How much Uranium
would it take to blow up the earth?

 T
his subject came up on Tom VanFlandern's forum so I thought I'd make a rough calculation (in the spirit of Christmas ;o) The basic idea is ... If a large concentration of uranium existed at the earth's core ... and it went critical ... how much would it take to accelerate 1/2 of the earth's mass to escape velocity (25,000 miles per hour)? I would count this as a reasonable example of a planet blowing up and it would serve as a ballpark estimate for planets of other types and masses.

The Earth's Mass

mass of Earth = 5.9742 × 1024 kilograms (pasted from Google)
That took all of 3 seconds. I just entered "mass of the earth" and the first entry was the number. Way to go Google!.

So, half of that is 3 x 1024 kilograms

To accelerate that much mass to 25,000 miles per hour. Google Search (kilograms per mile) ... 1 mile = 1.609344 kilometers x 25,000 = 40,000 kilometers per hour ... x 1000 (to get meters) / 3600 (to get per second) = 11,111 meters per second.

So, energy equals one half times mass times velocity squared and the "second squared" remains just "one".

1/2 x [3 x 1024 x 11,1112 ] / [12] = 1.8 x 1032 Joules

... to blow up the planet.

(a joule is related to the fundamental units in that a joule is 1 kg m2 /s2) - from Google search

One kilogram (about 2.2 pounds) of matter converted to energy is equivalent to ~ 9 x 1016 joules

U-235 + n ==> U-236
U-236 ===> fission fragments + 2 to 4 neutrons + 200 MeV energy (approx.)

from Google - 1 megaelectron volt = 1.60217646 × 10-13 Joules

So, one uranium atom releases 200 x 1.60217646 × 10-13 =
~3x10-11 Joules

Now then, 3x10-11 Joules goes into 1.8 x 1032 Joules =
~ 6 x 1042 Uranium atoms blowing up all at once to blow up the planet.

1 amu ˜ 1.6605387 × 10-27 kilograms times U-235 = ~3.90 x 10-25 Kg per U-235 atom

3.90 x 10-25 Kg x 6 x 1042 =
~2.3 x 1018 Kilograms of U-235 to blow the planet

6 x 1024 / 2.3 x 1018 =

About 1 part in 2,600,000 of the Earth's mass would have to be uranium at the Earth's core (at critical mass density) to blow the planet. This amounts to a ball of uranium about

hmmmm ...

Uranium is at 18,700 kilograms per cubic meter ... so ...

2.3 x 1018 divided by 1.87 x 104 =

About 1.23 x 1014 cubic meters, which translates into a ball about ...

4/3 pi r3 = 1.23 x 1014 or ...
r = [1.23 x 1014 x 3/4 x 3.14159 ]-3 which is ... of course ...

6.6 x 104 meters ... or ...

134 kilometers in diameter ... or ...

84 miles in diameter

This is a lot of Uranium

How can it be kept from exploding while it is forming? Simple ...

It must not reach critical mass, that's all. Then when the total is there in place ... after having drifted into position for millions of years ... some part of it goes to critical mass and that part blows up. Of course the rest will blow up as well in a second or two because it takes the critical density to start ... not continue. A big ball at near critical density will not blow up but it will all blow ... if ... some part of it starts the whole thing going, i.e. the non-critical density portion will not "damp out" the continuing explosion all through the entire 84 mile diameter ball.

So, I guess the Exploded Planet Hypothesis could be viable by uranium fission (unless I screwed up the math ;o). I can't think of any other viable candidate.