selected problems in interstellar navigation
DESCRIPTION
by Robert Cornog INSTITUTE OF NAVIGATIONSIXTEENTH ANNUAL MEETING23-25 JUNE 1960UNITED STATES AIR FORCE ACADEMYCOLORADO SPRINGS, COLORADOTRANSCRIPT
SELECTED PROBLEMS
IN
. INTERSTEllAR NAVIGATION
BY
ROBERT CORNOG
RAMO-WOOLDRIDGE
a division of
THOMPSON RAMO WOOLDRIDGE INC.
CANOGA P ARK, CALIFORNIA
INSTITUTE OF NAVIGATION
SIXTEENTH ANNUAL MEETING
23-25 JUNE 1960
UNnED STATES AIR FORCE ACADEMY
COLORADO SPRINGS, COLORADO
)
SELECTED PROBLEMS IN INTERSTELLAR NAVIGATION
INTRODUCTION
The title is ambitious; lest I seem unduly pretentious, I will spend
same time describing the scope of the material which I plan to cover, and the
motivations which led me to select it.
Motivation is the simple part. Twenty years ago, very few people were
professionally concerned with the Intercontinental Ballistic Missile. Still
fewer were professionally concerned with problems in space flight. As a con
sequence, most people were comparatively free to speculate about and discuss
publicly such impractical things as the properties and potentialities of Inter
continental Ballistic Missiles, or the engineering design of space vehicles.
Questions of military security and classified information were not very germane.
Anyone could speak freely.
Today, the situation has changed. The ICBM and space flight are reali
ties. Developments in both areas have budgets; both are festooned with facets
of classified information. So rapid has been our progress in space technology
that today the area of interstellar flight is almost the only remaining field
in which a corresponding situation exists. Interstellar space ships are still
deemed so visionary and so impractical that very few people are professi6nally
concerned with their properties. Consequently, one can still speak freely, un
hampered either by too many facts or by too many security restrictions. So
much for my motivation in choosing the subject of this paper.
The problem of formulating with intelligence the problems which may con
front the navigator of an interstellar space ship is not so simple. Some know
ledge of the properties and performance capabilities of the vehicle being
navigated is almost a prerequisite. Likewise, one should have a knowledge of
the motivations which govern the captain of an interstellar space ship. What
navigational requirements and objectives are likely to be presented to the
navigator? To answer these questions, I had to make some assumptions.
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ASSUMPTIONS
The laws of Nature
Who would have guessed, prior to the discovery of radioactivity late
in the 19th century, the possibility of anything so dramatic and cataclysmic
as the atomic bomb? Of course, poets and science-fiction writers did suggest
such possibilities. But, almost without exception, reputable scientists would
have asserted that such a device violated the known laws of Nature and that
consequently the possibility was not worthy of serious consideration.
I am rather confident that a similar situation exists today. For ex
ample, an overwhelming majority of scientists would, if polled today, em
phatically aver that it is impossible for there to be a source of energy more
concentrated than that corresponding to the utter annihilation of matter.
Einstein's equation, first adduced in 19~ is still the law of the land.
I am not going to assert that Einstein's equation will soon be discovered
to be untrue, or that some new, currently Unsuspected source of energy, or
some new body of pertinent natural laws, will be presently discovered. How
ever, I do suggest that it may be unrealistic and nearsighted to rule out
this or related possibilities. In other words, it may in time be discovered
that the assumptions and boundary conditions herein assumed are unneces-
sarily conservative and downright unimaginative.
It is not ~t all inconceivable that our descendants will discover new
laws of nature -- laws under whose aegis overnight trips to utmost'.limits
of our galaxy will be easy and simple. Or -- and I believe this to be easier
to accomplish -- we will be able to extend the life expectancy of :the average
human to ten, a hundred, or a thousand times its present value. Nevertheless.,
i~.order to give the reader some feeling of participation in a familiar game,<*)
I assume that all current knowledge is "true", that the properties of Nature
are complete~ described by the present laws of physics, and that man's bio
logical characteristics are still beyond human control.
r*JHere, "game" is used in the mathematical sense of the word.
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Technological Skills
In order to help reveal more clearly some of the key problems involved,
where necessary it will be assumed that the inhabitants of our space vehicle
have acqw..red infinite technical skill. Thus, it will be assumed that as long
as the known laws of nature are not violated, the crew of the astronautical
vehicle can build and launch space ships of any specified size and description;
they can build propulsive engines having high efficiency and great reliability;
they can make measuring instruments of remarkable sensitivity and precision.
It is the writer's belief that it will not be necessary to invoke these
assumed skills to any great extent. However, there is one impor~nt corollary
assumption which must be invoked. It is that the inhabitants of an interstel
lar space ship can perpetuate their skills, i.e., pass them on to their children.
The people in an interstellar vehicle must attain and maintain technological
control of their environment. They must attain and maintain some sort of a
stable social structure for many generations.
The Stellar Environment
It will be found helpful to examine in some detail the nature of the
stellar environment in which an interstellar vehicle is apt to navigate. Let
us examine some of our present knowledge about the universe.
Clustered together with an estimated 150 billion other stars, our Sun
is a member of a disk-shaped galaxy which is roughly 100,000 light years in
diameter. The thickness of our galaxy is roughly one-fifth its diameter, or
20,000 light years. By way of contrast, it would take less than 11 hours
for light to travel across the orbit of Pluto, the outermost known planet of
our solar system. It is seen, then, that the neighboring planets, when measured
on a galactic scale, are very close neighbors indeed.
There are other galaxies, besides the one to which our Sun belongs.(*)
In fact, galaxies come in ones, double or multiple galaxies, groups (with a
membership of the order of ten), and clusters of galaxies (with a membership
(*)Considerations pertaining to intergalactic flight were deliberately excluded during
this study. However, it is interesting to note that the speed required to escapethe gravitational potential of our galaxy is on the order of 400 km/sec.ll)
(l)H.N. RUssell, R.S. Dugan,,,~nd J.Q. Stewar~ Astronomy II Astrophysics andStellar Astronomy, Ginn and Company, 1955, p. 8121'1'.
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measured in hundreds, or thousands).
are known. The diameter of a cluster
light years.(2)
Some tens of thousands of galactic clusters
of galaxies is on the order of 3 x 106
(3,ODO,OOD)
The stars within our own galaxy are by no means scattered at random;
instead, they show a decided~ gregarious tendency. It has been estimated that
the spatial density of stars near the center of a globular cluster may be more
than 1000 times the stellar density in the neighborhood of Sol. In such a
highly populated region, the average distance between stars is only one-tenth
as great as that of stars near our Sun.(3)
How close are the neighboring stars? Nowadays, every cat who's hep
knows that Alpha Centauri is about four light years away. The distances to
other nearby stars are not as well known.
Gadomski has described properties of the 59 known stars (4:) which lie
within 17 light years of the Sun. Sa,p.dage($)has estimated that there are more
than 1700 stars which lie within 55.4 light years (15parsecs) of Sol. It is
apparent, then, that an interstellar vehicle, to have an interesting radius of
action, should be able to undertake journeys which are on the order of 100 light
years in length.
Propulsion
The problem of propelling an interstellar vehicle is a basic one. It
will be assumed that an interstellar vehicle, when located in field-free inter
stellar space, is able to achieve a speed on the order of 1000 km/sec by ap
propriately expelling approximately 10 percent of its initial mass. At a speed
of 1000 km/sec, 30,000 years are required to complete a journey 100 light years
in length.
(2) Rudolf ~urth, Introduction to the Mechanics of Stellar Systems, PergamonPress, 1957, p. 12.
(3) Russell, Dugan, Stewart'f799
(4) Jan Gadomski, "Die Sternenokospharen im Radius von 17 Lichtjahren um dieSonne" - Proceedings of·the VIIIth International Astronautical Congress, 1958,
pp. 127-136.
(5) Allan Sandage, "The Stars Wi thin 15 Parsecs of the Sun," Stellar Populations,Interscience Publishers, Inc., New York, 1958, p. 287.
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It is at this point that the designers of an interstellar space ship
have sometimes been tempted to invoke relativistic phenomena. It has been
shown that passengers in a vehicle traveling sufficiently close to the speed
of light will, when measured by a clock in the hands of the folks back home
(and on Earth':), avoid normal aging. Time will deal less harshly with our
cosmtc cousins. Carried to extremes, high-speed galactic astronauts can take
an interstellar journey lasting only a few "days" and return home to find
that millions of years have gone by and that the descendants of their stay
at-home relatives have undergone so many evolutionary changes that the return
ing traveler~ would undoubtedly be classed as "little green men from Mars."
There is one basic flaw in this development. The energies required
to accelerate a space ship to relativistic speeds are astronomical. Even if
one is able to effect the complete conversion of mass into directed photon
beams -- a process whose legality, according to the known laws of nature, is
at best somewhat controversial -- large masses must be consumed in order to
bring a space vehicle up to speeds close to the velocity of light -- in other
words, up to speeds at which one can contemplate completing an interstellar
journey during one human lifetime.
Many of the theoretical problems of the photon drive were first
investigated by ~·nger.(6) Stuhlinger has computed some interesting numerical
examples. (1)
It may very well be that the complete conversion of mass ·into radi
ation energy, postulated by Sanger as the energy source for the photon drive,
cannot be done without violating the known laws of nature assumed above.
(6) Eugen sanger, "Zur Theorie der Photonenraketen," (paper presented atthe Fourth IAF Congress, Zurich, 1953)
(1) Ernst Stuhlinger, "Propulsion Systems for Space Ships," Vistas in Astronautics, Pergamon Press, New York, 1958, p. 195 ff.
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Limitations on Specific Impulse
Unless one assumes an interstellar ramjet in which the fusion energy
of scooped up deuterium is used to accelerate the associated hydrogen, it
would appear that the best, most practical source of propulsion energy for
an interstellar vehicle is either the fission of heavy nuclei or the fusion
of light nuclei. The difference between the two processes is a factor of
only about 5 in energy released per unit mass of fuel. If it is assumed that
25 percent of the energy released is converted into kinetic energy of the fission
or fusion products, the corresponding exhaust velocities are, for fission two
percent of the velocity of light, and for fusion about five percent of the
velocity of light. The properties of a space ship using such propulsive en
gines are given in Table 1.
TABLE 1
Nuclear Propulsion
Mass Fraction
(NuClear Material)Initial Mass .
Impulse Capability
~4~~ss~(Exi t Speed = t!/o c) (Exi t speed = 5% c)*
0.01
0.10
60 km/sec
632 km/sec
13,800 km/sec
151 km/sec
1,580 km/sec
34,500 km/sec
*Assuming 25% of energy released is given to exhaust products.
Notes: 1) 3,000 km/sec is one percent of velocity of light. A vehicle moving atthis speed would require 10,000 years to complete a journey100 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.
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Duration of Flight
It is at this point that a basic difficulty becomes clear.{8) Either
one postulates processes in which the conversion of mass into energy is
vastly greater than the 0.64 percent theoretically obtainable in deuterium
fusion and incorporates them in space ships most of whose initial mass is
to be converted into energy, or one must assume that the interstellar journey
lasts at least several thousand years. Again, one is tempted to look for
some method of making the interstellar journey within a single lifetime.
It is the writer's opinion that the preoccupation with high-speed
interstellar ~light may be symptomatic of an emotional compulsion. The ethnic
~ores of our society are still so ephemeral and transitory that no one in his
right mind will plan an experiment or venture which may take more than 10,000
years to complete. The designer of the interstellar vehicle MUst then, I
think, adopt one of two courses. One course would be to slow down the bio~
logical processes of the human race -- either by a sort of cold storage.at
some part of the individual life cycle, or by some kind of controlled evolu
tionary change -- so that a drastically revised set of actuarial tables will
be acquired, and the average life span will be 10,000 years or more. This
course may be incompatible with the known laws of nature previously assumed.
The other solution calls for making the journey more pleasant. In
short, if life on shipboard is more pleasant than it is in the new land ahead
or the old one behind, the traveler will no longer begrudge the joUrney. In
stead, he will consider his vehicle the center of the universe -- even as we
now consider Earth as our native land.
(8) See for example:
·a) John Gustavson, "The Possibility of Interstellar Flight," Jet Propulsion, January, 1957, p. 69 f.
b)
c)
L.R. Shepherd, "Interstellar Flight," Journal of the British Inter
planetary Society, Vol. 11, No.4, 1952, p. 149.
W. Peschka, "Uber die Uberbruckung interstellarer Entfernungen,"Astronautica Acta, Vol. II, 1956, p. 191 ff.
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Emotionally, one is tempted to consider speeding his spacecraft to a
distant sun surrounded by verdant planets whereon lotus blossoms perfume a
mosquito-free air. As Huang(9) and Gadomski(lO) have pointed out,- it is not
at all unlikely that this dreamy vista may be in fact an exciting possibility.
However, I do not think one needs to invoke such a nirvana in order to prod
sizeable segments of mankind off into space. A reliable, time-tested and
attractive space ship will suffice. Interstellar vehicles of the type described
below will probably be tested for many generations before they are, launched
on interstellar journeys. The technologies which are required, even though
they completely conform with natural laws, will take time to perfect. Ac
cordingly, it is assumed that life aboard an interstellar space ship will be
attractive to sizeable groups of properly qualified inhabitants.
Description of Assumed Interstellar Vehicle
Recently, there has been considerable speculation on possible methods
of meeting biological requirements of human beings in a closed ecology of small
extent. In order to avoid dwelling on the nuances of so controversial a sub
ject, it was arbitrarily assumed that each person aboard the typical astral
abode would be allocated an initial mass of 10 tons.
The number is not too critical. For example, one hundred tons per
person could also have been assumed. From each person's mass allocation, a
portion will be used to provide the structure which houses him; from other
portions will come the propulsive machinery to actuate the vehicle, the machinery
that.generates his food supply, and such other equipments as may be necessary
to provide for him, or her, a complete, rich and rewarding life.
In order to avoid excessive statistical fluctuation in the population
level, and in order to insure an adequate spectrum of personalities, tempera
ments, and professional skills, it is assumed that a stable population of at
(9) Su-Shu Huang, "Occurrence of Life in the Universe," American Scientist
Autumn, 1959, Vol. 47, No.3, p. 397
(10) Gadomski, 127-136
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least 10,000 people will be required to man an interstellar vehicle. If it is
assumed that each person is allocated a volume equal to half of a 2,000 ft2
house (three bedrooms, two baths, and wall-to-wall carpeting1), it turns out
that a sphere only 534 feet in diameter would provide this volume for a popula
tion of 10,000 people. Interestingly enough, a sphere 10 times this diameter
will house 10 million people, and one only 100 times the reference diameter __
namely, about 10 miles in diameter -- will house 10 billion people, more than
three times the present population of the Earth.
Shielding the population against cosmic rays and other environmental
hazards may be a problem in an interstellar vessel. Suppose that 10% of the
initial mass allowed each person (10 tons/person) is used to provide the ex
ternal walls of such a spherically shaped vehicle. In the case of the largest
vehicle (10 miles in diameter), it may easily be computed that this weight
requirement will be met even though the external walls are of solid steel and
five feet thick. Properly disposed, such walls can be made to afford the
traveler a greater protection against noxious cosmic radiations and meteoric
debris than is currently being provided to his progenitors here on Earth.
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NAVIGATION PROBLEMS·
Now for the big question: What sort of navigation problems might
confront the denizens of such a world?
Once launched, a self-sustaining interstellar vehicle of the type
described could, in principle, travel through interstellar space for an in
definite period of time -- even as Earth and the rest of the solar system are
now drifting through space. However, such a purposeless existence'may be
emotionally repugnant to many people. Assume, therefore, that our astral
colonists will from time to time wish to move from one star to another.
If such journeys are to be other than pre-set "ballistic" trajectories,
mid-course corrections must be made. In order to make mid-course corrections,
mid-course position and velocity must be known.
Interstellar Fixes
In principle, one's position in interstellar space can be determined
by taking bearings on nearby starsj but which are the nearby stars? Parallax
measurements cannot ordinarily be made from an interstellar vehicle. If paral
lax measurements are lacking, some other method must be used to measure distances
to newly discovered objects in interstellar space.
The distances of nearby objects (i.e., less than 10,000 light years:)
can be measured if triangulation techniques are used by the space ship navigator.
Suppose that the navigator has established one or more observation points located
at some distance from his vessel. Bearings on nearby stars are taken from each
such outpost and the results are communicated to the parent vessel. By use of
Doppler radar techniques, the distance between outpost and parent vessel can be
determined with great accuracy, even at distances of hundreds of millions of
kilometers. With such extended baselines, the distances to nearby stars or
other objects can be measured accurately.
The velocity of the space ship is also of navigational interest.
Velocity can be determined by differentiating the position function. Thus if
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position relative to nearby stars has been determined at two or more times,
relative velocity can be computed by determining the rate of change of position
with time.
A direct determination of relative velocity also can be made by measur
ing the Doppler shift in known spectral lines in the light from nearby stars. A
simple, practical device in which this procedure is used "to measure stellar range.. (11)
rates has been described by J.E. Abate. Called an "astro-digital Doppler
speedometer," the device measures Doppler shift of known spectral lines.
It appears, then, that it would not be difficult for the navigator
of an interstellar vessel to have a continuous display showing both the posi
tionof his vessel and the direction and speed with which it is moving.
Profitable Encounters
In 1929 Oberth(12)pointed out that it is profitable for an interstel
lar vehicle to do its accelerating at the bottom of a potential (gravitational)
well. Thus a vehicle which accelerates while it is moving in orbit close to
a massive star will have, at great distances, a much higher residual speed than
it would if it were to cause its accelerational impulse to occur at any other
time.
Mathematically, the problem of navigating an interstellar vehicle during
a hyperbolic encounter with a massive star is very similar to that of guiding
an interplanetary vehicle as it approaqhes a planet for a landing. Baker, (13)
Stearns,(14)and others have investigated the latter problem.
Ordinarily it is desired that the vehicle be guided along an entry cor
ridor such that aerodynamic braking in the planetary atmosphere is possible.
It may be desirable for a space vehicle to approach closely an even more massive
object, i.e., a star. A somewhat similar problem in navigation will be encountered.
(11) James A. Fusca, "Speedometer Proposed for Space Vehicle," Aviation Week,22 June 1959, p. 201 ff.
(12) Hermann Oberth, Wege zur Raumschiffahrt, Munich, R. oIdenbourg, 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 concern. In the first case, a star is either stationary,
or moving slowly (relative to the space ship and to its destination).
A numerical example will illustrate the principle. Choose a white
dwarf whose size is equal to that of Earth, whose mass is 1,000,000 times
that of Earth (and thus three times the mass of Sol), and whose temperature
is so low that approaches as close as 10 Earth radii are practical. At the
surface of such a body, gravitational acceleration is 106 g, and the period
of a low altitude satellite is less than six seconds. At 10 Earth radii, the
corresponding numbers are 104 g and 190 seconds. A space ship approaching along
a parabolic path will, at the point of nearest approach, be moving with the1/2
speed of 11,000/R km/sec, where R is the distance to the center of the star,
measured in Earth radii. If the point of closest approach is 10 Earth radii
from the mass center, the speed will be 3480 km/sec.
Suppose that at or near the point of closest approach, rocket engines
are turned on so as to increase the vehicle's speed one km/sec, i.e., from
3480 km/sec to 3481 km/sec. Under these circumstances, the velocity at a great
distance from the star, namely, at what I will call local infinity, will be
83.5 km/sec.
As can be seen from Table 1, 83.5 km/sec is not inconsequential. With
appropriate guidance accuracy, the space ship can now effect a rendezvous with
many nearby stars in 30 or 40 milleniums. On the other hand, even with chemical
propellants, less than 1/400 of the ship's mass need be ejected to attain a
velocity increment of one km/sec assumed at the point of closest approach.
With the use of a nuclear reactor which heats hydrogen so as to produce
a specific impulse of 2035 Ib-sec/lb (20 km/sec exhaust speed), even more impres
sive results can be obtained. If, after a parabolic approach, 1.25~ of the vehi
cle mass is ejected at periaps+s, the resulting speed at local infinity will
be 418 km/sec.
As can be seen from Table I, this is a much more effective use of ejected
mass than one can hope for in any conventional engine in which nuclear fusion is
used as a source of power.
There is a second method of extracting energy from a stellar system.
Suppose that our space vehicle is slowly approaching a double star, each member
of which is a massive dwarf having properties identical to those of the dwarf
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assumed in the previous example. Assume further that the stars are moving about
each other in a circular orbit with a speed of 1000 km/sec. Granted consummate
navigational skill, a space ship could approach such a fast-moving star in a
hyperbolic orbit which is almost parabolic. After the encounter, the space
ship would be moving away from the double star with a speed which at loca'l in
finity would be 1000 km/sec -- all of this tremendous acceleration and no pro
pulsive engines. Final direction is also under control -- if it lies in the
orbital plane of the double star.
Interstellar' Courier Pigeons
Assume there are 1000, or 10,000, inhabited communities -- each aboard
its space ship -- spread throughout our galaxy. Each group will be a separate
civilization; each will be pursuing its own objectives. Unless there is some
workable scheme of intercolony communication, each colony will be completely
isolated throughout all tim.e. It has been suggested that unless some minimum
size requirement is met, such sociologically isolated groups may be unstable;
in too small a group, sociological and technological stagnation and regression
may be the norm. Completely aside from these possible dangers, the different
cOlJDllunitieswould probably like to exchange useful environmental information.
For example, they may wish to know where desirable double stars are to be found.
Perhaps they would wish only to pass the time of millenium •
.sol'!TSome ~ of electromagnetic radiation is often chosen as a communication
medium. Radio waves are used extensively. Modulated light beams or focused
X-rays could be used. Regardless of the frequency selected, the energy required
to transmit information at a given rate increases as the square of the distance
between sender and receiver. I am going to suggest that if the distance between
sender and receiver is measured in light years, the direct transmission of in
formation electromagnetically may not be the most feasible method. Wi th l1mi ted
power and limited geometrical size of the apertures of the sending and receiving
antennae, there are quantum restrictions on the rate at which energy can be
transmitted. Thus, even with infinite technical skill, it may not be practical
for the people on one space ship to "talk" directly to the inhabitants of space
ships which are more than a few light years away.
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Under these circumstances, communication capability can be improved
in the following manner. Suppose that N two-way relay stations are" evenly
distributed between the two communicating space ships. It may be found that
the total power required to maintain a given rate of communication {incl~d
ing the power requirements of all the N relay stations) is now only l/N that
required for direct communication. Thus, even as Theseus unwound twine behind
him when he penetrated the Cretan labyrinth, so the inhabitants of a newly
launched space ship may unwind a string of communication relays behind them as
they penetrate the layrinthine intracacies of our galaxy.
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· .•.