X-Edited: Last modified on Thu Jul 30 01:11:29 1987 PDT by stolfi

References: <623@cfa.cfa.harvard.EDU> <8707042042.AA00520@angband.s1.gov>
            <830@jumbo.dec.com> <8233@utzoo.UUCP>
            <8706301703.AA11822@ames-pioneer.arpa>


>   ME: I have the impression that collisions with largish "dust
>   grains" may be a serious obstacle to interstellar travel.
>   At the speeds usually considered necessary for interstellar
>   trips, such collisions seem unavoidable and too energetic to be
>   shielded effectively.  Has anyone analyzed this problem before?  

>   EUGENE MIYA: ...  There are [2 solutions I can remember off the top]:
>   1) is the equivalent of armor plate.  ...  2) is to
>   use a thin layer of aluminum to dissipate energy (of small particles)...  

Thanks for the info, but these methods don't seem to be applicable to 
speeds near the speed of light. Because of the
much higher collision energies, plain shielding against 1 gram pebbles
would require an armor plate at least tens of miles thick (which would be
quickly destroyed by a few impacts).  As for the second method, at
relativistic speeds there is not much difference between hitting a 1 gram
pebble or a 1 gram of gas.


>   HENRY SPENCER: Check out the Project Daedalus report from the British
>   Interplanetary Society, for example.  Results are sensitive to
>   estimates of the density of interstellar debris of size X, but in
>   general the problem does not seem intractable.  The Daedalus report
>   studied a large unmanned probe at about 15% of the speed of light, and
>   concluded that some simple precautions would suffice.
>   Basically all that was necessary in interstellar space at those speeds
>   was a bit of armor on the leading face.  That cut the probability of
>   real trouble down to 0.1% or so.  [...] The solution was to maintain a
>   fine dust cloud some thousands of kilometers ahead of the probe;
>   incoming particles would hit the cloud and vaporize.  The distance
>   between cloud and probe was calculated so that the resulting fireballs
>   would expand to a safe density by the time they reached the probe.
>   While it looked possible to maintain the cloud from the probe itself, a
>   simpler method was to use a secondary probe, a "dust bug", flying in
>   the cloud itself.  Occasionally the dust bug itself would be destroyed,
>   so the main probe would have to carry several.  

Thanks for the reference; I will try to find it.
Meanwhile, I still have some questions.  For one thing, how did they
propose to keep the protective dust cloud plowing through the
interstellar medium at 0.15c?  If I have not bungled my physics, a
particle moving at 5e7 m/s through a gas with 1e6 atoms/m^3 (1 per
cubic centimeter) will encounter the same resistance as one moving at 5
m/s through a gas with 1e20 atoms/m^3 --- not impressive, but not
negligible either.  

Also note that interstellar particles will probably have proper motions
on the order of 1e4 m/s or more.  Therefore, if the dust shield is a
thousand km ahead of the ship, it would have to be about 1km
wide to give adequate protection.  

>   ME: 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.  

>   PAUL DIETZ: Is 10^17/m^3 too low to detect?  The way to detect large (gram
>   sized) particles from interstellar space is to look for meteors with
>   high velocity.  This has been done in the midwest with multiple cameras
>   (equiped with rotating disks to chop the trails to measure velocity).
>   Interstellar grains should have velocities in excess of solar escape
>   velocity.  I don't believe any such grains have been detected.
>   
>   Assuming extrasolar meteors are moving in parabolic orbits, a 10x10
>   km patch of sky will sample about 7x10^12 m^3/second, or 10^17 m^3 in
>   about four hours.
>
>   This detection method will fail for very heat sensitive grains.  But
>   grains can't be made of solid hydrogen, which would evaporate even in
>   interstellar space, and organic blobs would get polymerized by cosmic
>   rays.

A couple of questions:

1) Suppose interstellar pebbles in the neighborhood of the solar system
move at about the same speed as comets in the Oort cloud, which I
believe is on the order of 1e3 m/s or less (Pluto's orbital speed is
5e3 m/s, right?) As they fall to the Earth orbit, their speed will
increase at least 70-fold, to some 7e4 m/s.  It is not obvious to me
that their density (particles/m^3) will remain unchanged; offhand, I
would expect it to be reduced by about the same factor.  If this is
true, then in your scenario a density of 1e-17 particles/m^3 (in
interstellar space) will give only one event every 280 hours.  

2) I have read somewhere that interstellar dust grains (the ones we can
see, 0.1 micron or so) probably consist of a silicate core covered by a
layer of water ice.  Large "pebbles", if they exist, will likely be
loose aggregates of such dust grains.  Think of them as very small
comets.  When such a pebble falls towards the inner solar system, it
will heat up and start to boil away, just like a comet.  Well before it
reaches Earth orbit, its ice will evaporate, and the puff of dust that
remains will be blown apart by the solar wind.

In other words, the experiment you describe may put a limit on the
density of refractory pebbles; however, it doesn't seem to say anything
about small dusty snowballs.  

(Incidentally, it seems that estimates of the size and density of the
Oort cloud have been growing steadily in the last years.  Maybe it
extends all the way to Alpha Centauri?) 

>   STEVE WILLNER: Present data on interstellar particles come from
>   three sources: 1) Observations of dimming, reddening, and
>   polarization of light of distant stars.  These observations ...
>   tell us directly about dust grains with radii of order 0.1
>   micron or or mass ~1E-14 grams.  2) Knowledge of "heavy
>   element" abundances [which constitute] about 3% of the mass of
>   most stars ...  3) Depletion of heavy elements from the gas
>   phase.  
>   
>   In spite of the varieties of information, almost nothing is
>   directly known about dust grains larger than a couple of
>   microns (~1E-10 g) or so.  The best that can be done is to
>   combine the limit from item 2 above with estimates of gas
>   density [which range] from 1E-2 H atoms per cm^3 inside the
>   shell of supernova remnants to 1E5 in the densest molecular
>   clouds.  However, a typical density in regions near the Sun is
>   about 1 atom per cm^3.  Thus a typical density of solid
>   particles is 2E-26 g cm^-3.  ...
>   

Thanks for your posting; I have long been looking for this information.
However, I still don't think the evidence is conclusive.  If I have not
bungled my algebra, it would seem that 0.1 micron is roughly the
maximum size for which the dust grains can be expected to be carried
along by the parent gas cloud.  Grains much larger than that seem able
to lead an independent life.  For example, they may remain behind when
the gas cloud dssipates or is blown away by stellar wind.  In a cloud
that is stable against collapse, embedded large grains still may
collapse on their own.  When two clouds collide and lose their
kinetic energy into heat, large dust grains may still keep
going in their original trajectoriy and speed.  And so on.  

If this is true, then maybe there is an open cycle where the metal
content of stars and gas clouds is more or less stable at 3%, without
that posing any constraint on the pebble density: 

     
    supernovas, stellar winds             dust aggregation & separation
     ---------------------->  gas clouds ---------------------
    |                         w/ fine dust                    |
    |                                |                        |
    |                                |                        V
 stars                               V                   Interstellar
    ^                                |                     Pebbles
    |                                |
     --------------------------------
      Collisions, compression, cooling,
      collapse

I agree that this is a bit far-fetched.  However, consider that
something like it happened in our solar system: most of the primeval
gas cloud was blown away, leaving behind a few metal-rich pebbles
(such as the Earth).  Why should we assume that this phenomenon happens
only in planetary systems, and not in interstellar space?

Also, I think I read somewhere that there has to be some process that
removes grains larger than 0.1 micron from gas clouds, to explain the
observed size distribution.  Could that be aggregation into much larger
pebbles?

I recall there was a theory suggesting that the mysterious "dark
matter" (aka "missing mass") required by galaxy dynamics consisted of
"orphan" planets (Jupiter-size and smaller) floating away in
interstellar space.  Waht happened to that theory?  

By the way, what happens to any planets that form around stars in dense
star clusters?  (Is that possible?) Do they remain tied to their parent
star?  Or will they eventually "boil" off the cluster?  

Well, nuf said. Sorry for bothering you with my late night elucubrations...

  Jorge Stolfi   (stolfi@src.dec.com, ...decvax!decwrl!stolfi)
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    Barbicane could not help smiling at Michel's reply; then, returning to
    his theory, said ---

    ``Thus, in case of a shock, it would have been with our projectile as
    with a bullet which falls in a burning state after having struck a metal
    plate: it is its motion which is turned into heat.  Consequently I
    affirm that, if our projectile had struck the meteor, its speed thus
    suddenly checked would have raised a heat great enough to turn it into
    vapour instantaneously.''   
                                  ---Jules Verne, _Round the Moon_ (1870)
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