This will be an upper bound estimate. I am going to use "Pegasus" to determine this yield because, really, it's quick and straight-forward, and I'm going to use some loose parameters, but I should be on the proper order of magnitude here, and that's what I'm looking for.
Start with the 5km wide asteroid. Yes, I know it is not solid, but this will overestimate the yield of a photorp. That gives a volume of 6.4*10^10 m^3 of nickel-iron. Assuming iron's density of 7.874 g/cm^3, this yields 5.1*10^14 kg of material.
Now, I'm interested in the gravitational binding energy. This is the minimum energy necessary to blow this mass apart. Now, I do know that in an actual destruction, it won't be scattered to infinity, and I'm also neglecting to include the mass that may be vaporized or melted in the process. Again, I don't think that this will be a terribly large difference, but if you want to go through the time and effort to prove me wrong, go ahead. Please show your work!
This energy is 3GM^2/5r--G being the gravitational constant (6.67*10^-11 m^3/(kg*seconds^2), M being the mass in KG, and r being the radius in meters. So, quick calculation: 4.25*10^15 joules. Sounds like a lot? Well, a kiloton of TNT is 4.184*10^12 Joules. The gravitational potential energy of that asteroid? 1 megaton. And it's supposed to take 250 warheads to take it out? That's pretty weak.
Well, suppose that I melt the thing instead. Melting point is 1811 k, and the heat of fusion is 13.8kJ/mole and the heat capacity is 25.1J/mole. Iron has an atomic weight of 55.845g/mole. So we have 9.22*10^15 mole of iron. Space is pretty close to 0K, so I'm going to use a temperature difference of 1800K for this calculation. This yield 5.44*10^20 joules of energy, or about 100 gigatons of energy.
If it took 250 torpedoes to do this (the payload of the Enterprise), then we have 400 megatons of explosive yield per torpedo. That's much better. However, this is probably a gross overestimate. The asteroid would be blown apart far earlier than this--the gravitational potential energy is much lower, so it is not unreasonable to believe that huge sections would be blown off with each torpedo.
If it took 250 torpedoes to do this (the payload of the Enterprise), then we have 400 megatons of explosive yield per torpedo. That's much better. However, this is probably a gross overestimate. The asteroid would be blown apart far earlier than this--the gravitational potential energy is much lower, so it is not unreasonable to believe that huge sections would be blown off with each torpedo.
Of course, there is a third possibility: that Riker is just a moron, and it would take far less than 250 photorps to destroy it. It wouldn't take 250 modern nukes to blow that thing to dust.
I'll let you all draw your own conclusions.
(Edited because I erred greatly--I used the heat of vaporization instead of the heat of fusion! That's a huge energy difference.)
(Edited because I erred greatly--I used the heat of vaporization instead of the heat of fusion! That's a huge energy difference.)
No comments:
Post a Comment