I was wondering how small of an object, if accelerated to 90% the speed of light could destroy life on earth.
The size of a car?
An apple?
A bb?
Also, assume they are all made of solid iron.
Start with a baseball and work up - the results probably are not much different - maybe a bit more mass, slightly bigger boom, but at higher altitude.
Oh, and the kinetic energy scales directly with mass. At some point, the atmosphere cannot retain the blast and much of the resulting blast radiation will blow off into space.
This link suggests you need a 5,000,000,000,000-tonne rock travelling at 90% c to destroy the earth (as in completely shatter and break it up), but you might blow off a good proportion of the atmosphere with somewhat less. Still bigger than a car, though.
Short answer: At 0.99c it’s an extinction event, at least with a rock that size. An apple-size hunk of iron at 0.9c might not be quite so dramatic but it wouldn’t be far off.
I hadn’t seen that one. But I will note that the energetic difference between an object travelling at .9c and .99c is rather large due to both the v[sup]2[/sup] relationship between velocity and kinetic energy and the relativistic effects of getting something to that speed.
And that’s why we won’t let photons have any mass.
Or take confession.
Note that the v[sup]2[/sup] relationship is only a low-v approximation which isn’t good for v large compared to c, as is the case here. The kinetic energy of a relativistic meteor scales with 1/sqrt(1-(v/c)^2) which is much more dramatic.
Using Wolfram Alpha and wiki:
An iron ball 7cm in diameter (which is the size of the apple on my desk) has a mass of 1.41kg (3.12lb)
The relativistic kinetic energy of this ball moving at 0.9c is 1.64x10[sup]17[/sup] Joules
1.64x10[sup]17[/sup]J equals 39.2 Megatons of TNT. The Soviet Tsar Bomba (largest nuclear explosion ever detonated) was 57 Mt, so it would be smaller than that one.
If we instead have an object with the same mass as a car (here defined as 1410kg for obvious reasons :)), the resulting energy would be 1000 times as large as well, so 1.64x10[sup]20[/sup]J
The Chicxulub impact blamed for wiping out the dinosaurs were 4.2x10[sup]23[/sup]J, or 2500 times as powerful as the latter impact, and while most life had a bad day, our ancestors survived.
I would ask how such an impact would compare to that of an asteroid the size of an orange, but of course such a comparison cannot be made.
Which is why Lucifer never did. Please say you get it.
Yeah, but has that been confirmed?
I see what you did there.
Awww… The poor BABIES! Can’t we at least let a few of them go to church? 
Also, at that speed, it doesn’t matter what the object is made of. Iron? Diamond?
It could be powdered sugar, and it would make very, very little difference.
Are you kidding? They’re always trying to sneak in through the stained glass windows.
Lucifer always was a polarized character, but discrete in his own way.
Hitting a planet with a single, massive relativistic lump is not the most efficient way of sterilising the Earth. A single explosion, even a very powerful one, could easily waste most of its effect by lifting local atmosphere rapidly into space. Sure, it would be nasty for lifeforms near the impact, but there is a chance that some life could survive hundreds, or thousands of kilometers away from the centre of the blast.
Much more efficient to split your massive impactor up into hundreds of little impactors, and spread them out evenly so that every square kilometer gets an even share of the blast.
This method is described in some detail in The Killing Star, quoted here.
http://www.projectrho.com/public_html/rocket/spacegunexotic.php#id--Relativistic_Weapons--The_Killing_Star
Plus, due to Coriolis effects, any atmospheric effects will have a hard time crossing the equator.
Is it even possible for a solid object with a substantive mass to be imparted that degree of acceleration without disintegrating? This assumes the .9c would necessarily have to be imparted by a one time kinetic explosion or push of some kind not a continuous acceleration over time like a spacecraft.