the long answer: sure it was said a couple of times in the show. and its been a popular theory with fans for a long time. but is it true? lets find out. first, it was stated that the enterprise was capable of destroying a planet exactly twice. once was because the surface was covered in explosive gas. the second kirk was bluffing to an enemy, and scoty later explained he meant destroy all the cities on the planet. and as far as TNG goes, im told they once destabilized a planet with only seven shots. however this is a sign of poor control and a weak planet, not actually firepower. so how powerful is it actully? lets find out. the government's guideline for building fall out shelters is 10 feet per person. assuming that this holds true for the future as well (i know this is kinda a long shot but its all i have to work with seeing as im not using guide books.) thats a 4000 foot ship, since the enterprise has 400 crewmembers. a klingon battle cruiser is probably around the same size, and the most firepower we see is the enterprise destroying one of those with one shot. we never see the enterprise use more then two phasers, but they do mention "phaser banks 2 thru 6" so lets say they have 6. so thats roughly 8000 meters of damage the enterprise is capable with one shot (6 phasers, each with 1333 meters of damage). are moons surface is 37000000000 square meters. even if you assume that the klingon warbird is made out of material ten times stronger then the moons surface it would take 4265000 blasts from each of the enterprises phasers to destroy the surface of are moon, much less a planet. so the idea that the enterprise can mach firepower with the death star is preety ridiculous to say the least.
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