Very massive object colliding with tiny mass at high momentum?

In summary, the conversation discusses the potential outcome of a collision between a proton traveling at near light-speed and the Earth. The participants consider the effects of an elastic collision and the possibility of an asteroid with the same momentum as the proton. They also mention the energy and velocity of cosmic rays and the potential impact of a high-energy particle colliding with Earth. Ultimately, they question the accuracy of the initial scenario and clarify the terminology used.
  • #1
daveyp225
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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.
 
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  • #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.
 
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  • #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
 
  • #4
daveyp225 said:
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
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.
 
  • #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.
 
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  • #6
nasu said:
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.

But they do not travel at, say, (1-10^(-200))*c.
 
  • #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.
 
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  • #9
nasu said:
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.

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.
 
  • #10
Oh, I did not see the "momentum far exceeding the Earth's" part in the OP.
You are right.
 
  • #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...?
 

1. What is a "very massive object"?

A very massive object is an object that has a large amount of mass, typically measured in kilograms. Examples of very massive objects include planets, stars, and black holes.

2. What is a "tiny mass"?

A tiny mass is an object that has a very small amount of mass, typically measured in grams or even smaller units such as atomic mass units. Examples of tiny masses include particles like electrons, protons, and neutrons.

3. What is considered "high momentum" in this scenario?

High momentum refers to a large amount of force applied over a short period of time, resulting in a significant change in velocity. In this scenario, it would mean that the very massive object is colliding with the tiny mass at a high speed, resulting in a large change in the tiny mass's velocity.

4. What happens when a very massive object collides with a tiny mass at high momentum?

When a very massive object collides with a tiny mass at high momentum, the tiny mass will experience a large amount of force and acceleration. Depending on the specific circumstances of the collision, the tiny mass may be destroyed or undergo a significant change in trajectory.

5. Why is studying collisions between very massive objects and tiny masses important?

Studying these types of collisions can help us better understand the laws of physics, such as momentum and conservation of energy. It can also provide insights into the formation and evolution of celestial bodies, as well as potential hazards in space such as asteroid impacts.

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