Less than one ounce of antimatter, when released from its "magnetic vacuum containment unit", was capable of ripping away half the planet's atmosphere. Tycho IV was Class-M, breathable atmosphere, and extremely careful, mathematically rigorous observation indicates a gravitational force of about one g at the surface. :-)
Less than an ounce of antimatter is on the order of 25 grams.
Now, from real science (as related in Scientific American, Spring 1999) that a kilogram of antimatter = about 20 quadrillion joules, or 20,000,000,000,000,000 joules, or 20,000 TJ.
However, to match the force required to blow off half the atmosphere from a world like Earth, you'd need more than 300,000 megatons (reference used is kinetic energy). . . that was what killed the dinosaurs, but the atmosphere was more or less intact. You'd need more than 3,000,000,000 megatons . . . that would just be enough to obscure the sun with dust for almost three years. No, you'd be needing at least 100,000,000,000 megatons, or 4.184x10^20J, or 418,400,000 TJ. That would vaporize about a tenth of Earth's ocean, were it from an impact.
The only data I could find in a quick search in direct reference to the energy requirements to remove an atmosphere is that 3x10^27J is 1/7 what would be necessary to remove Venus' atmosphere.
Until I get better data, I think that to be an acceptable figure for the energy needed to blow off half the atmosphere of Tycho IV. Of course, the 420,000,000 TJ figure is high enough for damn near any needs.
Thus, provisionally, 25 grams of Star Trek antimatter is equivalent to 3,000,000,000,000,000 TJ, or three quadrillion terajoules, according to canon. One gram is equivalent to 120 trillion terajoules.
(Do I personally believe that antimatter is that strong in Star Trek? No. However, by the rules of the ASVS newsgroup, "them's the facts".)
(Also, note that the ST:TNG Technical Manual gives a figure of 1.5 kilograms for the amount of antimatter in a torpedo, or 1500 times the above figure. Also, the E-D carried 3000 cubic meters of the stuff on a full load.)
(By the way, the most overinflated estimates I've seen of Star Destroyer shield strength place them at 100,000,000 TJ. )
(Update: Some have argued that this is mere dialog, not to be taken as factual. However, the Enterprise was rocked violently by the shockwave from the surface from high orbit.)
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