I'm watching the season two episode of TOS "Patterns of Force" where a nuclear missile is on an intercept course with the Enterprise, but is destroyed by the ship's weapons. This got me thinking as to whether or not the Enterprise-D would be able to take a nuclear missile. In the re-imagined Battlestar Galactica, the Cylons and humans basically throw nuclear missiles at each other constantly and the ships remain relatively unscathed. Would this be the case with the Enterprise-D?
They would survive with very little damage. Especially if the sheilds were up, but they could probably take it even without that.
Though I'm having trouble finding the numbers on how much force ship phasers deliver, a single Photon Torpedo delivers an explosive force of 690 Gigatons.
By comparison, the Tsar Bomba only manages 50 Megatons (Or .05 Gigatons). With shields up, the nuclear device would probably not even shake the ship.
With shields down, damage would be mitigated by the structural integrity field, which is an always-on field around the ship designed to protect it from background radiation in space and would definitely protect it from nuclear radiation. Given that it regulary protects the ship from warp-factor stress as well, it's unlikely that the nuclear blast would even break the field.
Finally, if any of the nuclear blast DID cause some damage to the hull, there are emergency force fields that can be activated all throughout the inside of the ship that would offer the same protection as the structural integrity field, shielding the rest of the ship from any harmful effects caused by the breach.
In short, a nuclear missile isn't even in the same scale category of destructive force as a Photon Torpedo. It would be like trying to blow open a tank with a firecracker.
In "Contagion" we saw Enterprise survive the detonation of its sister ship Yamato at close range, the latter having lost antimatter containment. A gram of antimatter reacting with a gram of matter produces the energy equivalent of 2-3 Hiroshima style bombs. Enterprise (and presumably Yamato) carried much more antimatter than that, given that the warp core produces 12.75 billion gigawatts (Data, "True Q"), which is around 700,000 Hiroshima bombs per hour.
Also in the original series episode "Balance of Terror", the Romulan commander dumped a nuclear warhead in amongst the garbage he scattered to confuse Enterprise's sensors. The device detonated less than a hundred meters away but Enterprise survived. It is unlikely that Enterprise D was a less sturdy design.
Outside of atmosphere, a nuclear bomb would cause negligible damage other than output radiation.
If a nuclear weapon is exploded in a vacuum-i. e., in space-the complexion of weapon effects changes drastically:
First, in the absence of an atmosphere, blast disappears completely.
Second, thermal radiation, as usually defined, also disappears. There is no longer any air for the blast wave to heat and much higher frequency radiation is emitted from the weapon itself.
THe US government has actually tested nuclear bombs in space before. The most notable test case being labeled Starfish Prime has a write-up on Wikipedia. You can even watch the video footage on Youtube.
[Romulan ship] (They are taking damage) DECIUS: How, Commander. How? COMMANDER: He's a sorcerer, that one. He reads the thoughts in my brain. Our fuel supply all but gone and he stays out of reach. DECIUS: We are beaten. Can it be true? The Praetor's finest and proudest flagship beaten. COMMANDER: Perhaps we can yet save your Praetor's pride for him. More debris into the tubes. Decius, do we have the old-style nuclear warheads aboard? DECIUS: Yes Commander, but only for self-destruction. COMMANDER: Place one with the debris. Proximity fuse. DECIUS: Yes, Commander. At once. [Bridge] SULU: More wreckage, sir, scattering across our path. KIRK: Cease fire. SPOCK: Debris on our scanners. KIRK: Analysis, quickly. SPOCK: Same type as before, sir, except, one metal-cased object! KIRK: Helm, hard over. Phasers, fire point-blank. STILES: Phasers, fire! (There's a big explosion, everyone gets thrown across the Bridge. Enterprise hangs crooked and motionless in space.) [Romulan ship] DECIUS: Glorious. Glorious. COMMANDER: Now we go home. DECIUS: They're at our mercy. Commander, I remind you of your duty. [Bridge] KIRK: Captain to Sickbay. MCCOY [OC]: McCoy here. KIRK: Casualties? MCCOY [OC]: Twenty two so far. Mainly radiation burns, mostly from the ship's outer areas. Could have been much, much worse, Captain. KIRK: Thank you, Doctor. (the lights come back on) Report, Mister Spock? SPOCK: Nuclear device of some kind, sir. Our phasers detonated it less than one hundred metres away. KIRK: Ship damage? SPOCK: Mainly overloads and circuit burnouts.
Given that the Enterprise D's shields extend quite a ways out from the ship, and given 80-ish years of technical advances, it seems likely the Enterprise D would be able to survive at least as long as her shields were working well.
Not exactly the Enterprise-D but in the Voyager's episode 6x12, "Blink of an Eye", Voyager sustains multiple hits from anti-matter missiles; with its shield slowly going down. Knowing that an atomic bomb like the one used on Hiroshima convert slightly less than one gram of matter into energy; it's safe to say that an anti-matter missiles can be at least one thousand times greater than that by carrying half a kilogram of anti-matter, a power that would put it on par with a thermonuclear bomb, and quite probably that they can be made even bigger. (In fact, it's a near certainty that they are bigger. The only question is by how much.)
While Voyager is more advanced than Enterprise-D, there is not much of a difference in term of power; so we can safely say that Enterprise-D could easily sustain many hits from thermonuclear bombs when its shield are up. However, when they are down, the hull by itself is much more vulnerable and a direct hit from a single thermonuclear bomb is probably capable of destroying the ship or at least, severely damage it.
As more of a Nerd than a Geek my take is a little different on this.
Nuclear weapons release a great deal of kinetic energy of it's constituent materials that cause localized heating and, in an atmosphere, creates an overpressure condition which does a tremendous amount of damage. In space, due to a lack of transmission medium, the energy is dissipated as radiation as a square of the distance, and radiation is a very inefficient method of energy transfer.
Increasing the yield of any destructive device is of limited value since it's effectiveness in a vacuum is the square root of the energy rise. Increasing the MASS of the weapon will increase the destructive force proportionally.
Since the amount of kinetic energy transmission is given as 1/2MV squared, the higher the velocity an object is given, the amount of raw destructive power goes up exponentially.
You can yell at me now if you already know where this is going, otherwise... The Battlestars a good, and I mean really good at exploiting basic physics to create death and mayhem. Assuming the shells a battlestar fires from it's main batteries are roughly the size and mass of similar ordinance from a Iowa class battleship, the mass would be about 3000 pounds. From observation of the ship in battle, it takes approximately 3 seconds to cross a ten mile separation between the battlestar and a base ship. This places ordinance speed in excess of 15,000 mph, or about 10,000 feet/sec (four times faster than chemical propellants are capable of and therefore adequate proof they are using rail guns)
When we do a "plug-and-chug" the amount of energy deposited directly into the mass of an enemy ship is 2,25 E11 Joules or 225 GJ. The fact that they work by carrying their own mass and break things by shredding them with shrapnel is brutally effective in space based combat. But then, that's why they put the word "Battle" in there I guess.
Now comes the heart breaking part.
In the episode of DS9 a Nebula class starship is destroyed by a suicide run from a Jem'hadar scout ship.
If we make the scout ship conservatively massive, say 10,000 tons or 20,000,000 pounds. We can see the scout is definitely moving less than 200 mph. or 300 feet/sec. This equates to 4.5 E8 Joules or 450 MJ. Clearly, Federation starships are not designed to weather kinetic energy insults. And this is only one of several times the Enterprise D or one like it has been disabled and/or destroyed from a low speed impact with a solid object, shields at full power or otherwise.
And a battlestar has 30 main batteries with a 6 second cycle rate. Worst case is a battlestar can only bring 50% of it's guns to bear, that's still a rate of 300, one and a half ton messengers of death every minute! And this makes sense from their standpoint. It takes a great deal of energy to maintain weapons that rely on mass and move it around exploring the galaxy. And first an foremost, the Enterprise is a ship of exploration. Capable of fulfilling a number of roles. Reliance on light weight weapons (directed energy) and armor (shields) are preferred. But she is not capable of effectively fighting a ship that was built as a no-compromise war vessel.
The Enterprise couldn't survive a glancing blow from a Reliant class vessel, while the Galactica used itself as a battering ram... A G** D*** BATTERING RAM!
The fact that a battlestar is passively protected (no shield failure, just another hole in a compartment) with feet of tungsten and depleted uranium armor and can absorb this incredible amount of energy should give any starship captain a reason to pause and consider "Do I really want to do this?".
So to wrap this up. Tactics, drive, maneuverability and such no withstanding. Just on the basis of weapons and armor, a battlestar can fire weapons that deliver 500 times what is necessary to completely destroy a Galaxy or Nebula class starship at a rate of five times every second!
Based on this as well as what I believe are superior tactics, drive, motivation and the ability to literally appear out of nowhere without warning and then disappear to anywhere in the universe (yes universe, not galaxy or star system), it is my opinion that in this conflict, the Enterprise would not survive the opening salvo.
I'll even go so far as to speculate that even if star fleet sent all their best ships en-mass, the aftermath would look like what happened a Wolf 249.
I hadn't seen much of TOS, but if I were to extrapolate from the dialogue, it is probable the Romulans used a 23rd century enhanced nuclear bomb. Even Spock was unable to exactly state what kind, so it stands to reason it was a Romulan equivalent nuclear bomb with probably far more radiation and probably destructive capability that 23rd century technology would allow.
We've seen that the Enterprise-A was able to withstand several direct photon torpedo hits on their hull and from inside the ship. Even Voyager showcased Chroniton torpedoes from the Krenim that bypassed the shields and detonated on the hull... one such torpedo got lodged inside the hull without detonating beforehand. Once it did detonate inside the ship, it didn't do much damage - though it could have just as well been a dud, or most of its explosive potential was never activated and it resulted in a much smaller explosion.
This suggests that for example weapons in the 24th century could end up being 690 gigatons in explosive capacity (at a minimum - whereas in DS9 we've had an example of a planetary bombardment going into teraton range from a single disruptor blast - which isn't that big of a problem), however, starships are usually designed from materials that are not only able to withstand high FTL/Warp velocities, but also direct torpedo attacks. It also suggest the interior of starships is made of similar materials that can minimize damage from such explosions.
Of course, if you detonated a torpedo near a power matrix or a Warp core, all bets are off.
So, different detonation points inside a starship could produce more or less damage.
Voyager managed to beam a photon torpedo inside a Brunali ship which was swallowed by the Borg sphere. After the torpedo detonate, the sphere sustained moderate damage (enough to prevent immediate pursuit so Voyager could get away). Another example however involved Voyager beaming a photon torpedo directly inside an attacking Borg 'probe' ship (which seemed to be of similar size like Voyager). In this instance, the torpedo detonated near the power matrix, resulting it the probe being completely destroyed (likely due to a chain reaction).
So, depending on the ship and materials its being constructed (plus where the weapons hit), they should be able to sustain at least a few direct hits, and more indirect ones.