You had two choices, when analyzing the "Alderaan's demise" movie sequence: limit yourself to the basics, which is that a green beam hit the planet and it exploded and that's all. You'd estimate how much energy you'd need to scatter the mass of a planet that violently, and there, you'd have a big nice figure. From there you would say that the weapon delivered that energy into the planet. Eventually, you'd use this evidence and either scale down the battle station's reactor to guess the power generation capacity of an Imperial warship, or you'd rely on the Dodonna and Solo quotes from ANH to make a big figure:
Han Solo wrote:
The entire starfleet couldn't destroy the whole planet. It'd take
a thousand ships with more fire power than I've...
Dodonna wrote:
The battle station is heavily shielded and carries a
firepower greater than half the star fleet. It's defenses are designed
around a direct large-scale assault. A small one-man fighter should be
able to penetrate the outer defense.
Or, still strictly working from the movie, you'd pay attention to ALL facts, all aspects of the event, all noticeable behaviours. Regardless of the topic about the presence of a shied or not, you would notice, first, that there were two explosions, that the second came after the beam had totally vanished from the screen. You would point ou the odd delay, question its cause. The other side wouldn't.
You'd point out that the major explosion, the second one, the one which really cracked the planet, occurred on the other side of the planet. Which means that the propagation of debris would be done under the same force in all directions, and that the side of the planet which the Death Star faced would actually fly slower than the opposite side.
Continuing your analysis, you'd see that the explosion slowed down, and that it even partially collapsed, meaning that the debris would actually not be flying as fast as they initially did.
Last but not least, since the Special Edtion (97), you'd notice the addition of the rings, which are a daring proof the other side hates to acknowledge or even attempt to explain, because it reminds them, rather bluntly, that something weird went on there, and that they hate it. They hate it, because they know that weird equals opening the door to technobabble, and they were rather happy with their selective raw Direct Energy Transfer (DET) stance on the question, that it was just a beam of highly energetic particles, nothing more, rated at x e38 J.
RSA made lots of clever observations about this on
website, under the Death Star section.
From his website, you can step to the second phase, the one which involves using inferior canon. From there, you'd look at the ANH novelization, and notice that some details begin to stick out.
But it really gets funny when you drop one level on the canon level and end in the Expanded Universe, the source of much information, accepted by the other side. So it means that they wouldn't dismiss it.
One striking element is that you would notice the conflicting sources, and the recurring claim in several of them that the battle station had a fusion core, which literally caps how much energy the Death Star could produce.
For example, even if it were a 120 km wide ball of iron, annihilating its entire mass (and therefore that would mean that half of it was anti-iron), you'd get 6.4 e35 joules of energy.
Three orders of magnitude less than the figure attached to the destruction of the planet. Then you'd remember that we're dealing with fusion, and that the best fusion reaction is a much less powerful reaction than annihilation of matter and antimatter, by roughly more than two orders of magnitude.
They would also ignore other sources which directly compared the firepower of the superlaser array mounted on the Eclipse-class warship to the Death Star's own weapon system. They'd also describe the effect of the Eclipse Superlaser (E-SL), pegging it a specific fraction of the DS-SL and you'd realize that the effects were terribly short of what you'd obtain if you applied this fraction to the figures claimed by the other side.
You can see more about this in the following thread:
Turbolasers make my head hurt, and perhaps those
two posts of mine.
While ignoring a great many older sources, Wong, Saxton and the people they exchanged mails with kept going on with the x e38 J, which Saxton finally enabled officially by inventing the annihilation of hypermatter through the AOTC:ICS.
Before that, hypermatter was only named in the first and much older ICS, with no explanation of what it did or how it behaved.
Then came out "Death Star", the book. There's been plenty of discussions about this book, and needless to say that it completely pulverized the DET model to the four corners of the universe. It also took care of the Dodonna quote, by explaining that the regular surface weapons would be greater than any fleet which could ever exist, even one that would include Super-class warships.
It also gave an example of the firepower of the superlaser and certainly proved beyond a doubt the exotic nature of the weapon.
It also pointed out that a portion of Alderaan's mass was boosted into hyperspace. Which meant the energy figure for scattering the planet's mass was now wrong.
They tried to apply a figure to the hyperspace boosting -that while ignoring that no hyperdrive was present- by looking at an old quote they have continuously misquoted for ages, and twisted to make it mean what it would not need to mean:
as a matter of fact, Saxton and Wong never managed to come with one unique, full and proper version of the quote on their respective websites (
alt link for the whole thread, or
l33telboi's first calc I can remember about the Death Star's low yield shots, which I consider still very generous since the quote also spoke of burning cities with several of those low powered shots).
Amusingly, the quote they twisted and abused, from page 18 of the SWTJ, also said that the reactor contained what in essence was a miniature sun. From the same book which also said that the Death Star was powered by a big fusion reactor. An annoying fact, for their teratons, surely.
Older sources, which would also point out that the reactor of the DS was fusion based, would repeat the movie and say that the superlaser had a firepower greater than half the starfleet.
However, between the effects observed with Death Star, the
real energy the beam has (petatons at best), and the fact that the entire starfleet would count millions of ships of varying tonnage, on the higher end of the spectrum you'd end with an average of a couple gigatons per warship, or megatons with the lesser ranges.