"1. Figure 7c shows the same ratio as a The maximum displacemen impace th f to t locatio Eartn no s hi function of both specific impulse and assailant velocity. For then given by the numerical examples we have chosen, we have 4 andn 1Q- X 0.316 (23) 4 = 0.204 (27) Mav g!v sp Q+ 2ID'x 0.77x 5 Fo a surfacr e burst, Glasstone use t takesbu 0s9 =0. particulay m r Sofo r selectio f parametersno rean e ca d th e w , x 10~ 6 41. gm— 1/2(a 1 -/3 cm")• 1 describee s*3• 3H . mediue sth m mass ratios in Figs. 7a, 7b, and 7c by multiplying the number as dry soil. Medium strength rock would be more consistent verticae onth l axi 0.204y sb . with a = 10~4 gm1/2(1 -/3) • cm''3 • s*3 and, in the 20-kton range, leare followinw e , nth 7c Frod an gm , qualitativ Figs7b , .7a e would roughly agree with- Cooper.nu e th f f 1abouo I 9 % 5 t features. clear-explosive energy goes int kinetie oth c energ blowe th f y-o interceptoe 1Th ) r weigh abous i t t three order f magniso - off, then d = 1/VIO = 0.316. tude less for nuclear-explosive deflection than for kinetic-en- Equation (23) can be rearranged to give the required initial ergy deflection. interceptore masth f so , advantage 2Th ) f nuclear-explosiveo e deflection decreases significantly with assailant velocity. eQ\M ve( advantage 3Th ) f nuclear-explosiveo e deflection decreases a (24) slightly with specific impulse. Downloaded by UNIVERSITY OF NOTRE DAME on January 13, 2015 | http://arc.aiaa.org DOI: 10.2514/3.11531 - Nuclear-Explosive Fragmentatio Pulverizatiod nan n where now Q is given by Eq. (20). By combining Eqs. (1), (5), (11), and (24), we find that the generalls i t I y known tha yiele tth nucleaf do r warheadn sca blowoff fractio gives ni y nb kilotonw fe b ekilograr a spe mthef i y weigh more than about hundrea d kilograms purpose th r thesf .Fo e o e estimates wil,I l 1 . take the conservative of y? = 1 kton-kg" . Figure 6 is MA analogous to Fig. 3, using the values of a and d given earlier. Ocean deflection of 1 Mm is sought, and the following values ev 2 are used: p = 3.4 gin-cm"3, v = 25 km-s'1, 0 = 0.9, 1 +- 1+f (28) 10-= a 4 gm1^1 - =« cm-*d • 0.316d s*3• an 3 . A good way to compare kinetic-energy deflection with nu- where Q is given by Eq. (20). Somewhat remarkably, Eq. (28) clear-explosive deflectio initiae ratie th looo th t f ot lo s kn i a is independent of Penetrators 1. 210x 4- biggese Th t cratet produceno s ri surfac a y db ey blasb t bu t explosivn a e buried some distance belo surfacee wth . Clearlyf i it is buried too deeply, it will produce no crater at all. The 10x 38 - optimum dept r craterin usuae hfo th f functiola o s gl i al f no parameters describing material properties but, quite impor- s tantly, gravity, whic larga o ht e ignoree extentb n r ca dfo , «? comet surfac e asteroidsEarthd e th soi sy th an n f ldr o e o , r .Fo 4 x 103- Glasstone gives the optimum depth as 150 EQ-3 ft, and he would obtai cratee nth r constan exponend an t d an /s 3 a t — 9 0. 10-x 4 48. e gm' OL- th . (5)r 72'1Eq Fo . - »n i •e cm-*us r ^3• fo moment, let us say that the value of a is increased an order of 30 50 70 magnitude. a) (kmv - sec"1) Lookin . (24) mighe Eq w ,t ga t expec initiae th t l maso t s decreas orden ea magnitudef o r penetrato t t optie bu ,th -o et mal depth the explosive has to be fitted with a weighty billet: a cylinder of metal (probably tungsten) that will erode during 1. 210x 4 penetration of the assailant's surface material. In general, this will increas weighe eth abouy b t orden a t f magnitudo r r eo decrease the yield-to-weight 4 tude. . Thus(24) decrease Eq th ,n ,i initian ei l interceptor mass 1.1 x 10 Mi owing to the increase in the cratering constant a is just about compensate decrease th y db yield-to-weighn ei t Downloaded by UNIVERSITY OF NOTRE DAME on January 13, 2015 | http://arc.aiaa.org DOI: 10.2514/3.11531 the soil. The cratering constants can still be used as in Eq. (5), but for this surface blowoff, /3 — 1 and a ranges from 10"6 to 2 x 10~6 cm"1 • s. If we select an assailant for which d = 0.3 10~x 5 61. fin e cm"= w d , a s fro 1• . d (24man Eq ) thae th t blowoff fraction will be about a factor of 35 times smaller 0.3 surface thath r nfo e burst blowofe Th . f fraction give Fign i . 8 would be in the range of 1% for RI = 1/10 AU and in the range of Vi% for RI = V* AU. Similarly, from Eq. (28) we 0.2-- find tha initiae th t linterceptoe masth f so r would e havb o et about 40 times as large. So in Fig. 6 the mass would be multiplied by 40, i.e., ranging from about 28 ton to about 28 kiloton. The latter would not be very practical. 0.1 Comments, Summary Tentativd an , e Conclusions The problem of terminal interception of comets and as- 100 200 300 400 500 teroids collision o n course wit componentsho Earttw s hha ) 1 : detection of these relatively small assailants and 2) smashing d(m) deflectinr o g them shoul endangerinn a dn theo e yb g pathn I . Fig. 8 Blowoff fraction for collision avoidance (10 Mm) using nu- this paper, I have addressed the latter issue. The relationships clear-explosive deflection. I have derived should guide thinking on how to counter such 228 SOLEM: INTERCEPTIO COMETF NO ASTEROIDD SAN S assailants maie Th .n valu shoo t functionae s ewi th l relation- References ship among the parameters. This paper is not intended to be z, L., Alvarez, W., Asaro, F., and Michel, H., "Extrater- an exhaustive study mucd an , h research wil requiree b l o dt restrial Cause for the Cretaceous-Tertiary Extinction," Science, Vol. evaluate the constants in the equations I have derived. But the 208. 4448No , , June 1980 . 1095-1108pp , . following observation compelline sar refractoryd gan . 2Krinov, E. L., Giant Meteorites, translated by J. S. Ro- 1) Kinetic-energy deflection is effective for ocean diversion mankiewicz, edited by M. M. Beynon, Pergamon, Oxford, England, for assailants smalle r interceptoe thath f ni , aboum s i 0 r 7 t UK, 1966, pp. 125-252. 3Sekanina, Z., "The Tunguska Event: No Cometary Signature in launched when the assailant is further than 1/30 AU. At Evidence," The Astronomical Journal, Vol. 88, Sept. 1983, pp. shorter range, interceptors become impractically massive and 1382-1414. the probability of fracture increases rapidly. Ocean impact is 4Morrison , "TargeD. , t Earth, Telescope,& y , "Sk 3 . No Vol , 79 . probably unacceptable for larger assailants, and an order-of- 1990 . 265-272pp . . magnitude larger interceptor is required for missing the planet 5Morrison, D., private communication, 1992. with concomitant increas fracturn ei e probability. Higher spe- 6Vershuur , "ThiG. , s Target Earth, , Space,& 10 r . "Ai No Vol , 16 . cific impulse interceptors are more effective at increasing de- 1991 . 88-94pp . . Morrison, D., Public Forum, International Conference on Near- flectio d reducinan n g fracture probability, mainly because 7 they divert the assailant at a greater distance. Objects less than Earth Asteroids, n JuaSa n Capistrano Research Inst. n JuaSa ,n Capistrano, CA, June 30-July 3, 1991, as reported by the Associated 10 m are better pulverized at short range. Press, printed in the Santa Fe New Mexican, July 1, 1991, p. A-6; 2) Nuclear-explosive deflection is imperative for assailants apparently the source of the article is a paper presented at the same greater than about 100 m detected closer than 1/30 AU be- conference by C. Chapman, Planetary Science Inst., Tucson, AZ, the enormoue causth f eo sinterceptoe masth f so r requirer dfo abstrac f whico t h appear conference th pagn f so o e6 e program. kinetic-energy diversion. Kleiman8 , L., ed., "Project Icarus," M.I.T. Press, M.I.T. Rept. 3) Nuclear-surface-burst deflection offer threa s o fouet r 13, Cambridge , 1968MA , . orde magnitudf ro e reductio intercepton i r mass advane Th . - Anon.9 , "Collisio Asteroidf no Cometd san s wit Earthe hth : Phys- tage decreases slightly with specific impulse and decreases ical and Human Consequences," Report of a Workshop Held at dramatically with assailant velocity. Fragmentatio proba s ni - Snowmass , JulyCO , 13-16, published)e 1981b o (t , . 10Hyde, R. A., "Cosmic Bombardment," Univ. of California lem for intercepts closer than about 1/30 AU. Lawrence Livermore National Lab., UCID-20062, Livermore, CA , 4) Nuclear penetrators offer no advantage for deflection March 19, 1984. but are better for pulverization. HWood, L., Hyde, IshikawaR.d an , , M., "Cosmic Bombardment 5) Nuclear standoff deflection greatly reduces fragmenta- II, Intercepting the Bomblet Cost-Efficiently," Univ. of California tion probability but involves a substantial increase in intercep- Lawrence Livermore National Lab., UCID-103771, Livermore, CA, tor mass. May 1, 1990. assailane Th t object depicte Fig roughldn s i i 1 . y spherican li 12Morrison, D., "Big Bang," . editeBeardsleyT y db , Scientific American, Vol. 265, No. 5, 1991, p. 30. shape factn I . , comet r asteroidso generalle sar y quite spheri- 13 cal, a "potato" or "peanut" being the most popular descrip- Glasstone, S., "The Effects of Nuclear Weapons," United States Atomic Energy Commission, Superintenden f Documentso t , U.S. tions. All of the deflection techniques except the standoff Government Printing Office, Washington , 1962 . 289-296DC , pp , . nuclear burst make a crater that is small compared with the 14Kreyenhagen Schusterd an , K. , , S., "Revie Comparisod wan f no characteristic dimensio assailante th f no lineae Th . r momen- Hypervelocity Impac Explosiod tan n Cratering Calculations," Impact tum impulse wil impartee b l d alon ga lin e connecting that and Explosion Cratering, . editeRoddyJ y . b d. Pepin R R , d an , crater and the center of mass, with corrections for local geol- Merrill, Pergamon Yorkw Ne , , 1977 . 983-1002pp , . ogtopographyd yan aspherin A . c object will also receive some 15Ahrens, T. J., and O'Keefe, J. D., "Impact on the Earth, Ocean, angular momentum, depending on the location of the crater Atmosphere,d an " International Journal of Impact Engineering, Vol. object'e th d an s inertial tensorimpulse th size f eo Th . e will 5, No. 1-4, 1987, pp. 13-32. 16Ahrens, T. J., and O'Keefe, J. D., "Impact of an Asteroid or Downloaded by UNIVERSITY OF NOTRE DAME on January 13, 2015 | http://arc.aiaa.org DOI: 10.2514/3.11531 depend on material properties, geology, and topography. Extinctioe ComeOceae th th d n ni an t f Terrestriano " l 2, Life . Pt , Thus, it will be necessary to characterize the geology and Lunar Planetaryd an Science XIII, Supplement, Luna Planetard ran y mechanical properties of the assailant when using the cratering Science Inst., 36R88, Houston, TX, 1982, pp. A799-A806. deflection techniques. Such characterization could be accom- 17Mader., C., private communication, Dec. 1991. plishe vanguara y db d spacecraft. Standoff deflectio mucs ni h 18Van Dorn . G.W ,, "Some Characteristic f Surfaco s e Gravity less sensitive to these details. In general, linear momentum will Waves in the Sea Produced by Nuclear Explosives," Journal of be imparted alon line gth e connectin detonatioe gth n point Geophysical Research, Vol. 66, No. 11, 1961, pp. 3845-3852. wit e centehth f masso r . Little angular momentum wile b l 19Cooper, H. F., Jr., Estimates of Crater Dimensions for Near-Sur- imparted, and this will depend on relative projected areas of face Explosions of Nuclear and High Explosive Sources, Univ. of various assailant topographic features compared with compo- California Lawrence Livermore National Lab., UCRL 13875, Liver- inertiae nentth f so l tensor. Thus, besid inherens eit t fracture- more, CA, 1976. mitigation virtues, the standoff deflector demands substan- Alfred L. Vampola tially less information abou objece deflectings th ti t i t . Associate Editor