The science of the Death Star:
Instead of storing energy on the Death Star itself, or creating energy to be spontaneously released towards the target planet, you can simply create-and-carry the antimatter mass you need with you. If 2.5 trillion tons of mass needs to be converted into energy in the planet's core in order to destroy it, then bringing half that mass in antimatter, delivering it to the planet's core and simply letting it collide with the existing matter will do the job for you.
1.25 trillion tons of mass might seem like a lot, but in reality, that's only the size of a modest asteroid. Images credit: NASA / JPL / Ted Stryk except: Mathilde: NASA / JHUAPL / Ted Stryk; Steins: ESA / OSIRIS team; Eros: NASA / JHUAPL; Itokawa: ISAS / JAXA / Emily Lakdawalla; Halley: Russian Academy of Sciences / Ted Stryk; Tempel 1: NASA / JPL / UMD; Wild 2: NASA / JPL. Montage by Emily Lakdawalla of the Planetary Society. is closest in mass to what we'd need, at just a few km in size along each axis.
It's not even technically impossible; we've already created antimatter atoms in the lab, with antiproton for nuclei and positrons in place of electrons. If we could bind these anti-atoms together in a lattice -- either asor with heavier anti-atoms that spontaneously bind together -- all you'd have to do is isolate it in a vacuum and you'd be able to transport it anywhere.
The Death Star may have begun as a symbol of imperialism, military power and hubris run amok, but thanks to our understanding of physics, it's only a resourceful mad scientist away from becoming a reality. The power of science literally holds the secret, if we choose to make it so, to destroying an entire world.
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