To: sci.space
cc: stolfi
Subject: The rocky road to the stars
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One obstacle to star travel that I haven't seen discussed is the danger of
collisions with pebble-sized "dust grains".  At the speeds usually
considered necessary for interstellar trips, such collisions may be
unavoidable and too energetic to be shielded effectively.  

For definiteness, consider a spaceship traveling at 10^7 m/s.  That is real
slug speed, only 1/30 of the speed of light.  At that speed it would take
120 years to get to the (next-)nearest star.  Still, since kinetic energy
is proportional to mass time velocity squared, hitting a 1g pebble at that
speed should be as bad as hitting a 1 ton boulder at 10^4 m/s (low Earth
orbit speed) or a 10,000 ton asteroid at 360 km/h.  Conversely, a 1g hit at
10^4 m/s, which would probably blow a hole straight through the Shuttle, is
energeticaly equivalent to a 0.000001g hit at 10^7 m/s.  (Here I am
ignoring relativistic effects, which would only make the picture worse
anyway.) 

How likely are such collisions?  A spaceship with 10 m^2 cross section
(about 4 m diameter) will sweep 10^17 m^3 of space per light year of
travel.  If the average density d(M) of particles with mass >M in
interstellar space is a bit more than 10^-17 per cubic meter, the
probability of colliding with one or more such particles will be
practically 1.  I dont have any idea of what is d(M) for "large" M
(say, 1 mg), but I expect 10^-17 particles/m^3 to be far below the
detection threshold.  

From some back-of-the envelope calculations it seems that no practical
amount of shielding would resist multiple hits by pebble-sized particles.
Destroying those particles before they hit the ship also seems unfeasible.
For example, if we try to vaporize each pebble with a laser beam, we must
do that while the pebble is very far away, so that the gas cloud has enough
time to dissipate completely before the spaceship gets there.  

I hope to give more details in a future message. Meanwhile, any comments?

  Jorge Stolfi
  
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    Then Nicholl, using his own calculations, demonstrated that it was
    absolutely impossible to give any object at all the velocity of 12,000
    yards per second.  And, algebra in hand, he maintained that even if
    such a velocity could be attained, such a heavy projectile could never
    be lifted beyond the limits of the Earth's atmosphere!  It would never
    reach even an altitude of twenty miles.  And furthermore!  Even if such
    a speed could be attained, even if it would suffice, the shell could
    not withstand the pressure of the gases produced by igniting 1,600,000
    pounds of powder.  And even if it could resist the pressure, it could
    not withstand the temperature, it would melt as it left the Columbiad,
    and a red-hot rain would fall on the heads of the foolish spectators.  

    Barbicane did not even wince at these attacks; he simply got on
    with his work.
                         -- Jules Verne, From the Earth to the Moon (1865)