I’m sure that most of you out there have been sitting at home and thinking to yourself, Golly gee! I wonder how much energy the Death Star needed in order to destroy Alderaan! No? Hm, it’s just me then. Truth be told, this quest for knowledge began on Wednesday.
For those of you who don’t know (which is probably most of you), I am a physics major at Grand Valley State University. I was at the first meeting of the Physics Book Club, having a lengthy discussion about the notion of spinning, time, space, and other such things that physics nerds ponder in their everyday lives. When we determined that we weren’t going to find a unifying theory until at least week two, we began brainstorming ideas for the next book we could read. I suggested a book that I have been reading, “Physics of the Impossible: A Scientific Exploration into the World of Phasers, Force Fields, Teleportation, and Time Travel” by Michio Kaku (with a title like that, who could go wrong?).
Since everyone in the room was a scientist, it’s only natural that they inquired as to the contents of the book. I told them that the book is about science fiction technology and the possibility of it being developed in the real world. “Well, what kind of technology?” (Physicists are inquisitive). Invisibility cloaks, light speed, antimatter, the Death Star…
As soon as I mentioned the Death Star, they asked if it was possible, so I told them that Kaku said it was not outside the laws of physics. One thing led to another and we began calculating the amount of energy the Death Star used to destroy Alderaan. We were only deterred because we couldn’t determine a realistic mass for the planet (Wookiepedia only had the diameter! *Psh*).
Fortunately (read unfortunately by non-physics nerds), I was determined to figure it out. So, when I sat down to dinner the next night, I worked it out.
But, I was not satisfied. I wanted to double check my work and make sure I didn’t mess up somewhere. So I worked it out again, this time in more detail. And I found the same conclusion: It would take at least 2.038 x 1032 J of energy to destroy Alderaan. [If you are interested in seeing my work, please see the section below the main article for a detailed description]
This is an unfathomable amount of energy, so to give us a point of reference, consider this: in one second, the sun produces 3.8 x 1026 J. That’s the equivalent of 100 BILLION hydrogen bombs… EVERY SECOND! So how does this compare with our value of energy? In order to match our minimum energy of 2.038 x 1032 J, the sun would need to provide output for 6 days, 4 hours, 58 minutes, and 16 seconds!
I bet you’re wondering if this is possible. Well, good news… or maybe bad, depending on how paranoid you are: according to Kaku, this is possible. Since there is no limit for the amount of raw energy a light beam can carry, it is entirely plausible that the Death Star could use thousands of x-ray lasers, all fired simultaneously. This seems to be the approach George Lucas was going for.
But there is one other possibility. Since the Death Star potentially exists in a very advanced civilization (also, in a galaxy far, far away), it is possible that they would have the opportunity to use gamma ray bursters. These are naturally occurring phenomena that could potentially be harnessed, but the Empire would need the ability to control the spin of a star before it reaches hypernova. By doing this, they could theoretically aim the resulting gamma ray burster at their target.
Well, I hope you’ve enjoyed the look into my world and maybe learned a little. If you enjoyed it, then you should follow my blog, A Day in the Life of a Physics Phanatic. Don’t forget to look at the specifics below! Just one parting thought: Alderaan is dangerously close to the mass and diameter of the Earth.
So, let me walk you through the process. I wanted to find the minimum amount of energy needed to destroy Alderaan. I thought that a good way to do this would be to find the amount of energy needed to tear the planet apart, chunk by chunk, at escape velocity (meaning just fast enough to pull free of the gravitational field). This is nowhere near as dramatic as it is in the film, but it’s a start. First, we’ll use the equation for the potential energy of an object in the gravitational field of the planet:
where G is the gravitational constant, M is the mass of Alderaan, and m is the mass of the chunk being torn off. We want to make this easier on ourselves, so we’re going to substitute an equation for both masses. We’ll do this by using:
where m is mass, ρ is the density, and V is volume. First up, the mass of Alderaan! We know the volume of a sphere to be:
so our new equation for M is:
We’re going to take a slightly abstract approach to finding an equation for m. We’re going to imagine that we’ll “peel” a layer off of the planet that’s infinitesimally small (really, really, really, small). We’ll find the volume of this layer by multiplying the surface area of the spherical layer (4πr2) and the width of the layer (dr). This will give us the following equation for the mass of the layer:
Now we’re ready to calculate the energy. We’re going to take the integral of our formula so that we can add up every layer from the surface to the core. Assuming Alderaan has a radius R:
Since most of the values in the equation are constants, we can take them out front and simplify the integral:
After integrating, we see that plugging lower boundary term results in zero, so we now have our final equation:
We can now plug in our values:
- G = 6.673 x 10-11 m3 kg-1 s-2
- Diameter of Alderaan = 12,500 km → R = 6250 x 103 m
- ρAlderaan*= 5515.3 kg m-3
Plugging in these numbers gives us:
E = 2.038 x 1032 J
*Note: I assumed that the density of Alderaan in equal to that of the Earth. I did this for several reasons: (1) Both Alderaan and Earth are terrestrial and support human life, (2) Alderaan’s diameter is only 250 km shorter than the Earth’s, and (3) Alderaan does not have any major oceans, just rivers and lakes. This means that it would have less water than the earth and more dense land mass.