Relativity question for Hard SciFi writing

I'm working on writing some hard science fiction stuff, and I have a question I was hoping you guys could help me with. See, my training is primarily in math and chemistry, and it's been quite some time since I've really had any dealings with more than just the most basic concepts in general relativity.

So here's my problem. Not worrying about the means of getting to these speeds, you have a large, massive object, say, an asteroid, travelling at relativistic velocities, colliding with something comparitively slow moving, like a planet. I know that as the velocity moves into larger fractions of c the momentum will increase geometrically, as both mass and velocity increase. Greater momentum means greater energy transfered upon collision, et cetera. That much is easy. What I'm wondering is, if that object is moving at or above the velocity of light (again, don't worry about how it gets moving that fast. just assume constant velocity until the moment of impact), what would happen on collision? How would an asteroid traveling at ten times c compare to one traveling at, say, five hundred times c in terms of relative damage?

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arildno
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It would be a wholly imaginary collision, in many senses of the word..

Tom Mattson
Staff Emeritus
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To elaborate a bit...

hellebyuck said:
What I'm wondering is, if that object is moving at or above the velocity of light (again, don't worry about how it gets moving that fast. just assume constant velocity until the moment of impact), what would happen on collision? How would an asteroid traveling at ten times c compare to one traveling at, say, five hundred times c in terms of relative damage?
The amount of damage caused by a collision can be measured by the 4-momentum transfer from one object to another. This is a measure of the violence of the collision. But if you put velocities of 5c and 10c into the equations, you get imaginary quantities. How do you measure imaginary damage?

If you want to write a book with which trained physicists can help you, then it would be better if your asteroid were moving at 0.9c. Then we can give you some quantitative and qualitative information.

Lren Zvsm
arildno