The goal of this discussion is to findout whether interstellar space travel(travel from star to star) might becomepossible for us in the far future, andmight therefore already be possible forother, more advanced beings. Is thereany hope of making direct interstellarvisits, or will all communication be-tween civilizations be confined to elec-tromagnetic signals? Certainly, frompresent estimates we cannot give adirect and conclusive answer of the yes-no type, but we can point out the sig-nificant basic facts and get as close toan answer as is possible at our presentstate of knowledge, leaving the finalconclusion to the reader.

I shall begin by summarizing the pres-ent limitations and problems of spaceflight, trying to pin down the few basicpoints, and trying to separate the gen-eral difficulties from the merely tem-porary ones. From this starting pointwe may then proceed to estimate thepossibilities of future space flight.The prime postulate in these estim4tes

is a technology much more highly ad-vanced than our present one. Thus, wecompletely neglect all technical prob-lems, however serious they actuallymight be. Only such fundamental prop-erties as time, acceleration, power, mass,and energy are considered.The results are given in terms of the

minimum travel times deriving fromvarious assumptions. Furthermore, wecalculate some basic requirements forreaching these travel times.

Chemical binding energy. The onlypropelling mechanism actually used atpresent is acceleration of exhaust mate-rial by combustion, where the relativelylow binding energy between atoms setsa limit in two ways: in the energy con-tent of fuels, and in the heat resistance

18

of combustion-chamber and nozzlematerials.

In order to remove 1 kilogram ofmatter from the earth against gravity,we need an energy of 17.4 kilowatt-hours. But the best fuel, burning hydro-gen with oxygen, yields only 3.2 kilo-watt-hours per kilogram of fuel (explo-sives yield still less-for example, TNTyields 1.1 kw-hr kg). Thus we need5.4 kilograms of fuel to remove 1 kilo-gram of matter, but the supply of fuelhas to be accelerated too, and this againrequires much more fuel, and so on.Despite this difficulty of low fuel energycontent, small payloads can still beremoved, but with an extremely lowefficiency.The availability of more energetic

fuels would not be of too much help.No nozzle material can stand tempera-tures above about 4000°C at the utmostlimit. If a combustion gas of that tem-perature escapes through a nozzle, itwill do so with an exhaust velocity of4.0 kilometers per second if it is watervapor, and of less than that if sub-stances other than hydrogen are burnt.But the rocket itself needs a velocityof 11.2 kilometers per second to leavethe gravitational field of the earth, andfar greater velocities if interstellardistances are to be covered within areasonable time.The velocity of a rocket after burnout

of all its fuel, V, the exhaust velocitygenerated by the propellant, S, and theso-called mass ratio, 31 = Mi/Mo, areconnected by the well-known rocketformula

Vv 5~~=1n91' (1)

where M, is the total initial mass of therocket (including fuel) and Mo is the

mass after burnout-that is, MA minusthe mass of fuel.- Now, the logarithm isa function which increases very slowlywith its argument; even if fuel consti-tutes 90 percent of the initial mass, therocket velocity will be only 2.3 timesthe exhaust velocity. And if a one-stagerocket with fuel constituting 99.9 per-cent of its initial mass could be built,even then we would achieve a velocityof only V = 6.9 S. We cannot at pres-ent build such a rocket, but we doimitate it through multistage rockets.,With these the difficulty remains thesame, because the mass ratios of allstages accumulate in a multiplicativeway (a tiny payload in the last stage,as compared to a huge fuel mass in thefirst stage), but the stage velocitiesaccumulate only additively. Thus, withcombustion-powered rockets, even ofmany stages, we are just able to leavethe earth, but we cannot reach veryhigh velocities.

In order to see this more precisely,we define the efficiency of a rocket, Q,as the useful energy (the energy con-tained in the final velocity of the emptyrocket) divided by the energy contentof all fuel burnt. We then have

Q (V/S)2 (2)

This efficiency has its maximum value,Q = 0.647, at V/S = 1.59, but it dropsoff very fast and is only 1 percent atV/S = 9. And in the case of manystages the efficiency gets still smaller bya large factor. The efficiency of anideal multistage rocket is only 0.1 per-cent for V/S = 6.

These difficulties connected with lowbinding energy are only temporary ones,because they are confined to combustionprocesses. In increasing the energy con-tent of fuels we can make a huge stepif we use atomic energy; the fissionof uranium, for example, yields 20million kilowatt-hours per kilogram.And nozzles as well as high tempera-tures can be avoided completely whenwe learn to use ion thrust as a propel-ling mechanism (charged particles-ions-are accelerated by electrical fieldsto a high velocity, with which theyleave the rocket). A 5000-volt accelera-tion, for example, could give S of theorder of 100 kilometers per second.With this mechanism, S increases withthe square root of the accelerationvoltage.The author is a member of the staff of the

Astronomisches Rechen-Institut, Heidelberg, Ger-many.

SCIENCE, VOL. 137

The General Limits ofSpace Travel

We may never visit our neighbors in space, butwe should start listening and talking tor them.

Sebastian von Hoerner

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In dealing with these difficulties wehave discovered one fundamentalprinciple:

In order to avoid unreasonablylow efficiencies, the exhaust ve-locity S should be about as largeas the required final velocity ofthe rocket, V, or at least of thesame order of magnitude. (3)

Power-mass ratio. As soon as thesetwo difficulties have been overcome, byobtaining a high energy content in fueland a high exhaust velocity, one willimmediately encounter the next funda-mental difficulty. The acceleration of arocket, b, is of course given by

b= Thrust of engineTotal mass of rocket

Now, the thrust equals the exhaustmass-flow (mass/sec) times the exhaustvelocity S; and the needed power ofthe engine equals the mass-flow timesone-half the square of the exhaustvelocity. We thus can write (insteadof Eq. 4):

b=2P/S (5)

where P is the ratio of power of engineto total mass of rocket.

This means that, if we are workingwith a high exhaust velocity S, weneed a high power-mass ratio P, asotherwise we would get only a smallacceleration b.

But nuclear reactors and all theequipment needed to give a strong ionthrust are so complicated and massive,as compared with the relatively simplecombustion equipment, that there is nohope at present of reaching, with re-actors, the value of P already attainedwith combustion rockets. The accelera-tion thus will be extremely small untilwe can find a way to increase thepower-mass ratio of a reactor by manyorders of magnitude.

Distances for Interstellar Space Travel

The only goal which may be impor-tant enough to justify the immenseeffort needed for interstellar space travelappears to be the search for other intel-ligent beings. In a recent article (1)I tried to estimate the distances betweenneighboring technical civilizations inorder to guide preparations and stimu-late a search for possible electromag-netic signals. The points of interest forour present purpose may be summarizedas follows:

1) It would be megalomania to think

6 JULY 1962

that we are the one intelligent civiliza-tion in the universe. On the contrary,we should assume from our presentknowledge that life and intelligence willhave developed, with about the samespeed as on earth, wherever the propersurroundings and the needed time havebeen provided. From our present limiteddata, we judge that this might have beenthe case on planets of about 6 percentof all stars. The nearest ten such starsare at an average distance from us ofabout 5.6 parsec (I parsec = 3.09 x1013 km = 3.26 light-years).

2) It would be equally presumptuousto think that our present state of mindis the final goal of all evolution. Onthe contrary, we should assume thatscience and technology are just one linkin a long chain and will be surpassedone day by completely new and un-predictable interests and activities (justas gods and demons unpredictably havebeen surpassed by science in offeringexplanations of many important phe-nomena). We should assume a finitelongevity L of the technical state ofmind; if we call T the age of the oldeststars and D the average distance to thenearest ten technical civilizations, weget

D = 5.6 parsec T 1) (6)

We may take about 10 billion yearsfor T, but it is extremely difficult toestimate the value of L. It is my per-sonal opinion that we should take someten thousands of years for L, but sincemany scientists regard this as being toopessimistic, we will take 100,000 yearsfor our present purpose-a value whichgives about 250 parsec for D. Fortu-nately, the uncertainty of L enters thevalue of D only with the power 1/3,and if we change L even by a factorof 8, D will change by only a factorof 2.

With respect to interstellar spacetravel we must clearly separate twoquestions: (i) We may want to knowwhat the possibilities are for our futureinterstellar travel. In this case we areinterested in locating any kind of intel-ligent life, and the distance we arerequired to reach is

5.6 parsec (= 18.6 light-years) (7)

(ii) We may examine the possibility ofother beings visiting us. In this casethe other civilization must be a tech-nical one, and for the calculations thatfollow we will use, for the above-men-

tioned distance to be covered by theseother beings

250 parsec (= 820 light-years) (8)

In order to help visualize these astro-nomical distances, I will describe themwith a model of scale 1: 180 billion.The earth, then, is a tiny grain of desertsand, just visible to the naked eye,orbiting around its sun, which now isa cherrystone a little less than 3 feetaway. Within approximately the samedistance, some few feet, lies the goal ofour present space travel: the otherplanets of our solar system, such asMars and Venus. But the nearest star,Proxima Centauri, is another cherry-stone 140 miles away; and the nextstars with habitable planets, where wemight look for intelligent life, are to beexpected at a distance of 610 miles.The next technical civilizations, how-ever, will be at a distance as great asthe circumference of the earth. Justfor fun one may add the distance tothe Andromeda nebula, the next stellarsystem comparable to our own galaxy:in our model it is as far away as, inreality, the sun is from the earth. Themost distant galaxies seen by astrono-mers with their best telescopes are 2000times as far away, and here even ourmodel fails to help.

Relativistic Treatment

One thing is now clear: in order tocover interstellar distances within rea-sonable times we ought to fly as closeas possible to the velocity of light, theutmost limit of any velocity, accordingto the theory of relativity (and inaccordance with all experiments withhigh-energy particles). But as we ap-proach the velocity of light, the formu-las of normal physics must be replacedby those of relativity theory.

This might be of some help, becauseone of the most striking statements ofrelativity theory is that time itself isnot an absolute property but is short-ened for systems approaching the ve-locity of light. If, for example, we areto move out and back a distance of800 light-years, then people remainingon earth will have to wait at least 1600years for the return of the rocket. Butif the speed of the rocket closely ap-proaches the velocity of light, then theflow of time for this rocket and itscrew becomes different from that onearth, and one may expect that the crewmembers will have to spend only a few

19

years, perhaps, of their own lifetimesbetween start and return.The equations that follow are derived

under the assumption that the formulasof the special theory of relativity stillhold under conditions of permanentacceleration and deceleration-a viewwhich is generally assumed but not yetaccepted. I will keep this part of thediscussion as short as possible, and anyreader who abominates formulas, rela-tivistic or not, may skip to the nextsection.We use the following definitions:

'r is rocket time and t is earth time(both equal zero at the start of therocket flight); v is the velocity of therocket (as seen from the earth); c isthe velocity of light; b is the accelera-tion of the rocket (as measured withinthe rocket by the pressure of a unitmass against a spring), assumed to beconstant; and x is the distance betweenthe rocket and the earth.The differentials of T and t are con-

nected by

dT= dt (I1- fvlc]2) (9)

and the differential equation for v reads

dt (1-[v/c l ==b (10)

which is easily integrated. Solving forv we get

v(t) ~btv(t) = (1 + [bt/c]2)/ (11)

With the help of Eq. 11 we can inte-grate Eq. 9:

t ~ ~ _C btT(t) = - [v/c]2) % dt - b-arc sinh -

(12)

while the distance is integrated accord-ing to

x(t) =vdt= (1 + [bt/c]2)Mo-1

(13)We realize that, in order to get an

equivalent to our rocket formula (Eq.1), thrust and acceleration, if both aremeasured within the rocket, should beconnected as usual:

_ S=MbdT (14)

where M is the total mass of the rocketat any time and - dMI dr is the exhaustmass-flow. But in order to reach v c,

20

Table 1. Energy per mass of fuel for nuclearreactions.

Final Energy/massFuel product (1018 ergs/g)

AnnihilationMatter plus Radiation 900antimatter

FusionHydrogen Helium 6.3Hydrogen Iron 8.3

FissionUranium Mixture, as pro- 0.65

duced in reactorsUranium Iron 1.1

we need also S c according to rela-tionship 3, and S in Eq. 14 should bereplaced by S(1 - S2/c2)-'I. Further-more, S c demands so much energythat in integrating Eq. 14 the mass lossdue to mass defect should be consid-ered, too. In the calculations thatfollow, however, we shall find that, evenwith atomic energy, both S and v stillare much less than c, so that no rela-tivistic treatment is needed, and Eq. 1may be used.The only means of reaching v # c

turns out to be complete annihilation ofmatter. In this case one will use photonthrust, and Eq. 14 should be written as

-dMd c=Mb (15)

We derive the following formulas forannihilation of matter as the energysource and photon thrust as the pro-pelling mechanism (ignoring all doubtsabout the practical realization ofeither). We integrate Eq. 15 from start(M = MO) to burnout of all fuel(M = Mo). The durations of thisperiod of acceleration for the crew, ro,and (from Eq. 12) for people on earth,to, then are

T=o lnX (16a)b

and

to= 2- (M--1) (16b)b

where, again, X = Ms/Mo, and the dis-tance traveled between start and burn-out, x0, is

xo= (7U+_e-'1 -2) (17)

After burnout, the final velocity ofthe rocket, V, is given by

V1=c (18)

-a velocity which causes a time dilata-tion, on the further (unaccelerated)portion of the journey, of

(dt _ X + W-1dr Jo 2 (19)

We notice that the final velocity andtime dilatation do not depend on b or to;it does not matter how quickly we burnour fuel.

The mass ratio should be, of course,as large as possible, and for X>> 1 theequations just given reduce to

to 2TX7xOsz% -(X-2)

V r- c(lI-2/2)

(20a)

(20b)

(20c)

and

(dt\ I1\dT/o 2 (20d)

(see 2). Finally, Eq. 5 needs a slightmodification, too; for photon thrust itreads simply:

b = P/c (21)

Energy Content of Nuclear Fuels

Having seen, earlier in this article,that the energy per mass of fuel is oneof the important considerations in spacetravel, we now ask for the most ener-getic fuels. The utmost possible limitis set by one of the fundamental lawsof relativity:

E=mc2 (22)

which gives the energy E obtained bycomplete annihilation of matter of massm. Or -we might say it another way:energy E has an inertial mass (itsresistance against acceleration) ofm = E/c'. If we call e the specificenergy content (energy/mass), we havefor complete annihilation, E = c' =9 x 102' ergs per gram.

Complete annihilation takes placeonly if matter and antimatter arebrought together: when a proton com-bines with an antiproton, electron com-bines with positron, and so on. But theworld we live in consists of matter only,and to store a large amount of anti-matter with equipment consisting ofmatter seems quite impossible, from allwe know. We thus have to look forsome other source of energy.

If antimatter is omitted, then accord-ing to another fundamental rule ofnuclear physics the combined number

SCIENCE, VOL. 137

of heavy elementary particles (protonsplus neutrons) must stay constant, andthe only thing left is to unite severallight nuclei into a heavy one (fusion)or to split up a heavy nucleus intoseveral light ones (fission), leaving thesum of protons and neutrons constant.In doing this we may gain or loseenergy, according to the differentamounts of nuclear binding energy ofthe various elements. The total energy

content per nucleon (proton or neu-

tron), in case of annihilation, would be931.13 million electron volts for hydro-gen; it drops quickly to 924.88 forhelium, and then slowly to a flat mini-mum of 922.55 for iron. From thenon it increases again, but very slowly,to 922.65 for uranium. The differencesin these figures represent the energy

available for nuclear reactions, and themost energy is gained if we start ateither end and stop at the lowest point,at about iron. Since hydrogen has a

higher value than uranium, we can gainmore energy by fusion than by fission;and furthermore, since the minimum isan extremely flat one, it is not importantto stop exactly at iron.At present we use fission in reactors;

the fission products are a mixture ofelements of all masses, and the gain inenergy is about half that which wouldresult if all fission products were iron.Fusion of hydrogen into helium is thesource of energy of our sun and of mostother stars; it is used in hydrogen bombsonly. Scientists in many countries haveworked hard to produce controlledfusion, but without success so far.The only fuel used at present for

space travel releases energy by chemicalreactions, where the burning of hydro-gen to water yields only an energy-mass

ratio of 1.15 x 1011 ergs per gram. Ifwe learn to use uranium reactors in-stead, the energy-mass ratio will beincreased by a factor of 5.6 million.If it ever became possible to use thefusion of hydrogen into helium as a

power source for space travel, one

would gain another factor of 10; andif complete annihilation were practi-cable, a further factor of 140 would begained. Table 1 summarizes these facts.

Acceleration and Time

Thus equipped with an understandingof nuclear fuel, if not with the realthing, and with relativistic formulas,we proceed with estimating the generallimits of future space travel.

6 JULY 1962

As a first step we neglect even therequirements of energy and power. Theonly limitation then remaining will bethe maximum amount of accelerationwhich a crew can stand. It has beenestimated (3) that a terrestrial crewcan stand, for a period of years, approx-

imately b = 1g. It seems likely that,over a long trip, any crew will standonly about as much acceleration as itsmembers are used to experiencing on

their home planet. This might differfrom our case by a factor of, say, 2or 3 in either direction, but probablyby less if the conditions for the develop-ment of life are carefully regarded. Inthe following discussion we will use alimit of 1g.

If the acceleration is limited to thisfixed value, the shortest travel time fora given distance will result if we accel-erate with lg half of the way and thendecelerate with lg over the second halfof the trip, returning in the same way.

On the basis of this assumption andof Eqs. 11 to 13, Table 2 has beencalculated.We see that the relativistic time dila-

tation yields an effective gain for thecrew only if the crew members spendmore than about 10 years of their liveson the voyage. The further increase,however, is a very steep one (exponen-tial); if the crew members spent 30years of their lives on the voyage theywould be able to fly to the Orion nebulaand back, and 3000 years would haveelapsed on earth between their depar-ture and their return. For our goals oftravel to distances of 5.6 and 250parsec, we obtain the values in Table 3.

With these results, many readers mayalready have lost hope of future inter-stellar space travel; others still may beoptimistic. But so far we have neglectedthe requirements of energy and power.

Energy and Time

Acceleration and deceleration requirea lot of energy, which has to come fromsomewhere. One might perhaps thinkof providing the rocket with a largefunnel in order to sweep up the inter-stellar matter for fuel. But the inter-stellar matter has only a very low den-sity (about 1024 g/cm3), and in orderto collect 1000 tons of matter (10 timesthe fuel of one Atlas rocket) on a tripto a goal 5.6 parsec away, one wouldneed a funnel 100 kilometers in di-ameter; we will rule out this possibility.We cannot refuel under way in this

Table 2. Total duration and distance reached,with constant acceleration and deceleration at Ig.

Duration (out and back)(yr) Distance

reachedFor crew Frec)on board For people (parsec)rocket on earth

1 1.0 0.0182 2.1 0.0755 6.5 0.52

10 24 3.015 80 11.420 270 4225 910 14030 3,100 48040 36,000 5,40050 420,000 64,00060 5,000,000 760,000

manner, or in any other way whiletraveling at high speed, and thus therocket must be provided initially withall the energy it needs to reach its goal.But we might allow for refueling at thedestination point, when the rocket willbe at rest. For our estimate we willconsider a three-stage rocket: stages 1and 2 are used for the trip to the desti-nation, there stage 2 is refueled, andstages 2 and 3 are used for returning.There is thus one stage for each periodof acceleration or deceleration.The next thing to be fixed is the mass

ratio X of a single stage. Our presentvalues for 9W are around 10, but thevalues would become very low if anyenergy source other than combustionwere to be used. Keeping in mind theextremely massive and complicatedequipment needed for nuclear reactions,and for propelling mechanisms such asion thrust, we think that a value ofIf = 10 could be used as an extremeupper limit, even for a much moreadvanced technology.The only source of nuclear energy

now in sight is the fission of heavynuclei such as uranium, where 1 gramyields 6.5 x 1017 ergs. The highestefficiency is achieved if the fission prod-ucts themselves can be expelled forpropulsion with their fission energy(although at present we have no ideahow this can be accomplished). In this

Table 3. Total durations, for rocket-crew mem-bers and for people on earth, of round-tripvoyages to distances of 5.6 and 250 parsec, withconstant acceleration and deceleration at 1g.

Distancereached(parsec)

5.6

250

Duration (yr)

For crew On earth

12.3 42

27.3 1550

21

case, we will get an exhaust velocity ofS = 13,000 km/sec = c/23-a valueso small as compared to the velocityof light that Eq. 1 still may be used.With a mass ratio of 10 as a limit, thefinal velocity after burnout then isV = 30,000 km/sec = ci10. Rela-tivistic effects, such as time dilatation,will not play a role of any importance.In order to reach greater distances wehave to fly most of the time withoutacceleration (after burnout of the firststage) and decelerate shortly beforereaching the goal with our second stage.The full travel time, out and back, is380 years for 5.6 parsec and 17,000years for 250 parsec. This certainlydoes not look very promising.

If one is optimistic enough to thinkthat the fusion of hydrogen into heliummight become usable for rocket propul-sion, with a mass ratio of 10, even thenonly V = c/5 can be achieved, andtime dilatation again will be unimpor-tant. The full travel time is 180 yearsfor 5.6 parsec and 8000 years for 250parsec-not much better than before.The utmost limit, which cannot be

surpassed, is set by the mass equivalentof the needed energy itself (its resist-ance against acceleration), no matterhow this energy is stored. Personally,I do not think that complete annihila-tion of matter, or some other means ofstoring "pure energy," ever will becomepractical for any purpose, let alone inrockets with a mass ratio of 10. Butimagine that it does: then 98 percentof the velocity of light can be achieved,according to Eq. 20c, and as a resultof the time dilatation, the time for thecrew will get shorter than the time onearth (after burnout) by a factor of5.0. For 5.6 parsec, the full travel timewill be 14 years for the crew and 42years on earth, and for a distance of250 parsec we get 300 years for thecrew and 1500 years on earth. We stillmust spend 14 years within a rocketin order to search for intelligent beings,and only after 300 years in a rocketwill the inhabitants of some alien planethave a fair chance of meeting otherbeings, like ourselves, who are in justthe same state of science and technologyas they are.

I should mention again that the finalvelocity after burnout does not dependon the amount of acceleration b, eitherin the classical treatment (Eq. 1) orin the relativistic one (Eq. 18). Onlythe energy content of the fuel and themass of the rocket are important, notthe rate at which fuel is consumed. The

22

latter rate will influence the durationof the acceleration period, of course,but not the final velocity. This meansthat if we should prepare the crew toresist very high acceleration (by freez-ing them in a solid block of ice, or thelike), we could shorten the accelerationperiods but not the duration of theunaccelerated flight in between.

In the case of fission or fusion, almostall of the travel time is spent in un-accelerated flight after burnout, andhigh acceleration will not help at all.In the case of annihilation, however, 9.5years of the crew's time is spent inaccelerated or decelerated flight, andthis period could be shortened throughgreater acceleration, but we are stillneglecting the power requirements. Fora distance of 5.6 parsec, 4.2 years ofthe crew's time is spent in unacceleratedflight, and this petiod cannot be short-ened in any way; again, for a distanceof 250 parsec, almost all of the time isspent in unaccelerated flight.

Power-Mass Ratio and Acceleration

For the interstellar distances dis-cussed earlier we need a travel velocityclose to the velocity of light, andaccording to principle 3 we must haveV S for reasonable efficiency. Thesecriteria taken together then demand thatS c. Furthermore, we have seen thatcomplete annihilation of matter is theonly hope as a power source in inter-stellar space travel, and since we mustnot waste any matter by using it forpropulsion, only photon thrust is left us.In that case Eq. 21 applies, andb = P/c.From Eq. 16 we see that the accelera-

tion must be as large as possible inorder to hold To small, but we haveargued that b must be limited to about1g. The two considerations then de-mand that b 1g.Now, if Eq. 21 holds and b 1 g,

then the power-mass ratio must have theextremely high value of

P = 3 x 101'1 cm2/sec3 (23)

or, in the power units of watt or horse-power,

P = 3 x 10'watt/g = 4 x 03'hp/g (24)

In order to understand the full mean-ing of Eq. 24 we might consider ourpresent fission reactors-those with thehighest power-mass ratios. Reactors forship propulsion, with power output of

15 megawatts and weight of 800 tonsgive P = 0.02 watt per gram-a valuetoo low by a factor of 1.5 X 108 tofulfill Eq. 24. If no shielding and nosafety measures were needed, then thehighest value theoretically possiblewould be P = 100 watt per gram, stilltoo low, by a factor of 30,000. In fact,according to Eq. 24, the whole powerplant of 15-megawatt output (enoughfor a small town) should weigh notmore than 5 grams (the weight of 10paper clips). Or to express it anotherway, to fulfill Eq. 24, the engine of agood car, producing 200 horsepower,could not weigh more than 50 milli-grams-one-tenth the weight of apaper clip.

But that is not all. Not only do weneed power, we have to get rid of it,too. Photons might be emitted in theoptical or the radio range, and propul-sion will result if all emission is in onedirection. A large transmitting stationof 100-kilowatt power output can thengive the tiny thrust of 30 milligrams,and so can an aggregate of searchlightswith combined power of 100 kilowatts.And all this should weigh not morethan 1/ 15 the weight of a paper clip.The power source and transmitter re-quirements must be combined, and themass entering Eq. 24 must containreactor as well as emitting stations.So far we have neglected payloads

and fuel, and the mass of these mustbe included in Eq. 24, too. As anexample we start with a "small" spaceship of 10-ton payload, and we addanother 10 tons for power plant plusemitters. If we want to reach a velocitywithin 2 percent of that of light (witha dilatation factor of 5), we need amass ratio X = 10, according to Eq.20d, and the total mass of the rocketwill be 200 tons. We find, from Eq. 24,that in order to get an acceleration ofb = 1 g, we would need a power outputof 600 million megawatts. Thus,

We would need 40 million anni-hilation power plants of 15 mega-watts each, plus 6 billion trans-mitting stations of 100 kilowattseach, altogether having no moremass than 10 tons, in order toapproach the velocity of light towithin 2 percent within 2.3 yearsof the crew's time. (25)

If requirement 25 is not fulfilled, weget equations for the periods of accel-eration and deceleration as follows.From Eq. 16a we have

c2ro = IIn XP (26)

SCIENCE, VOL. 137

and from Eqs. 20a and 20b we get

to=2p x (27a)

and

CaXo= 2P (3-2) (27b)

If, for example, we fail to fulfillrequirement 25 by a factor of 106 (ifwe have 40 power plants plus 6000transmitters, weighing, in all, 10 tons-still a fantastic value), then b = 10-'g,and it would take 2.3 millions of yearsfor the crew to approach the velocityof light to within 2 percent.

Or, to put it the other way round, ifone wants to get an acceleration of,say, b = 100g, in order to take fulladvantage of having a deep-frozen crew,then 100 times the weight of the equip-ment mentioned in requirement 25must not total more than 10 tons;

this means that power plants plus trans-mitters should have an output of 6000megawatts per gram. Purcell (4) hasarrived at similar conclusions from astudy of the requirements of relativisticrockets. There is no way of avoidingthese demands, and definitely no hopeof fulfilling them.

Conclusion

The various questions dealt with inthis article have not led to the definitiveanswer that interstellar space travel isabsolutely impossible. We have foundsimply the minimum travel times givenby different assumptions, and we havefound the requirements needed forreaching these limits. This is, at present,all we can do, and the final conclusionas to the feasibility of such ventures isup to the reader. The requirements,

however, have turned out to be suchextreme ones that I, personally, drawthis conclusion: space travel, even inthe most distant future, will be confinedcompletely to our own planetary system,and a similar conclusion will hold forany other civilization, no matter howadvanced it may be. The only meansof communication between differentcivilizations thus seems to be electro-magnetic signals (5).

References and Notes

1. S. von Hoerner, Science 134, 1839 (1961).2. A different derivation of Eq. 20, connecting V

and M, has been given by J. R. Pierce [Proc.I.R.E. (Inst. Radio Engrs.) 47, 1053 (1959)]together with a good explanation of the so-called clock paradox. Pierce also investigatesinterstellar matter as fuel, with the same nega-tive result as that given in this article.

3. Space Handbook: Astronautics and its Applica-tions (U.S. Government Printing Office, Wash-ington, D.C., 1959), p. 113.

4. E. M. Purcell, Brookhaven National LaboratoryLectures, No. 1.

5. I wish to thank F. D. Drake for reading themanuscript.

News and Comment

Military in Space: Air ForceSeems To Have Won ArgumentFor Expanded Program

The Administration has denied thatit is planning a major role for themilitary in space, but at the same timeit has explained that it is taking out''necessary insurance against militarysurprise in space."The dilemma that faces it on the mil-

itary's role in space is an enormouslycomplex one, with no simple answers

ready at hand. In many respects thedilemma is similar to the one- facedby the Truman Administration when itwrestled with the pros and cons of de-veloping the hydrogen bomb. The deci-sion in that case was that the UnitedStates could not afford the risk ofdenying itself destructive capacity ofa new order unless there were an as-

surance that the Soviets would alsoforego development of the weapon.

6 JULY 1962

There was, of course, no such assur-ance, and U.S. efforts were spurred onby uncertainty about what the Sovietswere up to, while the Soviets alsowent ahead, presumably figuring thatit was too dangerous for them to stayout of the race.

It would have been astonishing ifthe H-bomb question had been de-cided otherwise, for the sad fact isthat technological developments withmilitary applications have inevitablyended up in military hardware. As faras a military space role is concerned,the principal impediment is that therole is not yet clearly visible, at least,not from this country's vantage point.In other words, there is not yet anycertainty about what you can do inspace to hurt an enemy or preventhim from hurting you that could not bedone just as well-and more cheaply-from the earth.

This uncertainty need not remain

indefinitely, for it is a fair assumptionthat, with the investment of enoughmoney and talent, military functionscan be developed for space. Amongthose that seem most feasible are sur-veillance and rendezvous techniquesaimed at destroying hostile space ve-hicles; a more remote possibility, butgetting some thought, is orbiting bombs.

Against this background the Admin-istration has been trying to maneuverin the very limited area between ac-celerating the arms race and comingout second to the Soviets in militaryspace technology. At the outset, thedominant view in the Administrationseemed to be that the Soviets were notforging ahead with military spacework, and that therefore the UnitedStates would only touch off a new lineof arms competition if it undertooka major military space program. Thiswas the view held by the civilianmanagers of the Department of De-fense, and it seemed to be shared byKennedy. Strongly opposed was the AirForce, which argued that the SovietUnion had never demonstrated any in-terest in refraining from weapon de-velopment. Furthermore, the Air Forceargued, the great lead times requiredto develop space equipment shouldrule out any wait-and-see policy.The effect of these arguments, pos-

sibly reinforced by intelligence find-ings that have not been made public,has been to move the Administrationin the direction of the Air Force's

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