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C00024 00003	THE SOCIOLOGY OF INTERSTELLAR TRAVEL
C00031 00004	THE SOCIOLOGY OF THE INTERSTELLAR EXPEDITION
C00039 00005	Literature:
C00040 ENDMK
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\CTHE FEASIBILITY OF INTERSTELLAR TRAVEL


\F1\J	Optimists have proposed many schemes for interstellar travel,
usually aimed at reaching nearer stars within a human lifetime, but
these schemes usually involve extrapolations of present science.
Pessimists, finding flaws in these schemes, conclude that
interstellar travel is forever infeasible.
We show that interstellar travel is entirely feasible with
only small improvements in present technology
provided travel times of several hundred to several thousand years
are accepted.  Naturally no-one will start thousand-year journeys
within the next few hundred years unless fleeing
a danger, because improved technology may allow
earlier arrival with a later start.
However, our solar system will support life
for several billion years, so many-thousand-year journeys
will be undertaken unless a unified society forbids it and
can enforce the prohibition against even rather small groups.

	No scientific advance and only small technological advances
are required to use a nuclear fission reactor
to generate electricity which is used to expel a working fluid
at an exhaust velocity varied and optimized during the journey.
Too low an exhaust velocity gives an unacceptably large mass
ratio, but too high an exhaust velocity requires handling too much power
to get enough thrust.  Some of the articles purporting to refute the possibility
of interstellar travel have noted that photon rockets optimize mass ratios
and then pointed out that they require handling implausible amounts of
power.

	We derive formulas for the time required to travel
a distance \f2s using the above technology in such a way as to minimize
travel time.  Then the figure of merit of our propulsion system
(reactor + rocket) is expressed by the ratio \f2p of
power the system can handle to the mass of the apparatus.
Plausible values of \f2p are between one watt/kilogram and \F21000\F1
watts/kilogram.  Since the time \f2T turns out proportional to
\F2p\!sups(-1/3);\F1, this factor of a thousand uncertainty in \f2p gives
only a factor of ten uncertainty in the time required for a given journey.\.

	We introduce symbols as follows:

	\f2s = length of journey

	\f2T = time of journey

	\f2t is a time variable

	\f2M = initial mass of the system

	\f2m\!subs(0); = final mass of the system

	\f2m is a mass variable

	\f5a\F2 = M/m\!subs(0);\F1 = the mass ratio

	\f2w is an exhaust velocity variable

	\F2a(t)\F1 is the acceleration

	\f2p = power available for unit mass of system

	\f2P is a power variable.

\J	Conservation of momentum and conservation of energy give the
following equations:\.

\oz[11)]\;
\oa{2 -}\;
\!topi(mdot,m,(\f6.));\;
\oc{2w = ma}\;
\&a←z&a,BZ&mdot&c;\Oa;\;

\oz[12)]\;
\oa{2P = - }\;
\;the overlay 1O2 is 1 Over 2 defined in math.ovl
\oe{2w\!sups(2);\F1.}\;
\&a←z&a,BZ&1O2&sp&mdot&e;\Oa;\;

\F1\J	Solving for \f2w in 1), substituting in 2) and solving
for \!jtopi((\f2m),(\f6.));\F1 gives\.

\oz[13)]\;
\ob{2 = - }\;
\!divi(d,(m\!sups(2);a\!sups(2);),P);\;
\&a←z&mdot,BZ&b&1O2&sp&d;\Oa;\;


\F1\J	We  now  distinguish  two cases: in a single stage rocket, we
have\.

4)\←C\→.\F2P = pm\!subs(0);

\F1\Jexpressing  the  fact that the power available is proportional to the
final mass of the system.

	In a continuously staged rocket, we have\.

4')\←C\→.\F2P = pm\F1,

\Jexpressing the fact that the power available is proportional to the
current mass.  (We suppose that every so often a nuclear reactor or
a rocket is taken out of service, vaporized and expelled as working
fluid).

	In the two cases, we get the equations\.


\oz[15)]\;
\!adivi(a,mdot,(m\!sups(2);));\;
\oc{2 = - }\;
\!divi(e,(a\!sups(2);),(pm\!subs(0);));\;
\&a←z&a,BZ&c&1O2&sp&e;\Oa;\;



\F1and


\oz[15')]\;
\!adivi(a,mdot,m);\;
\oc{2 = - }\;
\!divi(e,(a\!sups(2);),p);\;
\&a←z&a,BZ&c&1O2&sp&e;\Oa;\;


\F1\J	Taking  into  account the initial and final masses, we get the
following results by integration:\.


\oz[16)]\;
\oc{2- }\;
\!divi(d,1,(m\!subs(0);));\;
\oe{2 + }\;
\!divi(f,1,M);\;
\og{2 = - }\;
\!divi(h,1,(2pm\!subs(0);));\;
\ok{2 }\;
\oa{30}\;
\ob{3T}\;
\!int;\∂i0T←i;\;
\oj{2a(t)\!sups(2);\F2 dt}\;
\&a←z&c,BZ&d&e&f&g&h&k&i0T&j;\Oa;\;



\F1and


\oz[16')]\;
\oa[1log \F2m\!subs(0);\F2 - \F1log \F2M = - ]\;
\!divi(b,1,2p);\;
\&a←z&a,BZ&b&Sp&i0T&j;\Oa;\;


\F1\J	Using  \f5a\F2 = M/m\F1   and setting for the two cases\.

7)\←C\→.\F2q = p(1 - 1/\f5a)

\F1and

7')\←C\→.\F2q = p \F1log \f5a,

\Jwe get the following equation valid in both cases:\.


\oz[18)]\;
\oa[2q = ]\;
\&a←z&a,BZ&1O2&sp&i0T&j;\Oa;\;


\F1\J	Assuming that the journey begins and ends at rest we have\.


\oz[19)]\;
\oa[2a(t) dt = 0]\;
\&a←z&i0T,BZ&a;\Oa;\;


\F1\JThe final distance is given by\.


\oz[110)]\;
\oc[2s = ]\;
\oa[30]\;
\ob[2t\!subs(1);]\;
\!int;
\od[2a(t) dt dt\!subs(1);]\;
\&a←z&c,BZ&i0T&i&d;\Oa;\;


\F1from which


\oz[111)]\;
\oa[2(T - t) a(t) dt]\;
\&a←z&c,BZ&i0T&a;\Oa;\;


\F1\Jfollows by integration by parts.

	Our  goal is now to determine the acceleration profile  \F2a(t)\F1
satisfying equations 8), 9) and 11) so that  \f2T   is  minimized  for  a
given  \f2s.  Before doing this, however, we shall treat the simple case
in which we use a constant magnitude acceleration reversed in sign at
the midpoint of the journey.  This assumptions gives from 8) and 11)\.


\oz[112)]\;
\oa{2q = }\;
\oc{2a\!sups(2);\F2T}\;
\&a←z&a,BZ&1O2&sp&c;\Oa;\;

\F1and

\oz[113)]\;
\oa[2s = a]\;
\!divi(b,(T\!sups(2);),4);\;
\&a←z&a,BZ&sp&b;\Oa;\;


\F1	Solving for  \f2T  and  \f2a  gives


\oz[114)]\;
\oa[2T = 2s]\;
\&b←2o3;\;
\!exp2;\;
\oq[2q]\;
\&a←a&q;\;
\&b←mi&1o3;\;
\!exp2;\;
\&a←z&a,BZ;\Oa;\;


\F1and


\oz[115)]\;
\oa[2a = s]\;
\!exp2;\;
\&a←a&q;\;
\&b←2o3;\;
\!exp2;\;
\&a←z&a,BZ;\Oa;\;

\F1\J	We shall now labor mightily to optimize  \F2a(t)\F1, but the  eager
reader  is  warned  that  this  only  changes  the  co-efficient \f22 in
equation 14) to \F21.817\F1 which might not be considered worth either  the
mathematics or the engineering.  Well, onward!

	Instead of holding  \f2s  fixed and minimizing  \f2T, we  take  the
equivalent   but  simpler  problem  of  maximizing   \f2s   holding   \f2T 
constant and maintaining the validity of 9).
Introducing Lagrange multipliers, we must hold stationary the integral\.

\oz[116)]\;
\oa[2I = ]\;
\ob[2(T - t) a(t) dt + λ\!subs(1);\F2(q - ]\;
\oc[2) + λ\!subs(2);]\;
\od[2a(t) dt]\;
\&a←z&a,BZ&i0T&b&1O2&sp&i0T&j&c&i0T&d;\Oa;\;

\F1\Jsubject to the conditions 8) and 9) for arbitrary variations of \F2a(t)\F1.
This gives\.

\oz[117)]\;
\oa[20 = \f5dI = ]\;
\ob[2(T - t - λ\!subs(1);\F2 a(t) + λ\!subs(2);\F2) \f5da(t) dt]\;
\&a←z&a,BZ&i0T&b;\Oa;\;

\F1which must hold for arbitrary variations  \f5d\F2a(t)\F1.  Therefore

\oz[118)]\;
\oa[2a(t) = ]\;
\!divi(b,(T + λ\!subs(2);\F2 - t),(λ\!subs(1);));\;
\&a←z&a,BZ&b;\Oa;\;

\F1\J	Combining  18) with 8), 9) and 11) gives (if we have finally
gotten the algebra right)\.


\oz[119)]\;
\oa[26]\;
\!sqr;
\!adivi(c,a,6);\;
\oa[2s = T]\;
\&b←3o2;\;
\!exp2;\;
\&a←a&q;\;
\&b←1o2;\;
\!exp2;
\&a←z&a,BZ&sp&c;\Oa;\;


\F1and


\oz[120)]\;
\oa[2T = 6]\;
\&b←1o3;\;
\!exp2;\;
\os[2s]\;
\&a←a&s;\;
\&b←2o3;\;
\!exp2;\;
\&a←a&q;\;
\&b←mi&1o3;\;
\!exp2;\;
\oc[2 = 1.817 s]\;
\&a←a&c;\;
\&b←2o3;\;
\!exp2;\;
\&a←a&q;\;
\&b←mi&1o3;\;
\!exp2;\;
\&a←z&a,BZ;\Oa;\;


\F1\J	Thus  if we optimize acceleration and use continuous staging,
we get\.


\oz[121)]\;
\oa[2T = 1.817 s]\;
\&b←2o3;\;
\!exp2;\;
\op[2p]\;
\&a←a&p;\;
\&b←mi&1o3;\;
\!exp2;\;
\oc[1log\F2(M/m\!subs(0);\f2)]\;
\&a←a&c;\;
\!exp2;\;
\&a←z&a,BZ;\Oa;\;

\F1\J	This result is valid in any consistent units such as MKS or CGS.
If we measure distance in light years and time in years and keep \f2p
in watts per kilogram, equation 21) becomes\.


\oz[121')]\;
\oa[2T = 2571 s]\;
\&b←2o3;\;
\!exp2;\;
\op[2p]\;
\&a←a&p;\;
\&b←mi&1o3;\;
\!exp2;\;
\oc[1log\F2(M/m\!subs(0);\f2)]\;
\&a←a&c;\;
\!exp2;\;
\&a←z&a,BZ;\Oa;\;


\F1\J	Table 1 gives the result of putting numbers in the above equations.
The times are given for two cases: continuous staging and single stage.\.

\8table(A,B,C,D,E,F)[\←A\→r\r\F2⊗A⊗\.\←A\→.⊗B⊗\←B\→r\r⊗C⊗\.\←C\→r\r⊗D⊗\.\←D\→r\r⊗E⊗\.\;
\←E\→r\r⊗F⊗\.]\;

        s(light\←.\→A years)    p(watts\←.\→B/kg)    α=M/m\←.\→C\!subs(0);\;
  Tcont(ye\←.\→Dars)     T1(year\←.\→Es)

\!table(4,(.2),1000,3000,335,670);

\!table(4,(.2),1,(\F1e),(\F26693),7799);

\!table(12,,100,(\F1e),(\F22903),3384);

\!table(12,,100,20,2015,2954);

\!table(100,,100,20,8281,12143);

\!table(600,,10,20,58908,83477);

\!table(600,,1000,3000,9147,18296);


\!table(,,,Table 1);



\F1\JRemarks:

	1. The numerical results illustrate the insensitivity of the
qualitative character of interstellar travel to the quantitative
technological assumptions as long as we don't assume power handling
capabilities that give velocities close enough to light speed to
get relativistic time dilation.  The times are long compared to
human lifetimes and short compared to the lengths of time that
solar systems will support life.  Large improvements in technology
or very large mass ratios don't help much, and long distances don't
hinder much.

	2. A group interested in many launches might use a mass ratio
of \f2e and take only twice as long as with a mass ratio of 3000.  At
high mass ratios, multiple staging is important, but at small mass ratios,
single stage rockets might as well be used.

	3. The  zero  in  acceleration  at the midpoint
in the variable acceleration case means that the
calculation is invalid at that time because with constant power, we would
have infinite exhaust velocity.  The actual optimum profile
involves emitting only the waste products of the nuclear reactor near
the midpoint.

	4. Since  the  time  is  proportional  to  the  \!frax(2,3);\F1 power
of the distance, clearly the formula is incorrect for  long  distances.   It
becomes  incorrect when it recommends exhaust velocities greater than that
corresponding to emitting only the  waste  products  of  the  nuclear
reaction.
We can calculate this condition most readily for the case of constant
acceleration and continuous staging.  Solving equations 1) and 2) for
\f2w  gives\.


\oz[122)]\;
\oa[2w = ]\;
\!divi(b,2P,ma);\;
\&a←z&a,BZ&b;\Oa;\;


\F1which leads finally to


\oz[123)]\;
\oa[2w = 2p]\;
\&b←1o3;\;
\!exp2;\;
\&a←a&s;\;
\!exp2;\;
\oc[2(\F1log \F5a\F2)]\;
\&a←a&c;\;
\&b←mi&2o3;\;
\!exp2;\;
\&a←z&a,BZ;\Oa;\;


\F1\J	As a numerical example,
choose  \F5a\F2 = e\!sups(8);\F1  and  \F2p = 1000\F1 again,
and solve for \f2s getting\.


\oz[124)]\;
\oa[2s = ]\;
\!divi(b,(w\!sups(3);),125);\;
\&a←z&a,BZ&b;\Oa;\;


\F1\Jin MKS units.  The limiting case of a fission reactor using all
fissionable material and expelling only the fission products as
reaction mass and using \F2200,000,000\F1 electron volts as the energy
of fission gives  \F2s = 600\F1 light years
assuming that half the energy is converted to exhaust velocity;
i.e. the equations of
this article are valid for journeys shorter than this.  Longer
journeys are mass-ratio limited, and the formulas customary for
chemical rockets apply.
A fission propelled rocket that puts half the fission energy into
the exhaust velocity of the fission products has an exhaust velocity
of 9,100,000 meters/second.  A mass-ratio of 3000 yields a total
velocity change of 0.24c, i.e. about a quarter of the velocity of light.
Taking into account the need for deceleration means that .12c can
be taken as an average velocity for journeys much longer than 600
light years provided shielding the travellers from the radiation
produced by impact of interstellar atoms is a solvable problem.

	5. The ability to handle a million watts/kilogram of propulsion
system would make the journey to the nearest star a mere 33.5 years.
Unfortunately this seems to require scientific and not just technological
extrapolation.

	6. Suppose that deceleration could be accomplished without
using rockets.  For example, a magnetic field produced by a
current in a superconducting cable would dissipate energy by exciting
the interstellar plasma into motion.  This would reduce journeys by
a factor of 2\F2\!sups(-2/3);\F1 = .63.  The same time reduction factor
applies to flyby missions which needn't decelerate.

	We conclude that the galaxy can be occupied by
humanity in a time small compared that for which our
solar system will support life.  There is some difficulty in
reconciling this with the idea that technological civilization
has probably evolved many times already combined with our not
yet having any evidence for the galaxy being already occupied.
One way out is the often proposed idea that technological
civilizations don't last long.  In my opinion, there are so many
possible motivational structures for intelligent beings that
it is hard to believe that they would all wipe themselves out
or retire to a contemplative life.  I would rather give greater
probability to our being among the first.  One interpretation
to the two billion year interval between the first algae on
our planet and the start of complex life in the Cambrian era
600 million years ago - is that the initiation of sexual reproduction
or possibly multicellular life is a rare event with a half-life
of billions of years.  In that case, maybe we were lucky and are
among the first.\.
THE SOCIOLOGY OF INTERSTELLAR TRAVEL


\J	Most discussions of interstellar travel assume a unified
society that decides whether to undertake interstellar travel
taking into account its feasibility and the "values of the society".
This is one possibility, but there are others,
including at least the following:

	1. Humanity remains divided into sovereign nations
into the era when interstellar travel is feasible.
Rival ideologies or national interests lead to competitive expansion into the solar
system and beyond it.

	2. A political group or a religion unable to gain or maintain
control of a country sponsors emigration from earth.
The Mormons and Mennonites emigrated repeatedly
when they were being pressed to conform.
At present there is a finite probability that Israelis or libertarians
won't be able to have the kind of society they prefer anywhere on earth.
However, while present science would support a technology permitting
large numbers of people to migrate into interplanetary space using a
much more austere version of the system advocated by O'Neill,
it is hard to see that a group could send more than a pioneer
expedition on an interstellar journey.  Since there is plenty
of room and resources in interplanetary space, interstellar
colonisation would most likely be undertaken by a group
that considers that its existence would not be tolerated anywhere in the solar
system.

	3. The loser in a war or other power struggle may escape.
In my opinion, either side in World War II, feeling doomed to
lose, would have launched an escape expedition if it could, and
quite likely either capitalism or communism, if doomed to
violent defeat, would do so.
I have in mind many people co-operating to let a few
escape in order to preserve an ideology or a leader or a way of
life.  According to his ideology, the winner might either tolerate
escape or try to prevent it.\.

\J	4. How soon is possible?  If the Shuttle is produced
on schedule and  Shuttles or Shuttle launches can be bought,
and if nuclear technology like that involved in submarines is available,
then a group might be able to launch an expedition before the year 2000 at a cost
between a few hundred million and a few billion dollars.  This would be an
absolutely austere expedition, but its cost is within the reach of almost
any government, many social movements, and a few individuals.

	5. If the world remains sufficiently
pluralistic so that no major way of life is threatened with extinction, then
interstellar travel will be postponed until it is clear that waiting
longer to start will not lead to an earlier arrival.
Emigration to interplanetary
space is an intermediate possibility that would probably be preferred
by pioneers and utopian colonists unless the governments on earth repress
independent pioneering.\.

\J	However, most expeditions will probably be launched by secure
governments with adequate preparation.  This means that orbital telescopes
or flybys will have already established that the target solar system
can support life, i.e. has some reasonably low gravity planets or an asteroid
belt.  Since the time to α-Centauri is about 400 years
assuming \f2p = 1000 which should be attainable by the year 2050, it is
reasonable to predict that the first expedition will arrive at another
star by the year 2500.  Curiously, we can predict when it will arrive more
confidently than when it will start.

	One can imagine a society so unwilling to subject its members to
risk or discomfort that it wouldn't launch interstellar expeditions
and sufficiently unified that no subgroup would do so.  However,
neither condition has held for human society during most of its history
and seems unlikely as well as undesirable in our future.  It
seems strange to assume in discussions of interstellar
communication that it holds universally.\.
THE SOCIOLOGY OF THE INTERSTELLAR EXPEDITION


\J	Since there is no scientific guarantee that suspended animation
is possible,
we will assume a multi-generation expedition.

	Since the society of such an expedition would be quite different from
our present urban culture, one may worry about whether the expedition could
maintain its purpose or even survive.  Science fiction writers
have imagined the crew relapsing into savagery or a terrorist dictatorship.
One close analogy in human existence would seem to be an isolated tribe on a
small island.  Such tribes have apparently
maintained cultural isolation in groups of a few tens to a few hundreds for
centuries.\.

\J	Besides totally isolated tribes, religious cults like the Samaritans
have maintained very small communities living according to a law for
many generations.  As I understand it the Samaritans have maintained a
population of a few hundred since Biblical times.

	An interstellar expedition has both advantages and disadvantages compared
to tribes and cults.  First, it has written records and can use computer aided
instruction.  Second, if it has friends on earth, it can maintain radio
contact with them even at interstellar distances with the delays imposed
by the speed of light and with limitations on information transmission rate.
Its disadvantage is that it must maintain a more complex technological
capability.
Probably ten adults could
keep the capability to maintain the nuclear rockets,
the electronics and computers, and the life support system and pass
the skills to the next generation, but you
can't prove it couldn't be done by one talented man with
the ability to learn from reference books how to do things that hadn't
been required before in his lifetime.
Much depends on whether the group can be initially selected for intelligence
and energy and the extent to which these qualities can be maintained, i.e.
the level of the mean to which the initially selected group will revert.

	As for maintaining the expedition's purpose, the only survivable alternative
to continuing would be to turn back or stop at a nearer star if there
was one.  However, a group sending an expedition might not have much
chance of insuring that the travellers would remain loyal to their doctrine,
especially if this doctrine prescribed a way of life not suitable to
a space ship.

	There is a key sociological question that present sociology
probably can't answer.  Suppose that living conditions on the expedition
are rather good even including the opportunities for individual
self expression and development of potentiality - no worse, let us
say, than allows most people to function quite well in twentieth
century America.  With all that, each individual voyager will be affected
by his knowledge that the expedition as a whole has a purpose
that will come to fruition only long after his death.
It is not apparent whether the institutions of the expeditions can
be arranged so that this knowledge will have an inspiring effect
or at least to be motivationally neutral or whether it would
inevitably be demoralizing.

	While some human groups of a few tens may have survived 1000 years
of inbreeding, a sperm bank is obviously desirable to maintain genetic
diversity.

	In the case of large mass ratio, there is only a small arrival-time
penalty involved in keeping a large population and life support system
until the mass ratio remaining till the end of the voyage is small,
perhaps until a few generations before arrival.  At that time
the facilities would
be stripped to the bone and births would be sequenced so that the group
to arrive would be small and would arrive in their twenties and thirties.

	It is quite likely that pioneers arriving at another solar
system would find it easier to take up residence in interplanetary
space than to commit themselves to a planet.  In order to start expanding,
they would have only to build apparatus for collecting solar
energy and for processing material taken from asteroids.

	It seems doubtful that a colony could quickly "occupy"
a solar system and exclude later arrivals, since a solar system
is much larger than even a planet.  Therefore, the nearer solar
systems might get a number of mutually independent colonies

	Naturally, the function of an article like this is not to provide
a blueprint for our descendants to follow; they will know more about it
than we.  It is more a response to the narrow small planet ideology
that has recently been prevalent even among people who should know better
and an attempt to indicate possibilities open to other peoples with
whom we may communicate.\.
Literature:

Powell, Conley and Hahn, Ottfried J., Propulsion system optimization
for interstellar probes. - Journal of the British Interplanetary Society,
vol. 26, No. 6, June 1973, 334-342

Seifert, Howard S., Space Technology, Wiley 1959 : Chapter 10 Low-thrust
flight: variable exhaust velocity in gravitational fields by Jack H. Irving.

Materials testing reactor .01 kg/kw