Borgholio wrote:Yeah that's way out of my pay grade...maybe someone who knows a bit more about relativistic physics can take over.
Atomic Rocket has a formula for this:
http://www.projectrho.com/public_html/r ... onvent.php
An object impacting at 3 km/sec delivers kinetic energy equal to its mass in TNT.
In other words there are 4,500,000 joules in one kilogram of TNT (3,0002m/s * 0.5 = 4.5e6). This means a stupid bolder traveling at 2,000 km/sec relative has about 400 kilo-Ricks of damage (i.e., each ton of rock will do the damage equivalent of 2e12 / 4.5e6 = 400 kilotons of TNT or about 20 Hiroshima bombs combined).
Ricks = (0.5 * V²) / 4.5e6
where:
V = velocity of projectile relative to target (m/s)
Ricks = kilograms of TNT worth of kinetic energy per kilogram of projectile
So a projectile moving at 200 km/sec (20,000 m/s) would have about 4,000 Ricks (4 kilo-Ricks) of damage, approximately the same as a standard one-kiloton-yield nuclear weapon. By that I mean it has the same damage per kilogram as a nuke, counting all the nuke's framework, electronics, fissionable material, and whatnot. (for the projectile to do the same damage as a standard nuke, it would need to be the same mass as a standard nuke, about 250 kilograms) A projectile moving at 3,500 km/sec would have about one mega-Rick, which is the same damage per kilogram as the ultra-compact 475-kiloton-yield W-88 nuclear warhead.
As a rule of thumb, anything with more than 100 Ricks (i.e., over 30 km/sec relative) does weapons-grade levels of damage. As an even more shaky rule of thumb, anything with more than 4,000 Ricks (i.e., over 190 km/sec relative) does nuclear warhead levels of damage. This is based on the assumption that a nuclear weapon has about a 4,000 fold increase in energy per kg released versus TNT.
And if you are thinking in terms of bombarding your enemy with asteroids, as a rule of thumb an asteroid's mass will be:
Ma = 1.47e4 * (Ra3)
where:
Ma = mass of asteroid (kg)
Ra = radius of asteroid (m)
This also means that when your impactor has enough speed and enough mass, a warhead is not needed at all.
Ladies and gentlemen, I can envision the day when the brains of brilliant men can be kept alive in the bodies of dumb people.