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.cb INTERSTELLAR TRAVEL WITH 20TH CENTURY TECHNOLOGY


	There are about a hundred billion stars in our galaxy (about 25
stars for each person on the earth today) and it would be wonderful if we
could travel to them in a few months or years.  Unfortunately, the galaxy
is a 100,000 light years across (30,000 light years from here to the
galactic core), and our present science tell us that we can't travel
faster than the speed of light.  Of course, our present science could be
wrong, and faster-than-light travel may someday be possible.

	However, for once let us take the opposite point
of view and ask what can we surely do rather than what we might
do if only Nature were more co-operative.  We shall assume only
present science and not much beyond present technology.  We must
resign ourselves to thinking about multi-generation journeys
and consider how it could be done and why people might do it.

	One rocket that will surely work
uses a nuclear reactor to generate electricity
and uses the electricity to propel charged particles out the
back - the reaction propelling the rocket forward.  Reactors
that could be used for this purpose have been built;
those used in nuclear submarines are best, because they produce
the most power for a given mass of reactor.  Rockets that
expel charged particles have been built, one is being
tested now in orbit, and NASA's hopes for a 1986 %2rendez-vous%1
with Halley's comet are based on an ion rocket.

	Optimizing a rocket system that generates power and uses
that power to expel a working fluid is more complicated than
optimizing a chemical rocket.  In a chemical rocket, the %2figure
of merit%1 (the number that
tells how good the system is)
is the velocity of the exhaust - the higher the better.
The highest imaginable exhaust velocity is the velocity of light,
and some years ago many scientists supposed that this would be
the best rocket, because it would give the highest ultimate
velocity of the rocket for a given expenditure of mass.  Pessimistically
inclined scientists then pointed out that the a photon rocket
must expend such enormous power in order to provide a moderate thrust
that interstellar travel is impossible.
Most of the discussion of interstellar communication
assumes that interstellar travel is
impossible.

	It turns out that there is a happy medium between too high
an exhaust velocity which wastes energy and too low an exhaust velocity
which wastes reaction mass.  Moreover, the optimum exhaust velocity
varies during the journey.  Consider a journey through a distance %2s%1,
starting from zero velocity and ending at zero velocity.  Assume that
the propulsion system has a %2specific power p%1, i.e. %2p%1 is the
the power output of the system divided by its mass.  Finally, let the
mass ratio be %2k%1, i.e. %2k%1 kilograms start the journey for every
kilogram that arrives.  The time %2T%1 of the
journey is then given by the formula

!!a1:	%2T = 1.8s__p__k%1.

	We will spare the reader the derivation of the formula
using calculus of variations.  (The part involving %2s%1 and %2p%1
follows from just dimensional analysis).   However, its consequences
are interesting.

	First consider the %2s%1__ part.  The time required for the
journey is less than proportional to the time.  A simple explanation
is that on a longer journey we can use our power source
longer, and therefore can use a higher average exhaust velocity and
achieve a higher average velocity during the journey.  Its consequence
is that reaching stars 80 light years away takes only four times
as long as reaching stars 10 light years away - not eight times
as long.  Since we can expect 512 times as many stars in that zone,
it means that if any stars are visitable, many will be visitable.

	The %2p%1__ term is even more interesting.  It means that
the rocket system must be improved by a factor of a 1000 in order
to reduce the travel times by a factor of 10.  Conversely, you don't
lose much by a bulkier system with a low specific power.

	The final term tells us that very large mass-ratios aren't
very helpful either.

	Here is a table that gives some travel times for different
assumptions about the distance, the specific power, and the mass-ratio.


table 1


	I am not claiming that this is the only possible method
of interstellar travel, %3but it is one I am sure will work%1.
Therefore, our speculations about the occupation of the universe
by humans or other intelligences should be based on having at least
this good a method of interstellar travel.

	Suppose that this is the best we can do technologically.
When can we expect what interstellar travel?


.cb SCENARIOS FOR LAUNCHING INTERSTELLAR TRAVEL

	There are several cases.

	1. Suppose that humanity remains relatively peaceful, solves
its energy and resource problems well enough so that life is no
worse than today.  In that case we can predict the time of arrival
at the nearer stars more accurately than we can predict the time
of departure.

	Clearly it is pointless to start a thousand year expedition
if waiting ten years to start will reduce the journey to 900 years.
If technology based on present science improves at its present rate,
this will be true for one or two hundred years, i.e. an expedition
starting in the year 2100 will arrive before an expedition starting
in the year 2000.
.skip 1
.begin verbatim
John McCarthy
Artificial Intelligence Laboratory
Computer Science Department
Stanford University
Stanford, California 94305

ARPANET: MCCARTHY@SU-AI
.end

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