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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?

Thanks in advance.