Selected Problems In Interstellar Navigation

SELECTED

PROBLEMS IN

. INTERSTEllAR

NAVIGATION

BY

ROBERT

CORNOG

RAMO-WOOLDRIDGE

a division THOMPSON

RAMO

CANOGA

OF

SIXTEENTH

COLORADO

NAVIGATION

JUNE

STATES

AIR

INC.

CALIFORNIA

ANNUAL

23-25 UNnED

WOOLDRIDGE

P ARK,

INSTITUTE

of

MEETING 1960

FORCE ACADEMY

SPRINGS,

COLORADO

SELECTED

PROBLEMS

IN INTERSTELLAR

NAVIGATION

INTRODUCTION The title

is ambitious;

same time describing motivations

)

which

Motivation professionally

the scope of the material

led me to select

concerned

with

publicly

such impractical

continental Questions Anyone

Ballistic

things

security

the situation

Developments

of classified

spend

to cover, and the

with

ago, very few people Ballistic

problems

free to speculate

and classified

Missile.

in space flight. about

design

were

Still

As a con-

and discuss

and potentialities

or the engineering

has changed.

in both areas

information.

in which a corresponding so visionary

concerned hampered much

years

as the properties

of Inter-

of space vehicles.

information

with

So rapid has been

situation

their properties.

either by too many

The problem front the navigator

is almost

the motivations navigational navigator?

facts

in choosing

of formulating

were

not very germane.

the subject

govern

requirements To answer

questions,

are professi6nally speak freely,

restrictions.

un-

So

of this paper.

the problems

which

of the vehicle

may con-

Some knowbeing

one should have a knowledge

of an interstellar are likely

I had to make

-I-

field

ships are still

ship is not so simple.

Likewise,

and objectives

these

security

capabilities

the captain

space

facets

technology

the only remaining

few people

intelligence

and performance

are realiwith

in space

one can still

or by too many

space

are festooned

Interstellar

that very

with

space flight

our progress

Consequently,

a prerequisite.

which

both

is almost

exists.

of an interstellar

ledge of the properties navigated

flight

and so impractical

for my motivation

The ICBM and

have budgets;

that today the area of interstellar

deemed

I plan

I will

could speak freely. Today,

ties.

Twenty

comparatively

Missiles,

of military

which

the Intercontinental

concerned

most people were

pretentious,

it.

is the simple part.

fewer were professionally sequence,

lest I seem unduly

space

to be presented

ship.

What

to the

some assumptions.

of

ASSUMPTIONS

The laws of Nature

Who would

have guessed,

prior

to the discovery

in the 19th century,

the possibility

as the atomic bomb?

Of course,

such possibilities.

But, almost without

have asserted

the possibility

I am rather ample,

confident

an overwhelming

phatically

and science-fiction exception,

violated

that a similar

situation

of scientists

than that corresponding

to the utter

equation,

first adduced to assert

in 19~

some new body

of pertinent

ever, I do suggest this or related

natural

possibilities.

that the assumptions conservative

and boundary

conditions

and downright

-- laws under whose

-- we will be able

human to ten, a hundred,

aegis

that all current

are complete~

r*JHere,

described

characteristics "game" is used

em-

of energy more of matter.

the law of the land.

equation

will

source

it may

soon be discovered of energy,

discovered.

and nearsighted

overnight

or How-

to rule out

in time be discovered

assumed

are unneces-

its present

of participation

is "true",

by the present are still beyond

human

in the mathematical

- 2 -

this to be easier of :the average

value.

Nevertheless.,

in a familiar

that the properties

laws of physics,

new

to utmost'.limits

the life expectancy

times

some feeling

knowledge

trips

will discover

Or -- and I believe

to extend

or a thousand

i~. order to give the reader

For ex-

today,

source

that our descendants

of our galaxy will be easy and simple. to accomplish

today.

annihilation

herein

would

unimaginative.

It is not ~t all inconceivable laws of nature

a

laws, will be presently

In other words,

scientists

if polled

Unsuspected

that it may be unrealistic

did suggest

consideration.

exists

to be

is still

that Einstein's

or that some new, currently

logical

would,

for there

writers

laws of Nature and that

of serious

to be untrue,

I assume

the known

late

and cataclysmic

reputable

was not worthy

majority

I am not going

sarily

so dramatic

aver that it is impossible

concentrated Einstein's

poets

that such a device

consequently

of anything

of radioactivity

of Nature

and that man's

control.

sense of the word.

game,<*)

bio-

Technological

Skills

In order to help where

necessary

vehicle

technical

that the inhabitants

skill.

and launch space

they can build propulsive they can make measuring

It is the writer's skills

assumption

engines instruments

belief

to any great

The Stellar

structure

is a member

20,000

there

to invoke these

is one impor~nt

i.e., pass

must attain

to examine

corollary

of an interstel-

them on to their

and maintain

and maintain

The thickness

our solar system. on a galactic

knowledge

galaxy which

of our galaxy

children.

technological some sort of a

the orbit

It is seen, then,

scale, are very

There are other galaxies, In fact, galaxies

is roughly

it would

come in ones,

besides

pertaining

100,000

one-fifth take

double

the outermost

stars, our Sun light years its diameter,

in or

known

planets,

planet

of

when measured

indeed.

or multiple

to intergalactic

Let

less than 11 hours

the one to which

of the order of ten), and clusters

(*)Considerations

other

that the neighboring

close neighbors

of the

is apt to navigate.

150 billion

of Pluto,

the nature

the universe.

is roughly

By way of contrast, across

vehicle

about

with an estimated

of a disk-shaped

for light to travel

in some detail

in which an interstellar

together

light years.

membership

and precision.

for many generations.

some of our present

Clustered

diameter.

sensitivity

reliability;

Environment

environment

us examine

and great

not be necessary

They must attain

It will be found helpful stellar

size and description;

It is that the inhabitants

vehicle

social

efficiency

However,

The people

of their environment.

high

skills,

that as long

the crew of the astronautical

that it will

which must be invoked.

in an interstellar

it will be assumed

of remarkable

extent.

involved,

of our space vehicle

of any specified

having

their

stable

Thus,

ships

lar space ship can perpetuate

control

some of the key problems

laws of nature are not violated,

can build

assumed

clearly

it will be assumed

have acqw..red infinite as the known

reveal more

our Sun belongs.(*)

galaxies,

groups

(with a

of galaxies

(with a membership

flight were

deliberately

excluded

during

this gravitational study. However, it is of interesting note that order the speed to escape the potential our galaxyto is on the of 400required km/sec.ll) (l)H.N. RUssell, R.S. Dugan,,,~nd J.Q. Stewar~ Astronomy II Astrophysics Stellar Astronomy, Ginn and Company, 1955, p. 8121'1'.

- 3 -

and

measured

in hundreds,

are known.

Some tens of thousands

or thousands).

The diameter

of a cluster

of galaxies

of galactic

of 3 x 106

is on the order

(3,ODO,OOD)

light years.(2)

The stars within instead,

density

than 1000 times highly

our own galaxy

they show a decided~

the spatial

clusters

gregarious

tendency.

of stars near the center

the stellar

populated

are by no means

region,

density

It has been

of a globular

in the neighborhood

the average

scattered

distance

between

estimated

cluster

of Sol. stars

at random; that

may be more

In such a

is only one-tenth

as great as that of stars near our Sun.(3)

How close are the neighboring knows that Alpha other nearby

Centauri

than 1700 stars

action, years

has described

17 light years

apparent,

four

stars are not as well

Gadomski within

is about

light years

properties

lie within

Nowadays,

every

away.

cat who's

hep

The distances

to

known.

of the Sun.

which

stars?

of the 59 known

stars (4:) which

Sa,p.dage($) has estimated 55.4 light years

then, that an interstellar

should be able to undertake

vehicle, journeys

that there are more

(15 parsecs)

of Sol.

to have an interesting which

lie

are on the order

It is

radius

of

of 100 light

in length.

Propulsion The problem will be assumed stellar

space,

propriately

an interstellar

that an interstellar is able to achieve

expelling

of 1000 km/sec,

of propelling

approximately

vehicle,

when

vehicle

is a basic

located

in field-free

a speed on the order 10 percent

30,000 years are required

It

inter-

of 1000 km/sec by ap-

of its initial

to complete

one.

mass.

a journey

At a speed

100 light years

in length. (2) Rudolf ~urth, Introduction Press, 1957, p. 12.

to the Mechanics

of Stellar

Systems,

Pergamon

(3) Russell, Dugan, Stewart'f799 (4) Jan Gadomski, "Die Sternenokospharen im Radius von 17 Lichtjahren um die Sonne" - Proceedings of· the VIIIth International Astronautical Congress, 1958, pp. 127-136. (5) Allan Sandage, "The Stars Wi thin 15 Parsecs of the Sun," Interscience Publishers, Inc., New York, 1958, p. 287.

- 4 -

Stellar

Populations,

It is at this point have

sometimes

been

tempted

shown that passengers of light will,

when measured

cousins.

at-home

relatives

to accelerate

have undergone

is one basic a space

to effect

-- a process

at best

somewhat

during Many

investigated examples.

so many

be classed

the complete legality,

controversial

one human

conversion according

close

with

astronauts home

can take

to find

of their

changes

our

stay-

that the return-

The energies

required

of mass

into directed

to the known

to the velocity

if

photon

laws of nature,

must be consumed

one can contemplate

Even

in order

is to

of light -- in other

completing

an interstellar

lifetime.

of the theoretical by ~·nger.(6)

problems

Stuhlinger

of the photon

has computed

drive were

some interesting

first numerical

(1)

energy,

postulated

cannot be done without

by Sanger violating

conversion

as the energy

the known

source

Stuhlinger, nautics, Pergamon

of mass ·into radifor the photon

laws of nature

(6) Eugen sanger, "Zur Theorie der Photonenraketen," the Fourth IAF Congress, Zurich, 1953)

(1) Ernst

less harshly

speeds are astronomical.

-- large masses

up to speeds

to the speed

as "little green men from Mars."

It may very well be that the complete ation

close

galactic

evolutionary

ship

of the folks back home

flaw in this development.

up to speeds at which

journey

deal

high-speed

ship to relativistic

whose

bring a space vehicle words,

in the hands

space

It has been

only a few "days" and return

would undoubtedly

There

one is able

lasting

sufficiently

Time will

to extremes,

phenomena.

of years have gone by and that the descendants

ing traveler~

beams

journey

traveling

aging.

of an interstellar

relativistic

by a clock

normal

Carried

an interstellar that millions

to invoke

in a vehicle

(and on Earth':), avoid cosmtc

that the designers

assumed

- 5 -

above.

(paper presented

"Propulsion Systems for Space Ships," Press, New York, 1958, p. 195 ff.

Vistas

drive,

at

in Astro-

Limitations

on Specific

Unless of scooped would

one assumes

up deuterium

appear

Impulse an interstellar

is used to accelerate

that the best, most practical

an interstellar

vehicle

of light nuclei.

ramjet

is either

The difference

of heavy

25 percent

of the energy released

percent

of the velocity

velocity

of light.

gines are given

is converted

in Table

exhaust

of a space

energy

for

or the fusion of

If it is assumed

velocities about

energy it

is a factor

into kinetic

of light, and for fusion

The properties

nuclei

the two processes

5 in energy released per unit mass of fuel.

the corresponding

hydrogen,

source of propulsion

only about

or fusion products,

the fusion

the associated

the fission between

in which

energy

are,

of the fission

for fission

five percent

ship using

that

two

of the

such propulsive

en-

1.

TABLE 1 Nuclear

Mass

Propulsion

Fraction

Ini tial Mass

Impulse

Capability

~4~~ss~

.

(NuClear Material)

(Exi t Speed

= t!/o c)

(Exi t speed =

0.01

60 km/sec

151 km/sec

0.10

632 km/sec

1,580 km/sec

13,800 km/sec

34,500

5% c)*

km/sec

* Assuming

Notes:

25% of energy

released

is given

to exhaust

products.

1)

3,000 km/sec is one percent of velocity of light. A vehicle moving this speed would require 10,000 years to complete a journey 100 light years in length.

2)

Relative to the centroid of the system of neighboring stars, the Sun is moving with a speed of about 20 km/sec. Other nearby stars have comparable speeds relative to the centroid.

-6-

at

Duration

of Flight

It is at this point

that a basic

one postulates

processes

vastly

than the 0.64 percent

greater

fusion and incorporates to be converted

into energy,

of making

~ores

~light

years.

the interstellar opinion

The designer

logical processes

of the human

some part of the individual tionary

change

be acquired,

The other short,

solution

if life on shipboard

or the old one behind, stead, he will now consider

(8)

consider

within

in deuterium

initial mass

is journey

to look for

a single

lifetime.

with

high-speed

compulsion.

and transitory which

Either

is

that the interstellar

One course would

The ethnic

that no one in his

may take more vehicle

than 10,000

MUst

then,

I

be to slow down the bio~

race -- either by a sort of cold storage.at

-- so that a drastically

course may be incompatible

of whose

of an emotional

life cycle,

and the average

obtainable

of the interstellar

one of two courses.

into energy

that the preoccupation

or venture

clear.{8)

one is tempted

journey

are still so ephemeral

right mind will plan an experiment

think, adopt

Again,

may be symptomatic

of our society

years to complete.

ships most assume

becomes

of mass

theoretically

or one must

thousand

It is the writer's interstellar

the conversion

them in space

lasts at least several some method

in which

difficulty

or by some kind revised

set of actuarial

life span will be 10,000

with

the known

calls

is more pleasant will

his vehicle

Earth as our native

years

laws of nature

for making

the traveler

of controlled

the journey

tables will

or more.

previously more

evolu-

This assumed.

pleasant.

In

than it is in the new land ahead

no longer begrudge

the center

the joUrney.

of the universe

In-

-- even as we

land.

See for example: ·a)

John Gustavson, "The Possibility of Interstellar pulsion, January, 1957, p. 69 f.

b)

L.R. Shepherd, planetary

c)

"Interstellar

Society,

Vol.

Flight,"

11, No.4,

Journal

Jet Pro-

of the British

Inter-

1952, p. 149.

W. Peschka, "Uber die Uberbruckung interstellarer Astronautica Acta, Vol. II, 1956, p. 191 ff.

-7-

Flight,"

Entfernungen,"

Emotionally, distant

one is tempted

sun surrounded

mosquito-free

air.

at all unlikely

by verdant

As Huang(9)

I do not think one needs

sizeable

segments

attractive

space ship will

below will probably on interstellar

journeys.

they completely

conform

it is assumed

attractive

to sizeable

Description

of meeting extent.

In order

natural

considerable of human

ship will be

on possible

in a closed

ecology

of so controversial aboard

For example,

machinery

which

the typical

one hundred

to actuate

and such other

mass

houses

methods of small a sub-

astral

it is assumed

127-136

- 8-

a

the machinery

as may be necessary

fluctuation

spectrum

allocation,

him; from other

rich and rewarding

statistical

tons per

the vehicle,

equipments

life.

in the population

of personalities,

that a stable population

Su-Shu Huang, "Occurrence of Life in the Universe," Autumn, 1959, Vol. 47, No.3, p. 397

(10) Gadomski,

Ac-

of 10 tons.

level, and in order to insure an adequate

(9)

space

speculation

beings

the structure

excessive

skills,

though

inhabitants.

From each person's

for him, or her, a complete,

and professional

even

take time to perfect.

on the nuances

is not too critical.

his food supply,

they are, launched

are required,

that each person

come the propulsive

of the type described

Vehicle

requirements

In order to avoid

ments,

which

qualified

will be used to provide

to provide

before

of properly

could also have been assumed.

that.generates

vehicles

groups

assumed

will

and

an interstellar

an initial mass

portions

time-tested

laws, will

ject, it was arbitrarily

portion

possibility.

A reliable,

generations

abode would be allocated

person

out,- it is not

to prod

life aboard

Interstellar

a

in order

Interstellar

for many

to avoid dwelling

The number

have pointed

perfume

to a

such a nirvana

off into space.

there has been

biological

his spacecraft

lotus blossoms

that

of Assumed

Recently,

to invoke

The technologies

with

cordingly,

whereon

Gadomski(lO)

suffice.

be tested

speeding

vista may be in fact an exciting

However,

of mankind

planets

and

that this dreamy

to consider

American

temperaof at

Scientist

least 10,000 people assumed house

will be required

that each person

(three bedrooms,

that a sphere

namely,

people,

10 miles

Shielding

of the Earth.

of such a spherically

requirement

will be met

five feet thick. traveler

a greater

even

Properly

though

than is currently

being

such walls

against

Suppose

is used

noxious

provided

walls

that

10% of the the ex-

that this weight

are of solid

steel and

to afford

radiations

to his progenitors

-9 -

than

environmental

to provide

can be made

cosmic

more

__

In the case of the largest

easily be computed

the external

disposed,

protection

vessel.

diameter

people,

rays and other

shaped vehicle.

it may

10 times this diameter

10 billion

(10 tons/person)

each person

(10 miles in diameter),

vehicle

debris

in an interstellar

cosmic

out

for a popula-

100 times the reference

population

If it is

it turns

this volume

a sphere

-- will house

against

carpeting1),

provide

in diameter

may be a problem

ternal walls

enough,

and one only

the population

initial mass allowed

would

vehicle.

to half of a 2,000 ft2

equal

and wall-to-wall

Interestingly

three times the present

hazards

a volume

only 534 feet in diameter

10 million

about

is allocated

two baths,

tion of 10,000 people. will house

to man an interstellar

here

the

and meteoric on Earth.

NAVIGATION

PROBLEMS·

Now for the big question: confront

the denizens

Once described definite

period

now drifting emotionally colonists

space.

from time to time wish

mid-course

corrections

mid-course

position

measurements

through

vehicle

interstellar

might

of the type

space for an in-

and the rest of the solar

such a purposeless Assume, to move

system are

existence'may

therefore,

be

that our astral

from one star to another.

than pre-set

In order

"ballistic"

trajectories,

to make mid-course

corrections,

must be known.

objects

radar techniques, with great

kilometers. other objects

objects

With

techniques

such extended

can be measured

The velocity

less than

on nearby

between

baselines,

If paral-

to measure

10,000

distances

light years:)

outpost

ship navigator.

observation

points

stars are taken

to the parent

even at distances

vessel.

and parent

of hundreds

the distances

from each By use of

vessel

of millions

to nearby

located

stars

can be of or

accurately.

of the space

can be determined

must be used

one or more

are communicated

accuracy,

Parallax

vehicle.

are used by the space

Bearings

the distance

stars?

space.

(i.e.,

has established

and the results

can be determined

from an interstellar

in interstellar

from his vessel.

space

are the nearby

some other method

if triangulation

at some distance such outpost

be made

of nearby

that the navigator

in interstellar

starsj but which

ordinarily

The distances can be measured

one's position

are lacking,

to newly discovered

Velocity

must be made.

on nearby

cannot

lax measurements

determined

problems

Fixes

by taking bearings

Doppler

interstellar

are to be other

and velocity

In principle,

Suppose

However,

to many people.

If such journeys

Interstellar

travel

of time -- even as Earth

repugnant

will

a self-sustaining

in principle,

through

sort of navigation

of such a world?

launched,

could,

What

ship is also of navigational

by differentiating

- 10 -

the position

interest.

function.

Thus if

position

relative

to nearby

relative velocity with time.

can be computed

A direct ing the Doppler simple,

determination

shift in known

practical

device

..

rates has been described speedometer,"

stars has been

by determining

of relative spectral

in which

by J.E. Abate.

tionof

and the direction

from nearby

"to measure

is used

spectral

not be difficult display

stars.

stellar

A

range

Doppler

lines.

for the navigator

showing

and speed with which

out that

to do its accelerating

Thus a vehicle

it would

in the light

both

the posi-

it is moving.

Encounters

lar vehicle

a massive

times,

can be made by measur-

Called an "astro-digital

to have a continuous

In 1929 Oberth(12)pointed

well.

also

shift of known

then, that it would

vessel

Profitable

(11)

Doppler

of an interstellar his vessel

velocity

lines

at two or more

the rate of change of position

this procedure

the device measures

It appears,

determined

star will if it were

which

it is profitable

at the bottom

accelerates

have, at great

while

distances,

of a potential

it is moving a much

to cause its accelerational

for an interstel-

in orbit

higher

impulse

(gravitational) close to

residual

speed than

to occur at any other

time.

Mathematically, a hyperbolic

encounter

an interplanetary Stearns,(14)and

the problem with

vehicle

object,

braking

A somewhat

(11) James A. Fusca, "Speedometer 22 June 1959, p. 201 ff. (12) Hermann

Oberth,

Wege

similar

a planet

vehicle

during

to that of guiding

for a landing.

Baker, (13)

the latter problem.

that the vehicle

be guided

in the planetary

for a space vehicle

i.e., a star.

an interstellar

star is very

investigated

it is desired

ridor such that aerodynamic It may be desirable

a massive

as it approaqhes

others have

Ordinarily

of navigating

to approach

similar

Proposed

problem

atmosphere closely

Munich,

Vehicle,"

R.

an entry

cor-

is possible.

an even more massive

in navigation

for Space

zur Raumschiffahrt,

along

will be encountered.

Aviation

oIdenbourg,

Week,

1959, pp. 143-145

(13) Robert M.L. Baker, Jr., "Accuracy Required for a Return from Interplanetary Voyages," Journal of the British Interplanetary Society, Vol. 17, Nos. 3 and 4, May through August, 1959 (14) E.V. Stearns, "Guidance for Interplanetary landings," (Paper presented at the 6th National Annual Meeting of the American Astronautical Society, 18-21 January 1960, New York City, New York)

.

- 11 -

Two cases merit or moving

slowly

(relative

A numerical dwarf whose

concern.

example

of such a body,

of a low altitude corresponding a parabolic

numbers

1/2

whose

mass

km/sec,

of Sol),

center,

and whose

acceleration

temperature

At 10 Earth

A space

approach,

of closest

At the

106 g, and the period

is

R is the distance

If the point

times

radii are practical.

of nearest

where

Choose a white

is 1,000,000

is less than six seconds.

radii,

the

ship approaching be moving

with

to the center

approach

along

the

of the star,

is 10 Earth

radii

the speed will be 3480 km/sec.

that at or near the point

on so as to increase

3480 km/sec

the principle.

the mass

at the point

in Earth radii.

Suppose

distance

illustrate

gravitational

stationary,

ship and to its destination).

are 104 g and 190 seconds.

path will,

from the mass

case, a star is either

as close as 10 Earth

satellite

speed of 11,000/R

are turned

will

(and thus three times

is so low that approaches

measured

to the space

size is equal to that of Earth,

that of Earth

surface

In the first

to 3481 km/sec.

of closest

the vehicle's

Under

from the star, namely,

these

at what

approach,

rocket

speed one km/sec,

circumstances, I will

call

i.e., from

the velocity

local

engines

infinity,

at a great will be

83.5 km/sec. As can be seen from Table appropriate

guidance

many nearby

stars in 30 or 40 milleniums.

propellants, velocity

With

of one km/sec

On the other

can be obtained.

is ejected

If, after

at periaps+s,

which

(20 km/sec

even with

With

hydrogen

exhaust

speed at local

chemical a

approach.

so as to produce

speed),

approach,

with

to attain

of closest

heats

a parabolic

the resulting

hand,

need be ejected

at the point

reactor

of 2035 Ib-sec/lb

is not inconsequential.

ship can now effect a rendezvous

assumed

the use of a nuclear

impulse

sive results cle mass

the space

less than 1/400 of the ship's mass

increment

a specific

accuracy,

1, 83.5 km/sec

even more

impres-

1.25~ of the vehiinfinity

will

be 418 km/sec. As can be seen from Table mass

than one can hope

I, this is a much more

for in any conventional

engine

effective

in which

use of ejected

nuclear

fusion

is

used as a source of power. There Suppose of which

is a second method

that our space vehicle is a massive

of extracting

energy

is slowly approaching

dwarf having

properties

- 12 -

from a stellar

a double

identical

star,

to those

system.

each member

of the dwarf

assumed

in the previous

each other

example.

in a circular

navigational hyperbolic

Assume

orbit with

further

a speed

that the stars are moving

of 1000 km/sec.

skill, a space ship could approach orbit which

ship would be moving

is almost

away

from the double

finity would be 1000 km/sec pulsive

engines.

orbital

plane of the double

such a fast-moving

After

the encounter,

star with

is also under

inhabited

communities

our galaxy.

civilization;

its own objectives.

each will be pursuing

isolated

throughout

of intercolony

size requirement

is met,

It has been

such sociologically

sociological

may be the norm.

Completely

cOlJDllunities would

probably

Perhaps

communication,

all tim.e.

in too small a group,

For example,

they may wish

they would wish

aside

medium.

Radio waves

to know where

only to pass

X-rays

could be used.

between

sender and receiver.

formation

electromagnetically

power and limited

there are quantum

transmitted. for the people

Thus,

useful

may be unstable;

stagnation dangers,

double

radiation

is often

Modulated

stars

and regression the different information. are to be found.

rate

increases

restrictions infinite

light beams

- 13 -

away.

of the distance

feasible

transmission method.

of the sending

on the rate at which

than a few light years

required

that if the distance

the direct

technical

or focused

the energy

as the square

to suggest

in light years,

chosen as a communication

selected,

skill,

on one space ship to "talk" directly

ships which are more

groups

some minimum

environmental

size of the apertures

even with

that unless

isolated

may not be the most

geometrical

is some

the time of millenium •

I am going

is measured

suggested

of the frequency

at a given

there

each colony will be completely

desirable

extensively.

Regardless

information

sender and receiver

antennae,

are used

Unless

from these possible

like to exchange

-- each aboard

Each group will be a separate

and technological

.sol'!T Some ~ of electromagnetic

to transmit

-- if it lies in the

Pigeons

its space ship -- spread throughout

scheme

and no pro-

star.

there are 1000, or 10,000,

workable

star in a

at loca'l in-

acceleration

control

consummate

the space

a speed which

-- all of this tremendous

Final direction

Interstellar' Courier

Assume

parabolic.

Granted

about

between of in-

Wi th l1mi ted and receiving

energy

can be

it may not be practical

to the inhabitants

of space

Under

these circumstances,

in the following distributed

manner.

between

the total power ing the power

Suppose

that N two-way

the two communicating

required

requirements

to maintain

space

a given

of all the N relay

required

for direct

him when

he penetrated

launched

space ship may unwind

they penetrate

communication

communication. the Cretan

the layrinthine

Thus,

relay ships.

- 14 -

are" evenly

It may be found

rate of communication stations)

of our galaxy.

that

{incl~d-

is now only l/N that unwound

so the inhabitants

of communication

intracacies

can be improved

stations

even as Theseus

labyrinth,

a string

capability

twine behind

of a newly

relays behind

them

as

·

.•.