Well, it turns out we were a little bit mistaken, and the mistake was chiefly mine.
It turns out that 1/8 c
is relativistic speeds, and therefore we need to use different equations.
So, thanks to Wolfram Alpha I got the following results:
0.195 g of mass traveling at 0.125 C has 138.55 Giga-Joules of energy.
link1 gram of TNT has 4.184 kilo-Joules of energy.
linkNow we get to play with decimal places!
1 kilo-gram (1000 grams) of TNT is therefore 4.184 mega-Joules.
1000 kg (1 ton) of TNT is therefore 4.184 Giga-Joules. (Which I could have found it if i had read the
Wikipedia article.)
So, 138.55 GJ is roughly equal to 33 tons of TNT.
linkNow, I'm feeling just a bit too lazy to find the yield of the smallest atomic bomb ever used, but here's my reasoning:
The first atomic bombs were much simpler, because everything was simpler "back in the day". So let's have a look at the first atomic bombs.
The Trinity bomb test, the first ever detonation of an atomic device yielded about 18-20 kilo-tons of TNT. That's around 80 TJ (Terra-Joules).
Little Boy, the bomb dropped on Hiroshima, yielded 16 kilo-tons (67 TJ).
So, even though I made an initial mistake (and you all followed me! For shame! (Except for CryptoMe)), the result is the same.
A collision at 1/8 C with a pea-sized rock massing 1/5 g will yield around 138 GJ of energy, equivalent to 33 tons of TNT. Deadly, but still three orders of magnitude less than an atomic bomb.
Thanks go to my father, always ready to find a mistake in my calculations
, for pointing this out.