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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 tells us that we can't travel
faster than the speed of light.  Our present science could be
wrong, but the theory of relativity has survived more experimental
tests than almost any other part of physics.

	For once, let's be conservative and ask what
interstellar travel is surely possible rather than what we might do if
Nature is more co-operative than we can be sure of.
We shall assume only present science and not much beyond present
technology.  We will have to accept multi-generation
journeys, consider how they can be done, and why people might want to.

	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.   The reactors
now used in nuclear submarines would even work; they produce
the most power for a given mass of reactor of any existing
reactor, but a new design could do much better.  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 electric rocket (solar powered).

	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 engineers believed 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
enormous power in order to provide a moderate thrust, and argued that
interstellar travel is impossible.  For some reason, 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.  However, this optimum exhaust velocity should
change 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%42/3%2p%4-1/3%2(log k)%-1/3%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%42/3%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%4-1/3%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 %2log k%4-1/3%1 term tells us that starting with a very large mass
isn'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 don't claim this is the only possible method of
interstellar travel or even the best, %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.  Suppose also that during the next thousand years
we do not become aware of any other intelligence in the universe.
In that case we can predict the time of arrival
at the nearer stars more accurately than we can predict the time
of departure.  Almost certainly interstellar expeditions will arrive
at the nearer stars before the year 3000 and most likely before 2500.

	Clearly it is pointless to start a thousand year expedition at a
time when waiting twenty 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.

	Most likely, before the first expedition, much more will be
known about the prospects of planets and asteroids around the
potential targets.  Large space-based telescopes can answer many of these
questions and are much cheaper than even unmanned probes.
A fly-by mission that accelerates all the way takes half the time
of a mission that must stop, but it must collect whatever information
it will radio back in a short time while travelling at high velocity.
notes:

1. can a multi-generation expedition succeed

2. do we need an earth-like planet
	What?  Go back in the well!

3. Will civilization fission into pro- and anti-technology?
	The bureaucratic ethic.

4. 
.skip 1
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John McCarthy
Artificial Intelligence Laboratory
Computer Science Department
Stanford University
Stanford, California 94305

ARPANET: MCCARTHY@SU-AI
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