Collision Question: Asteroid Impact & Water Drop Effects

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An asteroid measuring 10 km in diameter traveling at 0.99c would create a massive impact, likely resulting in a tunnel through the Earth, with the exit hole being significantly larger than the asteroid itself. The collision would produce substantial gamma radiation and particle emissions, leaving behind elementary particles and radiation. Such an event would devastate the Earth's biosphere, potentially vaporizing the atmosphere and causing catastrophic shock waves and earthquakes. A 1 cm water droplet impacting a steel wall at the same speed would release over 300 TeraJoules of energy, enough to destroy a city. Overall, both scenarios illustrate the extreme consequences of high-velocity impacts on Earth.
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This question is kind of strange, but I'm fascinated by it... Say an asteroid 10km in diamter crashes into the north pole at a right angle with a velocity of 0.99c! I imagine that it would punch through the whole planet and whatever is left will exit from the south pole, creating a temporary tunnel. Would the "exit hole" be much larger than the asteroid itself? Would there be a substantial amount of gamma radiation/particle production? What would be left of the asteroid? Elementary particles and radiation? What kind of an effect would this have on the Earth and its biosphere? A related question is: if a drop of water 1cm in diameter collides with a huge (and very thick) steel wall at 0.99c, what would happen? How large of a "dent" would it make?
 
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Hmm, I know that waterjets are used to cut though pieces of metal under very high pressures. I wonder why the water does not vaporize at such high speeds, maybe it shoots at such a small distance there is no time for it to vaporize before it hits the piece of metal. The same might apply for your question, if water could travel that fast without something happening to it. Also, for the case of the asteroid, I don't think its practical to talk about anything of that size traveling at .99C, so to comment on how it would impact would be meaningless. I do remember seeing on tv once that when a BIG, asteroid collides with a plannet, its not a big kaboom, like in the movies, but its actually a quite slow impact. It creates big nasty shock waves and Earth quakes, vaporizes the atmosphere and does a whole bunch of other nasty things to the inhabitants.
 
Last question first: Such a droplet of water would have an energy of over 300 TeraJoules, or more than 5 times the energy that was released by the Hiroshima bomb. So, you could wipe out a city with it. So scaling up, your 10km asteroid, would have over more energy yet. It would vapourize earth.
 
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