|Saturn's moon Mimas looks eerily like the Death Star.|
Luke mistakes the Death Star for a small moon, which suggests the mass of the Death Star is about that of a moon. I'll assume the Death Star's mass is equivalent to that of Saturn's moon Mimas (M=3.7×1019 kg) since it kinda looks like the Death Star. As we calculated before, the total energy required to blow up a planet is E = 2.1×1032 J. According to relativity, the amount of energy stored in a piece of matter with mass m is given by the equation
E = mc2,
where c = 3×108 m/s is the speed of light. If we solve for the percentage of mass lost with each laser shot, we find
fraction of mass = m / M = E / (M c2)
= ( 2.1×1032 J ) / [(3.7×1019 kg) (3×108 m/s)2]
It's a very small percentage. At this rate, the Death Star could blow up over 15,000 planets before it ran out of mass. This of course assumes that the energy is directly transferred to the planet without loss.