## Friday, April 9, 2010

### Death Star Physics

There’s a lot of Star Wars physics one could quibble with.  Take the Death Star.  How, exactly, is a giant laser supposed to blow up a planet?  How much energy would it take to blow up Alderaan?

To calculate how much energy you’d need to blow up Alderaan, you first need to know what’s holding it together.  Unless the Star Wars universe is vastly different from our own, Alderaan is likely being held together by gravitational forces, i.e. all the different chunks of matter that make up the planet are attracted to each other by Newton’s law of gravity.  In order to blow it up, you need to impart at least enough energy to overcome this attraction.  Fortunately, physics has a well-known solution for this problem.  Most introductory courses on electricity and magnetism teach you to calculate the energy required to assemble a uniformly charged sphere with the result1

E = (3 / 5) k Q2 / r,

where E is the energy, k is a constant, Q is the total charge on the sphere, and r is the radius of the sphere.  This can be derived from Coulomb’s law for the force acting on charged particles.  Since Newton’s law has the same inverse square dependence on distance as Coulomb’s law, the formula can be modified to calculate the gravitational energy holding together a sphere of uniform mass2,

E = - (3 / 5) G M2 / r,

where G = 6.67×10-11 N·m2/kg2 is a fundamental constant and M is the mass of the sphere.  According to Wookieepedia, the radius of Alderaan is 6,250 km and its gravity is “standard,” making it slightly smaller than Earth with a mass of about 5.7×1024 kg.  Using these numbers, we can estimate the amount of energy needed to blow up Alderaan,

E = (3 / 5) G M2 / r
= (3 / 5) (6.67×10-11 N·m2/kg2) · (5.7×1024 kg)2 / (6,250 km)
= 2.1×1032 J

As Marvin the Martian once said, “Where’s the kaboom?”  If you harvested all the solar power that falls on the Earth from the Sun, it would take about 40 million years to collect enough energy to blow up Alderaan.

[1] See, for example, The Feynman Lectures on Physics, Vol. II, Chapter 8.
[2] Strictly speaking, if Alderaan is like Earth, it will not have a uniform mass distribution, but this assumption makes the math a lot easier.