I remember once my friends were telling me I knew nothing about Star Trek, because a comet could not destroy the E-D with it's shields up (or down!) but if this is correct
http://en.wikipedia.org/wiki/Antimatter
and since photon torpedo's contain 1 kg of matter annihilated with a 1 kg of matter, and at least several photon torpedo's can take down and destroy the enterprise (though, we don't know how many) and say in Hale Bopp had hit us, instead of Jupiter, it would have impacted with 44 times the energy of the dino-killer asteroid. Yes, assuming they wouldn't just destroy it with their weapons. I'm talking about it actually hitting the ship with the shields up
I think something is wrong here though, according to wiki (yeah, I know it's wiki) also 1kg of anti matter is much greater than hale bopp-
http://en.wikipedia.org/wiki/Hale_Bopp#After_perihelion
But, obviously hale bopp would hit with a lot more energy than the Tsar Bomb, if the Tsar Bomb did explode with that much energy it would be much greater than the dino asteroid and we wouldn't be here right now. Not a physics expect either, just it lists Tsar as a greater yield which it can't be.
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*Claps like a seal....
One thing to remember about the Hale-Bopp impact is that it was accelerated by Jupiter's gravity. Thus it's only directly applicable if the Ent-D was inside Jupiter's atmosphere at the time.
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1.) Hale-Bopp has been estimated to have an impact energy of about 4.4*10^9 megatons TNT equivalent. That's over 77 million times the power of Tsar Bomba.
2.) 1 kg antimatter undergoing total mass-energy conversion with 1kg matter yields 1.8*10^17 Joules of energy, or about 43 megatons TNT equivalent, about 14 megatons shy of the Tsar Bomba.
But yeah, some of us(myself included) seem to have confused the two.
Anyways.... The issue here isn't the energy released on impact. It's that Hale-Bopp is estimated to be 35km in diameter. ANYTHING that big hitting the Ent-D would probably destroy it.....
My character Tsin'xing
I think your friends were hung up on the ship's Navigational Deflector, the big dish up front, which has a main function other than just being the socket that says "plug in technobabble solution here" overhead. It pushes space debris out of the path of the ship so you don't have Yuri Gagarin's toothbrush ripping a hole through the saucer before you can even break orbit.
Probably wouldn't function on that scale, though. Case in point, "Booby Trap", where they go through quite a lot of trouble not to hit a bunch of relatively slow-moving asteroids. If they're worried about those, they're not going head on with a comet. And definately not by accident. (Honestly admiral, that massive object on a fixed trajectory snuck up on us and threw itself in our path! Now can I have a new ship? I'm thinking sleek with a visible warptrail. And seatbelts.)
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Hale-Bopp's nucleus is estimated to be 70km in diameter - roughly 100 times the diameter of the Enterprise-D's saucer section. Sheer mass almost always wins.
And before you start to argue that the Enterprise is denser than an ice ball, let me remind you that any ship mostly contains air. The hull may be more dense than ice, but it's just a thin layer of tritanium and transparent aluminum meant chiefly to contain the air within. Generally whenever a metal ship meets a large ice cube, the ice cube wins. (Remember the Titanic?)
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I should mention that comets and asteroids, like the one that hit Siberia the other day, can explode on reentry, but that's because of the density of the atmosphere, gas pockets, reentry heating and all sorts of other physics, it wouldn't happen randomly in deep space.
An encounter between a starship and a comet is a completely different matter. Firstly they could just move out of its way, because comets are big, relatively slow and easy to track or predict because they follow orbital paths, they don't move randomly. Secondly, since they are slow and predictable, a ship could match the comets speed, even fly in formation with it. a collision at a relatively slow velocity wouldn't do nearly as much damage as a planetary impact. It might just get a bump. Although, as they mentioned above, if you set your ship in front of the thing and hit the brakes you'll get splattered all over the front of the comet, because again, like a planetary collision, there is a high impact velocity. However you still would not get a multi megaton explosion (except maybe from the warp core). Also, since comets are mostly ice, you could probably melt it easily with phasers, or deflect it with the main deflector before it hit. Even if god forbid you can't melt the whole thing with phasers, deflect it or fly out of the way, you could redirect it by melting the ice with a phaser beam to create a vapor jet. Scientists are already investigating this tactic against comets, an outgassing in the right spot would impart force, just like a rocket engine, and nudge it out of the way.
I'm pretty sure the Enterprise-D, if the shields were so poor (kinda like in this game! HINT HINT CRYPTIC), the crushing of the ship would destroy it faster than the fuel reserves would detonate.
Also, the warp reactor itself doesn't contain most of the antimatter, it is merely a fancy shell around deuterium and antimatter colliding through a dilithium refining crystal. The antimatter pods on the lowest decks of the ship (deck 42, exactly) would be the ones to lose electromagnetic containment and react with the normal matter that comprises most of the ship.
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