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Very massive object colliding with tiny mass at high momentum?

  1. Jan 20, 2014 #1
    For the sake of argument, say an proton traveling at near light-speed having momentum far exceeding the earth's were to collide with earth head on. What would happen in this case? Would the result be any different replacing the proton with a small asteroid of the same momentum? Is it possible the earth would deflect in the case of an elastic collision?

    Since the quantities involved need relativistic correction, I'm not sure if this is the right place to put this.
  2. jcsd
  3. Jan 20, 2014 #2
    Obviously, the collision would not be elastic. But, ignoring that...

    Since we are asserting it is an elastic collision, the proton and Earth will depart after the collision at the same relative rate that they were closing at before the collision. That being about 1c - but only as seen from point of view of the new Earth trajectory.

    Conserving momentum, the average velocity will remain 0.5c.

    From the original trajectory, the proton will bounce back at about the speed of light.

    Without working through the arithmetic, the Earth would pick up some significant relativist mass and be ejected from its orbit around the sun.

    Since we are presuming an elastic collision, the size and shape of the proton/asteroid is not an issue.
    Last edited: Jan 20, 2014
  4. Jan 20, 2014 #3
    And what might the aftermath be of the expected (non-elastic) collision? It's hard to imagine a proton could do much? That is my motivation for this question
  5. Jan 20, 2014 #4
    The Earth would not stop the Proton - but there would be a substantial amount of energy transferred to the planet.

    As the proton passed through the Earth, I would imagine it would loose at least 1% of its momentum and that would be enough to fragment the Earth.
  6. Jan 20, 2014 #5
    High energy protons collide with Earth all the time. See "Cosmic rays". It's about 90% protons.
    The Earth is not deflected from his trajectory. And the protons do not go through Earth.
  7. Jan 20, 2014 #6
    But they do not travel at, say, (1-10^(-200))*c.
  8. Jan 20, 2014 #7
    You would be surprised at the energy of some "cosmic rays".

    From NASA http://helios.gsfc.nasa.gov/qa_cr.html#crvel
    The velocity of cosmic rays can go from a small fraction of the speed of light up to about .999999999999 times the speed of light. Since cosmic rays are matter (typically the bare nuclei of atoms), they CANNOT exceed the speed of light. They also cannot escape from the event horizon of black holes, but it looks as if black holes can generate relativistic jets of material out along their poles. But these particles are accelerated outside the black hole and so they (and any light generated there as well) can escape.
  9. Jan 20, 2014 #8
  10. Jan 20, 2014 #9
    There's an upper limit to the size of cosmic rays. The biggest one detected carried about 50J of energy. I can't find the article now, but I read they can't get much bigger because particles with such mass can interact with the cosmic microwave background radiation. That amount of energy can be absorbed by our atmosphere without much notice.

    DaveyP's particle is way, way beyond a cosmic ray. Once it reached the atmosphere (which could only happen if it was created very locally) it would begin interaction immediately.
  11. Jan 20, 2014 #10
    Oh, I did not see the "momentum far exceeding the Earth's" part in the OP.
    You are right.
  12. Jan 20, 2014 #11
    so you want to destroy the earth with a single proton? It's not true to say a momentum exceeding the momentum of the earth. Depending on the frame, your proton has or has not a momentum, as the earth. So in a frame where the earth is at rest, any momentum is infinitely bigger than the momentum of the earth. Maybe you want to say the kinetic energy of the proton exceeds the rest mass of the earth....?
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