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Papers and exams

• I’ve graded everything but the water tower assignment (will returnthat on Thursday).

• I spent a lot of time making comments on your papers. I reallyfound them to be quite good! The large number of comments arenot to express unhappiness, but to give you constructive criticismfor future improvements.

• What about grades? I tend to not give many perfect scores, but togo along with that I tend to regard the A/B threshold as being in thelow 80% range on my grading scale (and the B/C threshold as inthe low 70% range).

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Last assignments

• Writing assignment due March 11: a briefing paper to the Presidentof the USA on a topic where some physics knowledge is required(see next slide).

• It is better to pick a specific subtopic with specific proposed actions.This is not a philosophy class but Physics for Future Presidents, soemphasize information relevant to the problem and solution. It’sgood to show passion for a solution, but passion without solidinformation is not well matched to this class.

• You are encouraged to email me about your proposed topic; I cangive you a few suggestions and ideas.

• Exam on Tuesday, March 19 at 7 pm. Exam will be open laptop ortablet, where you email to me your exam answers; otherwise,similar style to midterm exam. If you do not have a laptop or tablet,email me.

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Final paper due March 11

8–12 page briefing paper, double-spaced, with citations. Submit throughSafeAssign. I’ll set the SafeAssign deadline to be March 13 at 11 pm. . .

• Abstract (roughly half a page, summarizing your paper; use italicfont)

• Statement of problem• Relevant information (the quality of the sources you use will be

part of your grade)• Proposed action, including discussion of costs and benefits• Arguments against your proposed action, and your

counter-arguments• Conclusion

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Gun-type 235U bomb

Relatively easy to make a bomb; industrial-scale effort required toenhance the isotopic concentration of 235U from 0.7% to >∼ 40%.

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Implosion-type 239Pu bombEasier to get 239Pu (neutrons in a reactor on the common isotope 238U,followed by chemical separation. Harder to produce implosion usingconventional explosives.

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Little Boy and Fat ManHiroshima: Little Boy, 15 kt. Nagasaki: Fan Man, 21 kt.

USSR: copy of Fat Man tested on Aug. 29, 1949 before indigenousdesigns allowed.

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Modern example: W80

• B61: developed by Los Alamos 1961–1968 (airplane-droppedbomb; up to 340 kt).

• Smaller version sought for cruise missles; W80 developed by LosAlamos 1976–1982.

• 290 pounds, dial-a-yield from 5–150 kt, 31” long, 12” diameter.

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The Cold War

• At their peak around 1985, the US and USSR each had about20,000–30,000 nuclear weapons.

• Nuclear testing: a total of about 2000 tests worldwide, includingabout 500 above-ground.

• Both the US and the USSR developed a triad of weapons deliverysystems: bombers, intercontinental ballistic missiles (∼30 minutes“door-to-door delivery”), and missile-launching submarines. Othernations have one or two parts of such a triad.

• Strategic weapons: destroy big targets in the interior of theopposing country (missile launch sites, command and controlcenters, and cities as a last resort). First strike; “use them or losethem.”

• Tactical weapons: destroy troop concentrations, command centers,etc. on the battlefield.

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Nuclear weapons tests

From Wikipedia:

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Nevada test site

Test “Buster-Jangle Dog,” NevadaTest Site, 1951.

Craters at the Nevada Test Site.

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Perfecting nuclear weapons

• The WWII bombs were very conservative in design.• Weapons testing allowed various tricks to be perfected.

• Improved conventional high exposives that won’t go off in accidents(e.g., aircraft crash and fire).

• Levitated implosion cores (to drive a nail, do you push with ahammer, or swing it?)

• Small accelerators as neutron initiators.• 235U or 239Pu triggers with 238U fission boosts.• Improved radiation heating of Li-based fusion cores.• Permissive Action Links (PALs) of increasing sophistication, so that

only a specific, secret electrical signal sequence will arm a bomb.• A danger: are US weapons too “tweaky” to be robust to ageing? Will

they rust in peace? Codeword: stockpile stewardship. Newgeneration of robust, simpler weapons?

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MIRVsMIRV bus: multiple independent re-entry ve-hicle (on a missle). CEP (circular error prob-able) is 30 m for Tomahawk (cruise missile),80–100 m for LG-118A (land-based missile; 8warheads; decommissioned 2005!), 90–120 mfor Trident II (submarine-based missile; up to 8warheads each; in the past had 2700 warheadson 14 submarines).

US W-88 warhead:470 kT. 1.75 m long,0.55 m max diameter,∼ 360 kg mass.

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Delivering nuclear weapons

Both the USA and the USSR have had a triad of delivery systems:• Airplane delivery (originally “dumb” air-dropped bombs; now

“smart” or guided bombs using laser targeting, or GPS). Slow, butcan be recalled.

• Modern variant: bombers carrying Air-Launched Cruise Missiles(ALCMs) with ∼ 30 m circular error probable (CEP) or targetingaccuracy.

• Land-based InterContinental Ballistic Missiles (ICBMs): ∼ 30minute flight time, circular error probable (CEP) or targetingaccuracy of 80–100 meters. One missile can carry multiplewarheads.

• Submarine-based or Sea-Launched Ballistic Missiles (SLBMs):∼ 20 minute flight time, circular error probable (CEP) of 90–120m. Deep, quiet “boomer” or ballistic missile submarines withnuclear power plants are very difficult to detect.

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B-52 with AGM-86B

B-52 carrying AGM-86B cruise missiles (one B-52 can carry 20). TheAGM-86B is 20 feet long, weighs 3200 pounds, and has a range of over1500 miles. We have about 85 B-52s in service.

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Minuteman III ICBM

Minuteman III silo

Present sites (450 single-warhead missiles onactive duty)

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Ohio class submarines

Ohio-class submarine: artist rendering of missile launch. One sub cancarry up to 24 Trident II missiles; or 154 Tomohawk sea-launched cruisemissiles, including those with W80 (150 kt) warheads. We have 14Ohio-class subs in service.

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Trident II missile

Trident II missilelaunched from asubmarine. Witha load of fourW88 (475 kt) oreight W76 (100kt) warheads,the missile has arange of around7000 miles.

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Nuclear war strategies• Ballistic missile warheads arrive at ∼ 15, 000 mph and are

maneuverable; missile defense is not easy!• Mutual Assured Destruction (MAD): if you hit me, I’m sure to hit

you.• Destroying a city (mutually assured destruction, or MAD): a few

1,000 kt TNT equivalent (i.e., megaton yield) at 1–2 mile accuracy issufficient to kill a large fraction of the population in even the largestcities. China reached this capability ca. 1975 even as a poor, agrariansociety.

• Does MAD hold any meaning with enemies who practice suicidebombings?

• MAD requires knowing the return address. . .• First strike: I try to knock out all of your missiles, so you can’t hit

me.• No need to target cities.• “Winnable” or limited nuclear war? “Use ‘em or lose ‘em”–but you

can’t be sure of knocking out 100%.• Was actively discussed by the “nuclear priesthood” during Reagan’s

presidency (USA)/Brezhnev’s premiership (USSR).

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Gas centrifuges

The modern approach to uranium enrichment: put UF6 in centrifuges at50–70 krpm to get gravitational force of about 106g. Use 10–20 stagesto get good enhancement of 235U relative to 238U.

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Gernot Zippe

• Austrian physicist working forLuftwaffe during WW II.

• Captured by USSR at end of WW II,and ended up leading their centrifugeprogram.

• Released by USSR in 1956. Foundwestern centrifuge programs to beway behind.

• University of Virginia, late 1950s:recreated USSR design. Left US afterdemand that he become a citizen tocontinue this work.

• Returned to Europe, and was afounder of the UK/Dutch/Germancentrifuge enrichment companyURENCO.

Gernot Zippe(1917–2008), fromwww.uranuss.at

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Centrifuges in Iran

• Centrifuge technology likely spread from France to Pakistan, andfrom there to Iran.

• Countries that sign the nuclear Non-Proliferation Treaty (NPT;1968) gain the right to develop peaceful uses of nuclear power, withmonitoring from the International Atomic Energy Agency (IAEA).

• Iran is part of NPT and says it is only developing uraniumenrichment for nuclear power. Reactors only require enrichmentfrom 0.7% to 2.5–3.5%. IAEA found Iran to be in non-compliancewith nuclear materials reporting obligations in 2005.

• The pictures that follow: from the New York Times on April 29,2008; and March 14, 2009.

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Natanz, Iran

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Photos from Iran

AB C

D

E

F

G

H

I

J

K

L

M

N

O

P

A: Intelligence Minister. B. President. C: Defense Minister. D: Head ofAtomic Energy

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Centrifuge schematic

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The nuclear club

• Declared nuclear weapons states with fission/fusion: USA (1945),USSR/Russia (1949), United Kingdom (1952), France (1960),People’s Republic of China (1964).

• Additional declared states: India (1974), Pakistan (1998), NorthKorea (2006).

• Undeclared states: Israel (1967? 1979?), South Africa (1979?;dismantled six nukes and renounced program in 1990).

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Nuclear inbreeding?

Graphic from Dec. 8, 2008 New York Times based on Reed & Stillman:

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Getting good at it

Modern US arsenal: ∼ 500! (Figure: Reed & Stillman)

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Fission to fusion

(Reed & Stillman)

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India

First test: 1974, with yield about 10 kt. 1998 tests:

(Reed & Stillman)

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PakistanHelp from China around 1982. Pakistani test in China on May 26, 1990?(Reed and Stillman).Pakistan’s 1998 tests:

(Reed & Stillman)

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Abdul Qadeer (AQ) Khan• PhD in metallurgical engineering in

Belgium, 1972.• Worked at URENCO (founded by

Zippe) 1972–1975.• Head of Pakistani uranium enrichment

program in 1976; rivalry andindependence from Pakistani AtomicEnergy Commission.

• 2004: televised confession to sellingnuclear weapons technology to Iran,North Korea, and Libya. Plans andkits turned over by Libya toInternational Atomic Energy Agency.Khan under house arrest.

• 2008: in poor health; released fromhouse arrest but not allowed to travel.Publicly disavows 2004 confession.Died in 2009.

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North Korea

• A.Q. Khan’s CHIC-4/A 235U design, based on information fromChina to Pakistan circa 1982? Attempts at trickier 239Pu implosionweapons, since they are doing reactor fuel reprocessing?

• Oct. 9, 2006: first underground nuclear test. Yield about 0.5–1 kt?• May 25, 2009: second test. Yield around 4 kt?• Feb. 11, 2013: third test. Yield around 6 kt? 15 kt? Claim of a more

compact weapon.• As with missiles, they are far from perfecting nuclear weapons.

However, getting hit by 4 kt still leads to a pretty bad day. . .

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Are they gone?

• No! Still number in the thousands.• USA produced 994 metric tonnes of highly enriched uranium, and

111.4 metric tonnes of plutonium.• USSR produced 1200 metric tonnes of highly enriched uranium,

and 150 metric tonnes of plutonium.• 0.1% of USSR production is enough for 16 uranium bonbs and 25

plutonium bombs (Reed & Stillman).

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Pantex

USA has ∼ 14,000 plutonium pits stored at Pantex plant near Amarillo,Texas.

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The responsibility of physicists

J. Robert Oppenheimer, director of the Manhattan Project:In some sort of crude sense which no vulgarity, no humor, nooverstatement can quite extinguish, the physicists have knownsin; and this is a knowledge which they cannot lose.

Fromhttp://en.wikiquote.org/wiki/Robert_Oppenheimer

History of major war

deaths

1

Year (CE)195759

119313401354138715801639

16331658181018221858187018671916191619191942195219651984198419942001

http://en.wikipedia.org/wiki/List_of_wars_and_anthropogenic_disasters_by_death_toll

War

% world population killed

2.01%14.60%

0.83%11.32%

6.70%3.91%0.57%4.80%

1.02%0.65%0.53%0.20%1.83%0.73%0.04%0.05%1.70%0.37%2.30%0.10%0.12%0.83%0.02%0.02%0.07%

Three Kingdoms War, ChinaAn Lushan Rebellion, ChinaCrusadesMongol conquestsLate Yuan warfareConquest of TimurFrench wars of religionQing dynasty conquestThirty Year's War, Holy Roman EmpirePolish-Lithuanian warNapoleonic warsShaka's conquests, AfricaTaiping Rebellion, ChinaDungan revolt, ChinaParaguayan WarMexican RevolutionWorld War IRussian Civil WarWorld War IIKorean WarVietnam WarSoviet war in AfghanistanIran-Iraq warSecond Sudanese civil warSecond Congo War

History of major war deaths

2

0 500 1000 1500 20000.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

% w

orld

pop

ulat

ion

kille

d

Year (CE)

Earth’s atmosphere, and beyond

3

10 100Altitude (km)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Atm

osph

eres

200 40020 40 603 4 6 8

Mt.

Whi

tney

Mt.

Ever

est

Airli

ner

U-2

Shuttle(low orbit) ISS

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Basics of orbitsA stable circular orbit arises when centripetal force provided by gravity:

• Gravity: Fg = GmM/r2 where G = 6.67× 10−11 m3kg−1s−2, andM = 5.97× 1024 kg for earth.

• Centripetal: Fc = mv2/r where v = (2πr)/T with r being theradius from the center of the earth and T being the orbital period(time).

• Set them equal; m drops out.

GmMr2 =

mr

(2πr)2

T2 ⇒ T2 =(2π)2r3

MG

• Solve for r:

r =

(MGT2

(2π)2

)1/3

with T = 1 day, gives 4.2× 107 m or 26,000 miles (earth’s radius is6378 km or 4000 miles). Geostationary orbit.

• For r = 6578 km (200 km above earth’s surface), T = 5312seconds or 88.5 minutes.

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Energy of orbits• Expression for gravitational potential energy is U = −GmM/r, so

∆U = GmM[

1r2− 1

r1

]

• 1 kg from earth’s surface to 200 km above earth: r1 = 6378 km,r2 = 6578 km, so ∆U = 1.898 × 106 J.

• 1 kg to an infinite distance away from earth: r1 = 6378 km,1/r2 = 0, so ∆U = 6.243 × 107 J.

• Kinetic energy of an object in circular motion: v = (2πr)/T so

KE =12

m(2πr)2

T2

• Object on earth’s surface with r = 6378 km and T = 24 hours:KE= 1.07 × 105 J.

• Object at 200 km orbit with r = 6578 km and T = 5412 seconds:KE= 3.027 × 107 J.

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Energy of orbits II

Let’s look at all of these energies for 1 kg mass in units of MJ (106 J):

Kinetic energy KE Gravitational energy UEarth’s surface 0.1200 km orbit 30.3 1.9Outer space 62.4

So getting to 200 km orbit requires about half the energy of escapingearth altogether.

Gravitational potential energy

• Recall that putting 1 kg into a 200 km orbit around earth requires 32.1 MJ

• Raise 1 kg from moon’s surface radius r=1,700 (M=7.3x1022 kg) to r⇒∞: ΔU=2.9 MJ.

• Raise 1 kg from Mars’ surface radius r=3,400 (M=6.4x1023 kg) to r⇒∞: ΔU=13 MJ.

• If we could do this with 100% efficiency, it would be cheap! $1 of oil buys you 57 MJ of chemical energy.

• Short of building space elevators, however, we’re stuck with rockets...

• Shuttle launch: $500M for 25,000 kg, or $20,000/kg to low earth orbit

4

goal is $1,000/kg to earth orbit

Rockets

5

[A]fter the rocket quits our air and really starts on its longer journey, its flight would be neither accelerated nor maintained by the explosion of the charges it then might have left. To claim that it would be is to deny a fundamental law of dynamics, and only Dr. Einstein and his chosen dozen, so few and fit, are licensed to do that... That Professor Goddard, with his 'chair' in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react -- to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools.New York Times, Jan. 13, 1920(retraction issued on July 17, 1969)

Robert Goddard, 1882-1945

A Method for Reaching Extreme Altitudes, by Robert

Goddard (1919)