An object with mass striking another such object at 3 km/sec ("kips") delivers kinetic energy roughly 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 = 4.5 x 10^6). 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 2 x 10^2 / 4.5 x 10^6 = 400 kilotons of TNT or about 20 Hiroshima bombs combined).
Ricks = (0.5 * V^2) / 4.5 x 10^6
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 general rule, anything with more than 100 Ricks
(i.e., over 30 km/sec relative) does weapons-grade levels of damage. As an even more shaky general rule, 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 general rule an asteroid's mass will be:
Ma = 1.47 x 10^4 * (Ra^3)
where:
- Ma = mass of asteroid (kg)
- Ra = radius of asteroid (m)