Re: Space Rock 'on collision Course
Posted by Southern Man on Jul 26, 2002 at 08:32
Re: Space Rock 'on collision Course (Wozza)
“Sorry, wasn't there something about every action has an equal & opposite reaction. Therefore the explosion of the nuclear warhead wouldn't need something to 'push' on surely??”
I plead guilt to oversimplifying. The reason an explosion needs something to push on is that without a backing the explosion “reflects” off a heavy surface without imparting very much energy. Both energy and momentum are conserved in any collision. When a nuclear bomb explodes it sends atoms of the bomb in all directions. Assume it is next to a flat surface. Half the atoms go outward with no impact or energy transfer to the surface. The other half impact once and then go outward to follow the first half.
The half that impact the surface and transfer some energy to that surface as they bounce off and go back the other direction to follow the first half are the only “action and reaction” that we are going to get. Momentum is conserved so the mass of the atom times its change in velocity equals the mass of the surface times its change in velocity. The kinetic energy transferred is also conserved in an elastic collision. So assuming a reference plane of the surface (initial velocity of surface is 0), MaVa=MsVs and 1/2MaVa^2=1/2MsVs^2+1/2MaVb^2 where Ma is the mass and Va is the initial velocity of the atom, Vs is the change in velocity of the surface and Vb is the final velocity of the atom. Lots of math follows but the result is that Vs is approximately proportional to Ma/Ms. In other words, the atom bounces off the immovable object because it is so light. Yes, there are lots of atoms but the total energy transfer is still trivial.
Now let’s back up the explosion with air. We can start in the first picosecond about the same. Half the atoms going one way and half the other. But the half that are going outward and were completely lost to the system in the first situation now hit atoms of air and bounce back. They are now traveling toward the surface and can contribute some energy to that surface. Now let’s look at those that hit the surface the first time. Again the energy transfer is minimal but they also have a chance of hitting more than once when they reflect from the air. The math for all these reactions is far too complicated to do here in a message but we can step back from the trees and look at the forest. In an atmosphere the atoms of the bomb will ricochet back and forth between the surface and the air and eventually come to rest. The result was that the surface was moved one direction and a mass of air moved in the other. The mass of air is far larger than the mass of all the atoms of in the bomb. We could go back to the above equations and see that far more energy is transferred to the surface because of this larger mass of air moving away. So you get far more energy transfer if you have something to push against. In space there is nothing to push against.
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