I've always wondered about this scenario: if you had a small object (perhaps a sphere with a diameter of 1 meter), and you ran it into a planet at near-light speed, what would the physical consequences be? I realise that you'd be releasing a massive amount of energy in a very short amount of time, but I have a hard time imagining a 1 meter object would being able to destroy a planet.
Also, if you had a spacecraft going at 0.9c, and it collided with a 1mm speck of paint (assuming it's not carrying Whipple shields) - would that be bye-bye spacecraft, or not?
It is both essentially the same because of relativity - Earth runs into the small object just like your spacecraft into the paint flake.
If the impact happens at a multiple of the speed of sound of the materials of both colliding objects, the effects only scale by kinetic energy, a large slow impact causes as much damage as a fast small one.
The size of the objects doesn't really matter, A much smaller impactor as needed for the supersonic speed criteria will be instantly destroyed and vaporized on impact, just like a small part of the impacted object, but a large part of its energy travels on as shock waves inside the material of the bigger object. Only if the objects become similar in size, size starts to matter.
Lets choose 0.9c as example velocity in both cases:
That means a Lorentz factor of [math]\gamma = \frac{1}{\sqrt{1-0.9^2}} = 2.294[/math].
That means the kinetic energy at impact (complete rest of the projectile) is:
[math]K = ( \gamma - 1) \cdot mc^2 = 1.294c^2 \cdot m = 1.165 \cdot 10^{17} \cdot m[/math]
If you have a 1m ball of iron, weighting about 4700 kg, would have the kinetic energy equivalent of 130.9 Gigaton TNT - that is more than the sum of all nuclear weapons on the world.
The approximate energy released when the largest fragment of Comet Shoemaker-Levy 9 impacted Jupiter was estimated to be equal to 6 million megatons (or 6 trillion tons) of TNT - still 50 times more.
The paint flake would weight about one gramm, resulting in an energy equivalent of 27.8 kiloton TNT - about Hiroshima.
And in both cases, a fair amount of the energy will be in form of X-Ray radiation, because of the extreme forces.
Such, any such small objects would be really deadly against any spacecraft hull, the only way to prevent their damage is to slow them down or deflect them long before they reach the spacecraft hull.
