The Science and Stupidity of Kryptonite

So a few weeks ago I saw the most recent Superman movie again.  Something has been always bothering me about Superman and Kryptonite, and earlier today while sitting in traffic on the Bay Bridge it suddenly occurred to me what it was.  For this explanation we will have to turn to true friend of all nerds, science.

(Superman image courtesy of the Superman t shirt category)

Here’s the deal.  I will buy that Jor-el was a super scientist who could make a space ship capable to traveling to earth in a matter of a few hours (any more than that might have resulted in a bad case of SIDS).  However, if the planet Krypton blew itself up, how long would it really have taken for chunks of the planet to arrive on Earth?  If we assume Krypton was close to us (and not on the other side of the galaxy) then at best it’s 4.5 light years minimum distance.  Now, an explosion that propels an object is essentially a bullet.  The fastest rifle bullets travel at about 4,000 feet per second.  If we boost that up (assuming Krypton REALLY blew up) to about 5,280 feet per second, that’s about a mile a second (I never said I was going to make this science part hard on me).

So a mile a second (which is extremely generous) will essentially mean that it would take a chunk of Krypton 5,865,696,000,000 seconds to cover one light year.  A little basic arithmetic tells me that it would take a meteorite of Kryptonite 837,000 years to reach Earth.  Why, then, does the local museum have a chunk of it lying around for Lex Luthor to steal?  For that matter pieces of it are falling out of the sky all the time in the comics.  I’m sure some kind of argument could be made for a relativistic shift in time for Superman’s ship, but that would just make things worse.  If his ship were slowing down it time it could only be because he were traveling at close to the speed of light, which would still have had him arriving here in a few short years.

Now let’s consider the geometry.  I did some research and discovered that in order for a sizable meteor to arrive on the planet earth it has start out about basketball sized.  In order to make things easier for me, I am going to assume a 1 foot ball.  Now, assume Krypton were broken up into nothing but 1 foot squares (and none of it were broken up into marble sized of just vaporised outright).  If Krypton were about earth sized it would have a radius of 3,963 miles, or 209,246,440 feet.  Using the volume of a sphere equation, V=4/3(pi)(r)cubed, we get 3.86762×10(25)th power.  That’s a lot of basketballs.  However, if we take a volume of space with a radius of 4.5 light years, we get an area of space encompasing 8.4537×10(38)th power.  That’s one basketball of Kryptonite per 2.18578×10(13)th power.  At our largest point we are 94.5 million miles from the sun.  That means we occupy a disk of space that is 4.70614×10(12)th power.  In other words, in our little volume or space there should be exactly on chunk of Krypton big enough to land on Earth and, assuming it doesn’t get caught by Saturn or any of the other outer planets, there is only about a 1/10 chance of it landing on us.

Now that’s not entirely fair, as everyone knows that the basketballs would not be distributed evenly throughout the universe.  They would keep traveling.  So instead of volume, lets consider the explosion of Krypton the instigator of an expanding sphere of planetary debris.  I think the best way to think of this would be as 1 foot chunks of Kryptons surface expanding outwards.  Now the area of a sphere is determined by A-4(pi)r(squared).  Again assuming Krypton about the same as planet Earth means the surface is comprised of at most 5.50206×10(15)th power basketballs.  If they all blew up strait ahead (and assuming the debris underneath it more or less followed in a strait line from the center of the explosion) by the time the debris reach earth the area of the sphere would be 4.32363×10(26)th power square miles.  That’s one basketball per 7.8219×10(10)th power.  Assuming the eliptical plane of the planet rotation is exactly perpendicular to the expanding debris, our planet occupies a ring of about 5.9565×10(8)th power.  That’s even worse than going by volume.  And again, this is all based just on the area of space we are likely to occupy, not the fact that our planet is actually pretty tiny on an astronomical scale.

So you can see how dumb it is that Kryptonite be just lying around for any petty criminal or evil scientific super genius to find and fashion into a weapon.  Sorry if I spoiled the magic for you, but I have always been more of a Batman guy myself.

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