In Star Wars: A New Hope, Han Solo, Chewbacca, Luke Skywalker and Obi-Wan Kenobi watch from the Millennium Falcon as an imperial fighter heads toward what Luke identifies as a small moon.
Obi-Wan then remarks, "That's no moon. It's a space station."
That space station was the Empire’s first Death Star introduced in A New Hope. Obi-Wan and company had just bounced through a debris field, the remnants of the planet Alderaan. Such an act of destruction would seem impossible to us–it seemed so to many of the movie’s characters until it happened. But perhaps not, say three students at the University of Leicester in England who last year published a study on the subject in their university’s undergraduate physics and astronomy journal.
The study’s authors start off by making some simple assumptions: The planet being fired upon doesn’t have some sort of protection, like a shield generator. And it’s about the size of Earth but solid through and through (Earth isn’t solid, but the planet’s layers would have significantly complicated the math here). They then calculate the planet’s gravitational binding energy, which is the amount of energy required to pull apart an object. Using the mass and radius of the planet, they calculate that destruction of the object would require 2.25 x 1032 joules. (One joule is equal to the amount of energy required to lift an apple one meter. 1032 joules is a lot of apples.)
The energy output of the Death Star isn’t given directly in the movie, but the space station was said to have had a “hypermatter” reactor that had the energy output of several main-sequence stars. For an example of a main-sequence star, the authors look to the Sun, which puts out 3 x 1026 joules per second, and they conclude that the Death Star could “easily afford to output due to to its tremendous power source.”
It would be a different story, though, if the planet scheduled for destruction had been more like Jupiter than Earth. The gravitational binding energy of Jupiter is 1,000 times that of the Earth-like planet in the study. “To destroy a planet like Jupiter would probably have to divert all remaining power from all essential systems and life support, which is not necessarily possible.”
Of course, that assumes that the Emperor wouldn’t be willing to sacrifice a space station full of people to wipe out his enemies. And considering that he was just fine with wiping out whole planets, I’m not sure I’d take that bet.