The Sudan atmospheric impact's energy release was between 1.1 and 2.1 kilotons of TNT. That's about 10

^{12}calories or 4.184 terajoules. Little Boy released between 13 and 18 kilotons of TNT equivalent energy. Tunguska, another atmospheric asteroid explosion released about 5 to 30 megatons of TNT equivalent energy. These little rocks are moving so fast that they could really do some damage...

[rant]If you think NASA's budget is too high, consider the above information carefully. We can now detect rocks just a few meters in diameter. Such small rocks release 1/10 of the energy of the atomic bomb that destroyed Hiroshima. A rock just a little more massive, faster or bigger is a pretty scary proposition. An asteroid a lot bigger or more massive is quite nasty and we need to better understand our solar system so we can better understand our place in it.

We can, with some basic assumptions, work out the density of this asteroid, knowing nothing more than the amount of energy released, the size, and the escape velocity of Earth. I assume this information is somewhere out there, but let's just do this for fun. ;)

We all know that the kinetic energy of a body is its velocity squared times its mass. An object impacting the earth from space is moving close to the earth's escape velocity.

E=mv^2.

E = 4.184x10^12 J

v=11.86 km/s = 11860 m/s

(the actual velocity was 12.8 km/s, so let's use that instead of the escape velocity of the Earth)

m = E/v^2

m = (4.184x10^12 kg m^2/s^2)/(12800m/s)^2

= 4.184x10^12 kg m^2/s^2)/(163840000 m^2/s^2)

= 25,537 kg

Assume a spherical rock 3 m in diameter. Its volume is 4/3 * Pi * r^3 = 4/3 * Pi * 1.5^3 = about 14 m^3.

The density of an object is mass divided by volume. 25537/14 =1824 kg/m^3. That's the density of a rubble pile.

This asteroid was not made of nickel/iron. Nor was it solid rock; this was rock with lots of pore space (gaps between the rocks).

Let's go back to my little rant about more massive rocks. Let's assume this rock, with the same density, was ten times larger in diameter (not too unrealistic).

Its volume would be: 14000 m^3. With a density of 1800 kg/m^3, its mass would be 25,200,000 kg. If it were moving at the same velocity of 12800 m/s, the total energy released would be:

E=mv^2

E = 25,200,000 kg * (12800 m/s)^2

E = 25,200,000 kg * (163840000 m^2/s^2)

E = 4.12 * 10^15 joules.

That's about a megaton of TNT. That's 100 times as powerful as the bomb that destroyed Hiroshima.

## 1 comment:

Wow...and people are worried about the LHC...I think this would be a more realistic concern!

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