Relativity question for Hard SciFi writing

[hellebyuck]

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, traveling 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 transferred 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?

Thanks in advance.

 

[arildno]

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

 

[quantumdude]

To elaborate a bit...

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.

 

[arildno]

Alternatively, you might consider a playful fantasy-scifi novel set in a universe rather different than ours (art should, after all, be a free conception of the mind, to subvert a well-known quote from a well-knowner physicist).

But, also in this case, I would think it advantageous for you to learn what actually happens in our universe, in order to make a nice contrast to the developments in your own world.
Many PF'ers would be happy to provide info on our universe, but don't be too sure they will help you develop your own version.
They might buy the book, though, if turns out good..