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From: @S1-A.ARPA,@MIT-MC:redford%avoid.DEC@decwrl.ARPA
Newsgroups: net.space
Subject: cheap interstellar probes
Message-ID: <1946@mordor.UUCP>
Date: Fri, 24-May-85 10:52:33 EDT
Article-I.D.: mordor.1946
Posted: Fri May 24 10:52:33 1985
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From: redford%avoid.DEC@decwrl.ARPA  (John Redford)

Hmmm, what could we do to make a cheap interstellar probe?  The parameters
proposed were that the probe has to report back within a hundred years 
from a star no more than 20 light years away.  That seems a long way away.
How about if we just stick with Alpha Centauri at 4.3 ly, and say 
that it has to report back within fifty years?  That implies a trip 
time of 46 years, and a velocity of about 0.1C, or 30,000 km/s .  
We're not going to get that with chemical rockets.  One restriction 
was reasonably near-term technology, so matter-antimatter drives are 
out.  Fission drives seem a bit bulky, and we don't know how to do controlled
fusion drives, so we'll put those aside.  How about a laser-driven 
light sail, like in "The Mote in God's Eye"? Light sails work by reflecting
photons, thus gaining twice the momentum of the photon stream.  The
momentum, p, of a stream of photons is E/c where E is the stream's energy,
so the change in momentum of the sail is 2E/c.  The change in momentum
per unit time is 2P/c, where P is the power of the stream.  The acceleration
of the sail, a, is the change in momentum per unit time divided by 
the mass of the sail, m, so:

a = (2/c) * (P/m)

We want to get the velocity up t0.1C2C in 46 years, so

v = a*t = (2/c) * (P/m) * t

P/m = v*c / 2*t = 6e6 W/kg

For every kilogram of sail, we must apply 6 million watts for 46 years.
That works out to 2.6 billion kW-hrs of energy per kilogram of sail, or
(at seven cents per kilowatt-hour) 180 million dollars worth of energy
per kg.

This looks pretty grim.  Never mind the problems of keeping a laser focussed
on a sail 4 light-years away, or keeping the sail 
from melting in the beam.  A 1000 kg probe will cost 180 billion bucks 
just in energy to get to the nearest star.  Time to break out the hyperdrive.

John Redford
DEC-Hudson