
Math & Physics Mathematical and physical problems of space flight and astronomy. 

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09072019, 02:08 PM  #1 
Addon Developer

Relativistic largescale collisions
Does anyone know if any theoretical work has been done on the effects of a relativistic largescale collision? Like if an asteroid were accelerated to 99.999...% light speed and slammed into a planet?
The backstory. In a Star Trek Enterprise novel I'm reading, a major plot point centers around a ship at warp speed colliding with a planet. Obviously, the physics of a superluminal collision are well beyond us, but I figure the next best thing would be a relativistic collision. Obviously there would be devastation on a massive scale, but...I'm having a hard time wrapping my head around just what the actual interactions would be. Would the object be going so fast that it actually passes through a lot of the target? If the object hit something like a space station in orbit first, would it still impact the plant? 
09072019, 02:23 PM  #2 
Donator

Dosen't the mass decrease as you increase velocity?

09072019, 02:48 PM  #3 
Certain Super User

Quote:
Its opposite. The mass relative to other things increases. For you, nothing changes. Things get complicated a bit, if you merge two different inertial frames into one, two moving masses colliding, especially when observed by a third inertial frame. Conservation of momentum still applies, but it takes some more math with Einstein. 
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09072019, 06:28 PM  #4 
Orbinaut

So yield striking a planet is going to be on the order of 21 megatons pet kilogram, times the relativistic gamma for the impact velocity. For a manmadesized target, there will be, as you speculated, a tendency, the higher the impact velocity gets, for the objects to pass through one another. Which isn't to say that the target or impactor will survive the collision, just that the timescale for destruction will be much longer than the collision timescale. In the nanoseconds it takes to pass through each other they'll be intact, on the millisecond timescale they'll likely be plasma. At those speeds each particle in either object is highly penetrating radiation as seen by the other.
If an impactor hit a space station on the way, the plasma ball from the impactor would hit the planet (at high gamma, the impactor might not actually have started to flash into plasma yet). 
09072019, 09:16 PM  #5 
Heat shield 'tester'

A quick consult of the ever useful Atomic Rockets yielded the following equation:
where Ker is the energy, M the mass and P is the fraction of the speed of light. Taking the mass of the smallest asteroid on this list (1.4e11kg) and plugging in that and 0.99 as P gives Ker to be 7.7e28 Joules. Consulting Atomic Rockets' Boom Table tells us that's about enough energy to boil all the oceans and melt the crust of Earth. As for what the moment to moment interaction of the actual collision would look like, I'm not sure, but a good place to start would probably be Relativistic Baseball. 
09082019, 11:06 AM  #6 
Orbinaut

I think you can pretty much demystify the problem by considering energymomentum conservation and the rest mass vs. relativistic mass.
A relativistic asteroid will have a much higher mass (and momentum) due to relativistic effects when seen from the nearstatic target than its restmass would usually be. If the relativistic mass is much higher than that of the space station, it will smash through the space station, vaporize it and continue at the planet. The vaporized parts of the asteroid will keep the high relativistic mass, but expand from the core of the asteroid only at thermal speeds  which are unlikely to be more than a few km/s even in extreme cases  so over a scale of a few 100.000 km. the collision geometry will be in essence frozen, the impactor can't 'break up' in a meaningful way. When it hits a planet and the relativistic mass is much lower than the planet mass, there will be a big crater, atmospheric devastation and possibly seismic activity, but such an impactor can be stopped. When its relativistic mass is of the order of the planet's mass or higher, it will break up the planet / alter its orbit in a significant way. The impactor will smash through and generate a linear fault zone through the planet around which immense energy is deposited and the planet will blow up around this line. For the precise details of how the destruction happens, you need to run a model of the planet's deep geology, compute the stopping power of rock layers at various densities etc  but in a nutshell, the above is I believe what you can expect. 

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