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Move something about the size of the ISS

  1. May 24, 2004 #1
    This is for a story plot.
    Suppose for a moment that you actually had a way of boosting a slug of metal, say around the mass of your average bus, all the way up to 2/3c, and send it heading for Earth.
    1) Would there be any way at all of detecting the "incoming round"? Even if this thing was making its way in from all the way out past Pluto and there were plenty of telescopes of various kinds everywhere from Phobos to Europa? How likely would anyone be to spot something that small moving that fast?
    2) What would you detect? Some kind of X-Ray emissions from the slug smashing stray molecules and occasional pebbles into plasma occurring along a statistically unlikely straight line?
    3) Could its path even be calculated, or would relativistic effects start to render any such calculations pretty much an indeterminate moot point?
    4) Even if you could move something about the size of the ISS into its path, say as far out as the orbit of the Moon, wouldn't a slug like that pass clean through something like the ISS with just about zip in the way of lost momentum? I.e., short of pushing something the mass of the Moon itself into the slug's path, you ain't stoppin it, or even appreciably slowing it down?
     
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  3. May 24, 2004 #2

    chroot

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    1) Well, you're talking about futuristic technology, so of course, it's possible. On the other hand, the amount of time this thing would spend increasing from say magnitude 20 to magnitude 5 would be just a few hours, so you'd have to have surveillance over the entire sky to have a chance of catching it. Even if you had 1000 telescopes each with a field of view of a square degree looking every which way in the sky, you'd only be covering 1/4 of the sky.

    2) It'd probably be so heated up from collisions with molecules in the interstellar medium that it'd be glowing in x-rays. Of course, no real glob of any known metal could withstand those temperatures without just vaporizing, but we're talking sci-fi metal here. If you really need an exact calculation of the energy gained by such a mass moving through the ISM per unit length, it wouldn't be hard to do. Let me know. It's late at night right now and I don't feel like looking up all the numbers.

    3) If it were photographed repeatedly, its path could be extrapolated, in principle. Relativity is a well-understood theory.

    4) That's actually a very difficult question to answer. A 2000 kg slug of metal going 2/3 c would impart 10^20 joules of energy, or about the same energy as 10 million megatons of TNT. That sounds impressive, but it's only about as much as energy as was released by the Sumatra volcano explosion, and that certainly didn't rip apart the Earth or anything.

    The moon's structure is well known -- it's mostly rock, with a small iron core. I'm not even sure how to go about doing such a calculation, or even if such a calculation could be done and have any validity, but my gut feeling is that the slug would penetrate the rock rather easily, going right through it, but would essentially disintegrate if it hit the iron core. Perhaps someone else has some harder facts on such a situation.

    - Warren
     
  4. May 25, 2004 #3

    Nereid

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    This is a really cool engineering (and physics) problem! Maybe some teacher will set it as a challenge.

    At the OOM (order of magnitude) level, the answers should be fairly easy to work out. Suppose we start with a cubic metre of iron - what would its mass be? Let's also say its cross-section is 1 square metre. We know the density of inter-planetary space, we know how long our friendly bus will take to get from 30 au to 1 au ... how many collisions will it make with IPM atoms (etc) on the way? What energy will be transferred to the bus? to the hapless atoms? (assume some convenient energy conversion/inelastic energy measure, say 10%) Since the bus is iron, will there be any magnetic effects worth noticing? Of course, the IPM is a plasma, but assume it's a plain old gas for now; what's the speed of sound in such a gas? What will the inevitable shock waves set up by our friendly bus ploughing through the IPN look like?

    Now the fun part! Smashing into the Moon: let's start with an easy question - if instead of a nice compact ball, suppose the bus were neutral iron atoms spaced 10nm (or 100nm) apart, still with a cross section of 1 sq m; how long would the train be? In earthly particle accelerators, occassionally it's necessary to 'dump the beam' (remember that particles in such beams are travelling an awful lot faster than our bus!) - how deeply does such a beam penetrate? How long does it take the average particle to come to a stand-still? How hot does the beam stop become? Now scale that up for our long train of bus iron hitting the Moon (for now, assume the density of the Moon's surface is the same as that of a beam stop).

    Leave aside energy carried away from the Moon/bus collision for now; assume all the kinetic energy of the bus gets dumped onto/into the Moon. How much energy is that? If it were used to evenly heat the bus, how hot would the bus get? If instead it evenly heats 10 (100?) times its mass of Moon rock, how hot would that rock (+bus) get?

    Finally the collision itself: what physical processes take place in a collision? I.e., how does kinetic energy get converted into heat (and sound, and light, etc) when two cars collide head-on? A dud shell hits the ground? a meteor hits the Earth? Ignoring all kinds of interesting phenomena which no doubt become extremely important for a relativistic chunk of iron striking the Moon :tongue2: can an impactor 'feel' the impact faster than the speed of sound in the object?
     
  5. May 26, 2004 #4

    Chronos

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    it would have about the same effect as a mount everest size asteroid colliding with the earth travelling at speeds typical within our solar system. fortunately, none of those are travelling nowhere near 2/3 c so far as we know. it is unlikely anything is travelling much faster than that in our neighborhood, much less on a collision course with earth.
     
  6. May 27, 2004 #5

    Nereid

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    You're probably correct; would you like to give us some OOM calculations to show that? Even 2OOM (within a factor of 100, cf 10 :wink: )
     
  7. May 28, 2004 #6

    Chronos

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    f=mv, is the short answer.
     
  8. May 28, 2004 #7

    chroot

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    Chronos,

    Perhaps you meant F = ma?

    - Warren
     
  9. May 28, 2004 #8

    Nereid

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    half way between OOM and 2OOM

    Ignore relativistic effects. What mass of asteroid would have the 'same' kinetic energy as a 1 m^3 lump of Fe, travelling very fast (~0.1c, OOM only)?

    As an OOM, we take the v of the asteroid to be 10 km/s.

    So our Fe bus is travelling with a v that's 3,000 times that of the asteroid's v. The per unit mass KE ratio is then ~10^7, thus the mass ratio, for KE equality.

    How big would such an asteroid be? For OOM, its linear dimensions would be 10^(1/3) x 100, expressed in Fe-bus units (somewhat bigger if it had a lower density than Fe, but this is OOM, remember!).

    How deep a crater would a ~200m asteroid make on the Moon (if it hit at 10 km/s)?

    The key thing missing, even in OOM calculations, isn't relativistic effects, but the extent to which crater depth scales with impact speed, and to answer that (it seems to me) we need to know something about the physical processes that occur during high speed collisions, esp those ~3 OOM above typical asteroids-crashing-into-the-Moon speeds. :eek:

    Anyone?
     
  10. Jun 18, 2004 #9

    Nereid

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    Do I have to do everything myself? Sigh, a woman's work is never done :rolleyes: :uhh:

    Fortunately, no; Dr H. Jay Melosh (and others) have done much of the heavy lifting for PF members and friends. From one of his papers (on that site):
    "The three pillars of impact simulation: The
    physics needed to simulate large meteorite impacts lies
    squarely in the classical domain. The size scale is so
    large that quantum effects are not important (although
    quantum mechanics does determine the thermodynamic
    equation of state) and the velocities are well below the
    speed of light, so classical Newtonian mechanics, supplemented
    by classical thermodynamics, provides an
    adequate framework for modeling impacts. In addition,
    it has become clear that successful simulation of
    real impact craters often requires a detailed understanding
    of the response of real rocks to stress and heat.
    Of these three supporting pillars, Newtonian mechanics
    is probably the least troublesome. All modern
    “hydrocodes” (a now obsolete term that reflects the
    historical development of computer codes that, at first,
    did not contain material strength) incorporate the standard
    F = ma foundation of mechanics, although this is
    often obscured by an impressive amount of bookkeeping
    to keep track of all the pieces. All codes incorporate
    some form of gravitational acceleration, although
    only a few employ self-gravitation (only important in
    planet- scale impacts). It is notable that there do not
    appear to be any talks at this conference on this aspect
    of computer modeling.
    The next supporting pillar is thermodynamics,
    through the equation of state [4]. The equation of state
    for impact modeling is a little peculiar: Instead of the
    conventional thermodynamic relation relating pressure
    P to density [rho] and temperature T, P([rho],T), hydrocodes
    require a relation between P, [rho] and internal energy E.
    Equations of state for metals have been vigorously
    pursued by squadrons of physicists since the end of
    WWII, mainly to support the design and testing of
    nuclear weapons. However, few good equations of
    state exist for geologic materials, such as rock or ice.
    More research is needed to create these important relations.
    "

    For our purposes, all the nice work done on the proto-Moon smashing into the early Earth doesn't really help much; we *really* want to know how deeply our iron bus will penetrate the Moon's surface! BTW, these impacts are termed 'hypervelocity impacts', because the speed of impact is > speed of sound in the impactor and target, so shocks and shock waves are the principal physics (hence the use of Hugoniot relations).

    The speed of sound in rock is ~1-10 km/sec (OOM), ditto iron; so the trailing edge of our bus would feel the (sonic) shock of impact ~0.1 ms after impact, by which time it would have penetrated ~30 km! My guess is that for these hyper-hyper-hypervelocity impacts the leading edge will be converted to a very, very hot plasma, thus creating pressures far beyond the ~100 Gpa limits of the equations of state in current simulations, and ... what? (apart from perhaps penetrating more deeply than your average mountain-sized asteroid, the net effect on the Moon would be otherwise little different from an impact with the same kinetic energy - the shock wave in Moon rock dissipates rapidly with distance from the impact point)
    At OOM, ~400m. So, to answer one of the original questions
    If the incoming round were a cubic metre of iron, the ISS would have as much effect as tissue paper; a solid rock (or better, iron) asteroid of at least ~1 km diameter might do (but conservation of momentum suggests you may have a much worse problem, post-impact!).
     
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