Feasibility of interstellar travel

'^r'-' Iff. 32-23 3

N 64 -160 6 8

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lift

IS!*^*''i9^|i:M;iiiS.?te|^

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^^,.ip:;./;p||f|^ji§ -ipj;^

FEASffitUn OF INTERSTELLAR TRAVEL

by

DWAIN F. SPENCER
LEONARD D. JAFFE

JET PROPULSION LABORATORY

\409 \

INTRODUCTION / 4 ^

The prospect of interstellar exploration has aroused considerable spec-
ulation during the last 20 years. The earliest studies of relativistic rocket
mechanics by Ackeret (Refs. 1 and 2), Tsien (Ref. 3), Bussard (Ref. 4), and others
made two implicit assvunptions that severely limit the performance of the vehicles
considered. They assumed that the nuclear-energy rockets are limited to a single
stage and that the available energy corresponds to a fixed fraction of the final
vehicle mass. The latter assumption apparently arose from the thought that spent
nuclear fuel would either be retained on board or dumped, rather than exhausted
at high velocity. These assumptions are neither necessary nor desirable.

More recently, interstellar travel has been considered by Sanger (Ref. 5),
Stuhlinger (Ref. 6), and von Hoerner (Ref. 7). They realized that the amount of
available energy was a function of the propellant mass rather than the final vehicle
mass; however, they did not consider staging the vehicles as is done with chemical
rockets. They concluded, therefore, that interstellar travel using either fission
or fusion nuclear reactions as an energy source is impossible because of funda-
mental limitations on the amount of available energy and that the photon (annihila-
tion) rocket is necessary. In contradiction, this analysis shows that nuclear
fission or fusion rockets can theoretically perform interstellar missions w^ith
reasonable flight times.

The problem of utilizing the full potential of fission or fusion nuclear
reactions in a rocket engine is more difficult. The second portion of this paper
considers some of the requirements of a fusion propelled vehicle to perform an
interstellar probe mission.

BASIC EQUATIONS FOR SINGLE-STAGE ROCKET

The basic equations for single-stage rocket propulsion at relativistic
velocities were derived by Ackeret and have been utilized by subsequent workers.
Ackeret' s work is inexact, however, in that he considers the rest mass exhausted
to equal the rest mass of fuel consumed. More exactly, the rest mass of fuel
consumed is

M. = M + € M. (1)

f ex f ^^'

where M = rest mass exhausted and M^ = rest mass of fuel converted to

ex f

kinetic energy. The initial rest mass of the vehicle is

where M, is the rest mass of the vehicle at burnout.

D.O.

410

Let

X = ^•°- (3)

Mjj = Mj(l+X) (4)

Then

The stage mass ratio is

6 H ^0 -l±iL (5)

This is simply the result obtained with a chemical propulsion system.

To discuss the exterior energetics of the vehicle, a coordinate system
fixed in space and a system relative to the vehicle may be used (Refs. 4, 5, and 6).
By employing conservation of momentum, mass, and energy, and the Lorentz
addition of velocities, Ackeret showed that the final vehicle velocity is given by

^2w/c
^ = 6 - 1 (6)

g2w/c ^ J

A relationship between the exhaust velocity and the fraction of fuel con-
verted to energy gives the desired form for the final -velocity. This is given by
Sanger, Huth (Ref. 8) and Spencer (Ref. 9)

f = [c (2 . C ) ] a)

BASIC EQUATIONS FOR MULTISTAGE ROCKET

The kinematics of mxiltistage relativistic rockets have been treated only

by Subotowicz (Ref. 10); however, he did not examine energy requirements. As

shown in Ref. 10, the burnout velocity u for the nth stage is given by

n

(8)

2w. /C
6 . j/ +1

u
n

n

n

2w. ,c
J

- 1

c

n

n

2w. /C
6. j/

+ 1

411

As in the classical case (Ref. 10), optimum staging occurs for equal step mass
ratios or equal step burnout fractions if each step has the same exhaust velocity.
Then Eq. (8) reduces to

u

.2n w/<

g2nw/c ^j

(9)

where w/c is given in Eq. (7). Then

lim
n ^ »

= 1

(10)

for a fixed step mass ratio. Thus, if enough stages are utilized, regardless of the
exhaust velocity or mass ratio per stage, it is theoretically possible to attain a
final velocity near that of light.

Another important aspect in the feasibility of interstellar travel is the
final payload mass which can be delivered by a particular vehicle. Consider an
n-stage vehicle with stage burnout rest mass (XM ). and stage structural or dead
rest mass ( j3 M ).. Then the payload mass of the jth stage

(Mp). = (XM^). - iPM^). - (M^).^^

(11)

the initial mass of the (j+1 )th stage.
Generalizing Eq. (4)

J

= M^ ( 1 + X )
J

(12)

Successive use of Equations (11) and (12) produces the overall payload to initial
weight relation

M =
P

n

n (X.
j=i i

^i'

n (1 + X. )

j=i J

M,

(13)

Since the step fractions ^. and the stage fractions X. for optimum staging
should be the same for all stages, ^Eq. (13) reduces to ^

M
E

= * =

(X - |8)
(1 + X )'

(14)

412

It may be of interest to determine the maximum vehicle burnout velocity
for a given dead-weight fraction P and desired over-all payload fraction *.
Algebraic solution for X from £q. (14) yields

X = (*)

Substituting in Eq. (5) gives

1/n

1 +

6 =

P

1 - {*)

1 + P

77^

v^

(15)

(16)

and from Eq. (9)

2 nw/c

- 1

2 nw/c"

+ 1

(17)

Using Eq. (7), the final burnout velocity of the n-stage vehicle in terms
of over-all payload fraction, deadweight fraction, and fraction of mass converted
to energy, is

^ _ iirv^)

Zn

j^

2 - f )

- 1

(18)

+ 1

Figure 1 is a plot showing the over-all mass ratio required versus energy fraction
€ for various final vehicle velocity ratios u /c. The over-all mass ratio is given
by "

A ^6'

(19)

413

^-=p^^

V---H— V— 1 INI 1 — 1 — A

4- - \ 1 \ FRACTION OF — -J

I- JLA — _ LIGHT VELOCITY 4

A 44

-XL -T

URVE

1 " "

.oH _. ii

-Xt^-

--='r

'-{'AW'-

B
C

E
F
G
H

1

0.2

0.3
0.4
0.5
0.6

0.7

0.8
0.9

t--tt

i-v\XX-

- k----B^

lEtt----

-4==:H

5=Sn4::

o 4-44

--At^H--

ti ,o» --4-4

\W\^

I — E:i3-

r^XM

-

t tnT L

^ «• -'- — V-

P-S^4

i — : -±

"-rES&5

° \ ^

^ livSQ

lOS *\ '

W°W\W

v-

:::£

4::Ee-S

V-

_ 4

^ AAV\V

A

102 V-

:=mvs

V\

^

r-£4A^S

V\

S —

^" V^^A

\^v

^ ^.

lO'

._v KN.S

s\^

V A.

V

K)-*

I0-*

10-2

K)0

MASS FRACTION CONVERTED TO ENERGY €

Fig. L Over-all mass ratio required versus energy fraction for various frac-
tions of light velocity

EXAMPLES OF VELOCITIES AND TRANSIT TIMES

Following are some examples of velocities and transit times which may

be attainable. The fraction of mass converted to energy by uraniuna fission is

about 7 X 10"4; by deuterium fusion, 4 x 10"^, Table 1, obtained from Fig. 1, shows

the over-all mass ratio A necessary to reach various velocities u /c for a fission

«4 ' n

rocket with € = 7x10 . Table 2 shows the necessary mass ratio for a fusion

rocket with an energy conversion fraction e = 4 x 10"^. If deceleration at the

destination is required, the mass ratios must be sqxiared; for a two-way trip with

414

_4
Table 1. Mass ratios required for fission rockets* € = 7 x 10

Required over-all mass ratio A

rip. One-way trip. Two-way trip,

without deceleration with deceleration with deceleration

2.0 X 10^ 3.8 X 10^

4.8 X lO'* 2.3 X lo'

1.7 X 10^

9
8x lO''

Fraction of

light velocity

One-way
without dece

0.1

1.4 X 10^

0.2

2.2 X 10^

0.3

4.1 X 10^

0.4

9.0 X lO"*

0.5

2.1 X 10^

0.6

X 10^

_3
Table 2. Mass ratios required for fusion rockets, € = 4 x 10

Required over-all mass ratio A

Fraction of

ight velocity

u /c
n

One-way trip,
without deceleration

One-way trip,
with deceleration

Two-way t
with decelei

0.1

3.0 X

10°

9.0 X 10°

8.1 X 10^

0.2

8.9 X

10°

7.8 X 10^

6.2 X 10^

0.3

3.3 X

10^

1.1 X 10^

1.1 X 10^

0.4

1.1 X

10^

1.2 X 10*

1.5x10®

0.5

4.4 X

10^

1.9 X 10^

0.6

2.3 X

10^

5.2 X 10^

0.7

1.6 X

10*

2.6 X 10®

0.8

2.1 X

10^

0.9

1.4 X

10^

415

deceleration at each end, the mass ratios must be raised to the fourth power.
These values are also shown in the tables.

3 6

Mass ratios of 10 to 10 seem quite feasible in principle. For un-
manned probes, one-way trips without deceleration may well be adequate.
Feasible velocity ratios corresponding to the mass ratios mentioned above
are then 0.3 to 0.5 for uranium fission and 0.6 to 0.8 for deuterium fusion. The
corresponding travel times depend on the acceleration used. If approximately
1-g acceleration could be achieved, relativistic velocities would be reached
within a few months and the spacecraft could then coast to its destination at the
velocity indicated above. To reach Alpha Centauri at 4.3 light years, the transit
times would be 9 to 14 years with a fission rocket and 6 to 7 years with a fusion
rocket.

Figures 2 to 4 show the attainable vehicle burnout velocity as a function
of the number of stages for payload ratios of 10"!, 10"^, and 10"^ for a fusion
rocket with € = 4 x 10"^. An interesting feature of these curves is the fact that. a
five -stage vehicle attains nearly the maximium possible velocity increment for a
particular payload fraction.

>-
I-

u
o

>

X

o

0.20

0.18

DEAD-

-WEIGHT F

RACTION

^"^

'^ » 0. 1

0.16
0.14
0.12

aio

/

= 0.2

(,

^

)S«0.3

( ^

^

« «4

«'tO

<\0^

1

5

4

\ 6

NUMBER OF STAGES n

Fig. 2. Fractions of light velocity attainable for a deuterium fusion rocket
versus number of stages for various dead-weight fractions (payload
fraction^ 10- h

416

OMO

DPAD-

WEIGHT FRACTION]

>-
O

3

^ a4o

•-

X

o

3

/

^«0.l

/

^*0.3

^ OlSO

/ y

^ y

o ****

/ /

/

z
o

/

/

, « 4 X 10"'

u

'//

«.io

-5

0.10

'/

2 9 4

NUMBER OF STAGES m

Fig, 3. Fractioms of light velocity attainable for a deuterium fusion rocket
versus nmmker of stages for various dead-weigbt fractions (payload
fraction ^10'^)

arc

>

DE
1

:ao-

VEIGHT F

RACTION
p. 0.1

/

Z'

0«O.2

/

/

^«0.3

•-

1 0.40

//

^z-

/

/

/

O

/

//

r

o

/

/ /

V/

/

c*4>

•«io-

CIO-^
4

OJO

'/

2 3 4

NUMBER OF STAGES m

Fig. 4. Fractions of tight velocity attainable for a deuterium fusion rocket
versus number of stages for various dead-weigbt fractions (paylo^
fraction ^10-^)

417

Figure 5 displays the effect of the dead-weight fraction )3 for a five-stage
fusion rocket at various payload ratios. The relatively small effect of the dead-
weight fraction upon performance is a very significant feature in the design of this
type of system. It indicates that a strong effort should be made to obtain 100%
burnup even at the cost of additional structural weight.

bJ

>

X
(9

o

q:

10"* I0~* 10*'

OVER-ALL PAYLOAD FRACTION ♦

Fig. 5. Fractions of light velocity attainable for a five-stage deuterium fusion
rocket versus over-all payload fractions for various dead-weight
fractions

LIMITATIONS ON TRANSIT FOR A FUSION ROCKET VEHICLE

In general, the amount of fuel which can be utilized in a nuclear reaction
is less than the theoretical limit. This is the so-called burnup fraction which is
a number less than or equal to unity. The equation for the exhaust velocity of a
particular stage can then be generalized to be

1/2

w

€ b (2 - €b

(20)

In order to determine the effect of burnup on system performance, we
recall that for optimum staging, (Eq. 9),

u

n

g2 nw/c _ J

6

2 nw

7%T

(21)

Figure 6 shows the performance of a fusion vehicle with an acceleration
of one g per stage, and a stage mass ratio of 10. It should be noted that unless
burnups of greater than 1% can be achieved, there is little chance of the fusion
vehicle performing interstellar missions to five light years with flight times less
than 50 years.

418

< MASSuUTK)

\k-1.0

1 1

1 ,

? i

NUMSt or STAGS

Fig. 6. Effect of incomplete bumup on the performance of fusion rocket vehicle

GENERAL CHARAQERISTICS OF A FUSION ENGINE

Figure 7 presents a schematic of a typical fusion engine. The basic
components of the system are the fusion plasma, the^superconducting coils, the
structural vessels (including insulation), the refrigeration cycle, and waste heat
radiators (not shown). A separate refrigeration system would be necessary to
cool the superconducting coils from that u^ed to cool the structure. For purposes
of discussion, the heat load to the coils was neglected, and all energy escaping
the plasma was assumed to be absorbed in the structure.

Now, the thrust of the engine is simply

F = m w
ex

(22)

and the required fusion exhaust power is

P = 10'" Fw/2
ex

(23)

The total power output from the fusion reactor is

P = P

ex

1 - (y + a)

(24)

419

where y is the fractional power carried by the neutrons and a is the fractional
power lost from the fuel due to bremsstrahlung and cyclotron radiation. The
power which is absorbed in the engine walls is then

y + a

abs

1 - (y + a)

ex

(25)

TO RADIATOR

FROM RADIATOR

INSULATION -

RErtlGERAirON f*-
CYCLE1

STRUCTURE -

AND
SHIEID

loop OttOl 1

REFRIGERATION
CYCLE 2

Fig. 7. Schematic of a fusion engine

As pointed out in Ref. 11, the D - He reaction is of particiilar interest
for rocket propulsion since the products are all charged i>articles, and thus, can
be trapped by the external magnetic field. Now consider the competing reactions
in such an engine (Ref. 12),

D+ He"

He

+ H

3.6 Mev 14.7 Mev

(26)

50% yield
of each

D+ D

D+ D

^ He + n

0.82 Mev 2.45 Mev

^ T + H

1.01 Mev 3.02 Mev

(27)

(28)

D+ T

^ He + n

3.5 Mev 14.1 Mev

(29)

420

If we neglect reaction (29), the fractional energy release which is
imparted to the neutrons can be estimated. Liet y represent the fuel fraction of
He and then (1-y ) is the fuel fraction of D. Define the fraction of power carried
by the neutrons as

P

Then,

P^ (30)

0.5 (1-y)^ (a v)jj (2.45)

y= __ .^-—

y(l-y) (av) (18.3) + 0.5 (1-y) (0^\ (7.3)

wrhere Q v determines the reaction rate for a Maxwellian velocity distribution.

The fractional energy lost by bremsstrahhing and cyclotron radiation, a ,
is defined as

" = «br *«c (32)

The equation for O. (Ref. 17) is

%r

5,35 X 10"^^ N (N, z/ + N Z,^ ) T ^^^
ell 2 2 e

12

(33)

2.93 X 10 Nj N^ <^^>i2

above

mately

Rearranging and using the definitions of the He and D fractions given

-19 '^/^
1.8 X 10 T^ (3y + 1 ) (y + 1 ) (34)

y(i-y) (<yv)j2

The fractional power going into cyclotron radiation (Ref. 13) is approjd-

8.5 X 10"^* r (y + 1 ) T'. T' + (y + 1 )^ T' ^ 1 ( 1 + T' .

L 1 e e J e )

9 = 204 (35)

y ( 1 -y ) (<'^)i2

421

Due to self absorption of the cyclotron radiation in the plasma and
reflection from the chamber walls (if properly designed) the fractional power lost
through this mode may be reduced. In the region of interest for these studies,
the fractional energy lost is approximately 1% of 9 thus

a

10'^ e

(36)

Figure 8 shows the fractional power entering the wall versus He
fraction in the fuel for various ion temperatures. In all cases an ion to electron
temperature ratio of Z is assximed. There appears to be an optimum operating
temperature of 100-200 kev in the region from 0.5 to 0,7 He^ fuel fraction. It
should be noted, however, that the minimum fractional energy escaping the fuel
is 20%. This simply means that 20% of the generated energy must be dumped by
a thermal radiator. A similar problem has been well known to designers of
gaseous fission power plants (Ref. 14).

^.4 4-

JZ .2 --
2

H.'' FUEL FRACTION, y.

Fig. 8. Fractional energy loss from He^ — D plasma versus fuel fraction of He^
at various plasma temperatures

The remaining equations which are necessary to determine the per-
formance of the system will now be considered. The rest mass of fuel exhausted
is generalized to

m = m. ( 1 - b e )
ex f

(37)

422

and the rest mass of fuel burned is

(m^)^ = bm^ (38)

But this is governed by the reaction rate in the chamber. Then,
neglecting the DD and DT contributions.

S>b = iC ) NlN2<^">12^f <39>

where V is the volume of the fuel.
The thrust is given by

F =

[ i^— j NjN^ (av)j2 V^£ (l-be) ^c(2-bc)\

1/2
(40)

If the engine thrust and size are specified (along with the reaction
temperature), the required fuel concentration may then be determined from
£q. (40). This, in turn, sets the required magnetic field for confinement. Under
optimum conditions, the confining magnetic field strength is simply

B = (8v N^ kT)^/^ (41)

REFLEQION OF ENGINE CONSTRAINTS ON VEHICLE PERFORMANCE

In order to assess the potential of an actual vehicle, some estimate must
be made of the major system weights. In this analysis, the weight of the engine
chamber and waste heat radiator are considered. In this analysis, the engine
structure is assumed to be tungsten. Since the strength to weight ratio of tungsten
is a function of temperature, so also is the weight of the structure. The strength
to weight ratio for tungsten is given in Ea. (42).

p/s = 7.45x10 T^ (42)

Due to the fact that the coolant must be heated from its temperature
leaving the structure T to some radiating temperature, T , the amount of heat
to be rejected by the radiator is also a functioning of T . This may be seen by^
considering a simple refrigeration cycle where

j(^^)

^ad = n — T ^abs "■ ^bs <^^>

423

For purposes of discussion, we assume an efficiency of the recrigeration
system, TJ of 0.3. Then,

(3.3 T ^ - 2.3 T

p = p "^ L. (44)

rad abs T

s

By extrapolating the results of Ref. 15, the weight of a belt type radiator
is given by

17
1.25 X 10 P ,
^ ^ Ead_ (45)

rad ^

rad

It is obvious that we wish to operate the belt at as high a temperature,
1 possible. This temperature is then <
Eq7l44) and (45), the weight of the radiator is

T ,, as possible. This tenaperature is then assumed to be 2500^K. Combining
rad

*„. = ^^^ -,.. --'^ -...

s
The weight of the chamber structure is

W = - R^ B^
s s

or for a diameter of 10 m and an l/d of 2 (at a thrust level of 10 lbs.)

(47)

W = 2.05x10'^ B^ ( 5-|T/'" (48)

By combining Eqs. (46) and (48), it is obvious that there is an optimum

channber coolant temperature, T . Then

s

dW^ 1.06x 10" P ^ ^ ^

^ = = . :: ^^ +1.23xlO"^B^ X

dT

s

(49)

V \

f \ T -0.4

15.7 xlO« ' «

424

18

After rearranging aAd solving for T , the optimum structural temperature

s

T =

s

8.61 X 10 P

abs

B ( 1 )

L V 15.7x10® L

0.625

(50)

of T into

s

The minimum weight can then be determined by substituting this value

V, „ 0.6

W„ =,.i.06^il£_ . 2.94 1 p^^^ + 2.05 X 10-5 ^2

15-7 X 10

8

(51)

Although all other system weights are neglected, this at least provides a basis
from. which the vehicle performance can be estimated*

In order to obtain the required vehicle characteristics, the gross payload
necessary for an interstellar mission is estimated to be 10,000 lbs. The principal
portion of this weight is necessary to provide telecommunications capability.
Using X-band communication to a 200' terrestrial dish (Ref. 16), an information
rate of 1 bit/miin requires a 1 Mwe power transnoitter at a distance of 5-10 light
years. The auxiliary powerplant necessary to provide this power will probably
weigh on the order of 2000 - 5000 lbs. This weight is consistent with the payload
weight of 10,000 lbs. that has been assumed.

Figure 9 presents the flight time of a typical 5- stage fusion vehicle to
deliver a 10,000 lb. gross payload to a five light-year distance. Notice that the
required flight time is substantially longer than that shown previously since the
dead weights of the chamber structure and radiator decrease the achievable stage
mass ratio. The minimum flight time for a particular dead weight fraction per
stage occurs with continuous propulsion and occurs with a burnup fraction of 0.15
in this case. Comparable results are obtained for other dead weight fractions*
Increasing the initial weight of the vehicle also does not significantly decrease
the required flight time.

Also shown is the required propulsion time to perform this mission.
The propulsion time beconaes longer with increasing burnup fraction, simply
because the higher specific impulse of the engine produces lower thrust and thus
vehicle acceleration at the same reactor power level. The initial acceleration
for a burnup fraction of 10"^ ig 3.7 x 10"^ g's and at b = 0.15, it is 1.3 x 10"^ g's.

425

ftUKNlV FRACTION, b

Fig. 9. Transit time to a 5 light year star with a 5 stage fusion vehicle

Figure 10 graphically demonstrates the engineering problems associated
with the development of a system such as this. Confining magnetic field strengths
from 200,000 to 300,000 gauss are required, even with the assumption of optimum
confinement conditions. Finally, the power which must be dissipated in the ra-
diator of the first stage is 40,000 - 50,000 M w. A typical radiator size at these
power levels would be 1 square mile radiating from both sides. Thus from an
engineering standpoint, some method to either decrease power losses or mini-
mize the energy absorbed in the chamber walls is necessary in order that this
system be feasible for interstellar nnissions.

426

I

X

6W«.

w « 10,000 hi

#^4

< o

o

NOMENCLATURE
B

b

c
F

g
I

J
k

1/d
M

la

m

mtNUP HtACnOKb

Fig. 10. Magnetic field strength and power absorbed in the structure versus
bumup fraction for a fusion engine

magnetic field strength, gauss

fuel burnup fraction

velocity of light = 3 x 10 cm/ sec

engine thrust, dynes

acceleration of gravity .= 980 cm/sec

specific impulse, sec

stage number

Boltzmann constant = 1.38 x 10~ erg |^K atom

length to diameter ratio

rest mass, gm

molecular weight, gm/mole

rest mass flow rate, gm/sec

427

23

N Avogadros Number = 6,023 x 10 atoms/mole

o

N particle concentration, particles/cm

n number of stages

P power, Mw

R radius of structural shell, cm

/ 2

s design stress of structure, dyne/cm

T temperature, ^K

u burnout velocity, cnci/sec

V volume, cm

V relative velocity of particles, cm/sec
W weight, lb.

w engine exhaust velocity, cm/sec

y He fraction of fuel

Z atomic numtber

a fractional power lost from fuel due to bremsstrahlung and
cyclotron radiation

P stage dead weight fraction

y fraction of power carried by neutrons

A overall mass ratio

6 stage mass ratio

TJ efficiency of refrigeration system

9 fractional power going into cyclotron radiation

e fraction of fuel mass converted to energy

p density of structural material (tungsten), gm/cm

2

a microscopic reaction cross section, cm

$ over-all payload to initial vehicle weight ratio

X stage burnout weight fraction

428

SUBSCRIPTS

abs

absorbed

b

burned

b,o.

burnout

br

brems strahlung

c

cyclotron radiation

e

electron

ex

exhaust

f

fuel

i

ion

J

jth stage (j = 1 to n )

n

final stage

ne

neutron

P

payload

rad

radiator

s

chamber structure

t

total (fuel plus electrons )

o

initial

1
2

species 1 (D)
species 2 (He )

SUPERSCRIPTS

average value
tenaperature in kev

429

REFERENCES

1. Ackeret, J., "Theory of Rockets/' Helvetica Physica Acta , Vol. 19, 1946,
pp. 103-112.

2. "Theory of Rockets," Journal of the British Interplanetary

Society , Vol. 6, 1947, pp. 116-123.

3. Tsien, H. S., "Rockets and Other Thermal Jets Using Nuclear Energy,"

The Science and Engineering of Nuclear Power , Addison Wesley, Cambridge,
Vol. 11, 1949, pp. 177-195.

4. Bussard, R. W., "Galactic Matter and Interstellar Flight," Astronautica Acta ,
Vol. 6, 1960, pp. 179-194v

5. Sanger, E., "Atomic Rockets for Space Travel," Astronautica Acta , Vol. 6,
No. 1, 1960, pp. 4-15.

6. Stuhlinger, E., "Photon Rocket Propulsion,", Astronautics, Vol. 4, No. 10,
October 1959, pp. 36, 69, 72, 74, 76, 78.

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15. Weatherstone, R. G., and Smith, W. E., "A Method for Heat Rejection from
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16. Golomb, S., Private Communication.

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DISCUSSION

2^^. IiaROCCA (Propulsion Consultant, General Electric Company):
I would like to know if you are employing relativistic mechanics and the time you
are giving are vehicle "proper-times". Also: Is the vehicle arriving there with
a velocity, let's say, 0.6 of the light velocity, or are you decelerating the vehicle
when you arrive at the star configurations?

MR. SPENCER: Yes, we did use relativistic mechanics but as you can
see, when you only talk about three -tenths the velocity of light, both time dilation
and distance is very similar to the sancie old Newtonian mechanics. When you get
up to six-tenths the velocity of light, this is a significant factor and it was taken
into account in the equations. To your second question, most of these are fly-by
missions then one would simply accelerate until you got to that velocity then
coast the rest of the way. Well, a rule of thumb is that one G for one year will
almost get up to the velocity of light. So you can see that when we are talking
about six-tenths the velocity of light, if we accelerate at one G, the propulsion
time would be less than a year. If you want to do an experiment which would
require you to renaain in the vicinity of that particular star, then you would have
to decelerate perhaps, but we are talking here about probe missions, fly-by
nmissions, simii6.r to the Mariner.

CONCLUDING REMARKS

DR. SLAWSKY: I should like to take this opportunity to thank the speakers
and the chairmen. This meeting would not have been what it is if it weren't for them.

Second, I would like to thank the General Electric Coxnpany foV a superb
job. They had support from the office of Aerospace Research, and I know how hard
everyone worked on plans and arrangements for this symposium.

Finally, I would like to take this opportunity to let you know that the guid-
ing spirit in our venture this year was Colonel Paul Atkinson. Though Colonel
Atkinson is out of our office, he still keeps a very watchful eye over what we are
doing.

This symposium will be very hard to beat. I thank you all very much.

Whereupon at 12:55 p.m. the symposium adjourned

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