The use of the Trilithium torpedo on the Amagosa sun by Doctor Tolian Soran represents one of the most awesome acts of destruction in known Trek history. There is little solid evidence concerning the operation of the trilithium torpedo, but some facts are known. Lieutenant Commander Worf reported that trilithium could cause all nuclear fusion to break down in a star; when the Amagosa star was destroyed, the following sequence of events occured :
1) The star flared up to many times its normal brightness. This flare-up peaked rapidly then faded out over approximately seven seconds.
2) The star began to darken and shrink in size considerably over the next several minutes. We are explicitly told that all nuclear fusion is breaking down by this point.
3) A shockwave was produced which proceeded outwards. This shockwave covered a distance equal to 60% of the diameter of the star in a period of 5 seconds - roughly equal to 50% the speed of light.
It was later revealed that the mass of the Amagosa star had altered sufficiently that it significantly affected the gravitational fields within the region. When the Veridian star was later destroyed, the shockwave produced had sufficient energy to shatter a habitable planet completely over a period of some seven seconds.
For the purposes of calculation, I will make the following assumptions :
1) The Amagosa and Veridian stars both have approximately the same mass as Sol - 2 x 1030
2) The Veridian detonation was identical to the Amargosa detonation.
3) The planet Veridian III is the same size and distance from its sun as Earth.
When the shockwave produced by the destruction of the Veridian star reached Veridian III, the planet was completely destroyed over a period of approximately seven seconds. The rubble produced was moving at a rate approximately equal to one planetary diameter every five seconds - equating to 2,500,000 metres per second. The energy required to do this is given by :
Planet destruction energy = 0.5 x mass of planet x rubble velocity2
= 0.5 x 6 x 1024 x 2,500,0002
= 1.875 x 1037 Joules.
But this is only that portion of the total energy which was intercepted by the planet - the entire energy would be evenly distributed over a spherical shell with a radius equal to the planets orbital distance. To calculate the entire energy of the shockwave we must determine what fraction of the wave was intercepted by the planet. This is given by :
Fraction = (area of a circle with radius of planet) / (area of a spherical shell with radius of planets orbit around sun)
= (pi x (radius of planet)2) / (4 x pi x 1 AU2)
= (1.247 x 1014) / (2.828 x 1023)
= 4.409 x 10-10
So the total energy of the shockwave would be given by :
Total energy output = Energy to destroy planet / Fraction
= 1.875 x 1037 / 4.409 x 10-10
= 4.25 x 1046 Joules
This energy was delivered over a period of some 7 seconds, equating to a power output of P = 6.075 x 1045 Watts
This represents the minimum energy output of the Amagosa and Veridian detonations - in fact it is perfectly possible that the energy release was considerably above this level, if the planet absorbed less than 100% of the energy incident upon it.
To produce an energy release of this magnitude some 4.73 x 1029 kg of matter must be converted completely to energy with 100% efficiency. This represents some 23.6% of the total mass of the star involved.
Shortly after the Amagosa detonation, Captain Picard and Lieutenant Commander Data spend some time analysing Dr. Sorans motives in the Stellar Cartography imaging room. During this analysis, Data explicitly states that the stars destruction has caused a significant change in the gravitational fields in the area. This fits in ideally with the loss of a significant percentage of the mass of the star, and is strong confirmation of the above calculations.
Some have suggested that the gravitational changes are due to a large amount of mass being blown off the surface of the star - that in fact this material comprised the shockwave which destroyed the planet. But this simply cannot be so - in the Viridian detonation Dr. Soran planned to alter the course of the Nexus so that it would take him off the planet. But the centre of gravity of a spherical shell lies at the centre point, so the course of the Nexus would only be significantly altered once it had passed through the shockwave... which would mean that the planet would have to be inside the shockwave... which would mean that Soran would be dead before the Nexus reached him. In order to alter the combined gravity field of the shockwave-star before it reached, the mass must have been significantly reduced in the initial implosion/explosion.
So far as I know, the use of the trilithium weapon against the Amargosa system is single largest destructive energy release in all of Star Trek history - possibly in all of science fiction history. Since the Trilithium warhead can be contained within what appeared - in the case of the Amagosa detonation - to be a standard Starfleet torpedo/probe casing, then it could presumably be used by any existing Starfleet ship. This would, for example, allow a Galaxy class starship to destroy some 250 solar systems without any form of replenishment. Indeed, if the ship where to stock its cargo bays with extra weapons then several thousand could easily be accomodated.