Inspired by this video: https://www.youtube.com/watch?v=K6-q2edmiGk
Assuming destruction absolute enough that no two molecules will gravitationally recombine ever seems like an extreme upper bound on the problem. The biggest thing immediately evident in Alderaan’s debris field was the death star itself when the Milenium Falcon showed up, but it looked to me more like the majority of the planet’s mass formed a pulverized debris cloud only a few planet-diameters across when we did witness one of these explosions. Leaving a planetoid/dwarf planet and an asteroid field in the area (much of which would most likely be scattered further through the influence of other nearby planets without needing to provide the energy to keep them apart up front) would be perfectly sufficient to count as ‘completely destroyed’ imho. And if you did knock it down into nothing bigger than asteroid-sized chunks, have having the planet slowly fall back into itself after having gone boom still doesn’t seem like it would contradict any of the lore – the fact Chernobyl’s reactor cover fell back down doesn’t change our general understanding that Reactor 4 was ‘completely’ destroyed by the explosion. (Plus, Alderaan was a city planet – theorizing extremely large quantities of fissionable material, kyber crystals, and/or any other explosive sci-fi fuel you can dream up seems reasonable – we don’t have to assume that was the average result of using this thing.)
If I ever get around to re-learning calculus, I’ll give it a shot with these assumptions 😀 I’m pretty sure it still comes out to ‘death star has serious problems’ but I’m curious about the % energy difference required.
I’m willing to posit a death star that’s the size of earth’s moon (which is pretty damn big for a moon of a rocky planet, but it’s the moon the writers would be most familiar with, so hey) and a surface gravity of 1.5 earth g (which is ridiculously heavy to be living on but I think within the bounds of what could be adapted to, especially if the living/recreation areas were at lower levels of the station. Artificial gravity could be used to counter higher gs rather than induce 1g like on smaller ships, but there’s also a reasonable construction argument. Even using super-dense materials for the majority of the construction, you’ve got a lot of void spaces in there. I feel like 1.5 g @ moon size is a decent enough guess to plug into a Fermi approximation, though obviously you could math out something more ‘accurate’ from more primitive assumptions. So given that and the results of the above energy calculation, it should be possible to work out the momentum transfer again.