As iconic as the spherical death-bringer is, the inner tinkerings of the Death Star still remain a great mystery. For example, if the Death Star suddenly materialized in the Solar System, how much energy would the vessel require to pulverize the Earth into bloody gravel?
A group of physics students at the University of Leicester took it upon themselves to divine the Death Star's energy requirements (using many an admittedly radical assumption). From the paper titled "That's No Moon":
This planet is going to be modelled after earth with the exception that it is a solid planet. It is then possible to use the gravitational binding energy of the target planet to estimate the amount of energy required to be supplied to the Death Star's laser beam in order to destroy it [...] The energy required to destroy the planet in question is 2.25 ⨉ 10^32 J. However, the destruction of large planets such as Jupiter can require much larger energy demands [...] we can estimate this energy to be 2 ⨉ 10^36 J [...]
Since the Death Star outputs energy equal to several main-sequence stars, even if the actual composition of Earth is used in equation, the value yielded is only a few orders of magnitudes larger and the Death Star can still easily afford to output that energy due to its tremendous power source. However as mentioned above Jupiter requires much greater energy demands which would put considerable strain on the Death Star. To destroy a planet like Jupiter it would probably have to divert all remaining power from all essential systems and life support, which is not necessarily possible.
I wouldn't put it above the evil Empire to cut off the oxygen just to eke out that last joule of murder. When you're spending $15.6 septillion, a Luxembourg worth of Stormtroopers is but a drop in the bucket.