It's a question that has vexed generations of Star Wars fans - even among academics - since 1977.
And it's reared its ugly head again: the new movie Star Wars Rogue One is all about the mission to steal the secret plans that revealed the weapon's achilles heel.
Now, Swinburne University astrophysicist Dr Alan Duffy has applied himself to figure out what it was for.
Sure the real universe, as opposed to the Star Wars story universe, conforms to a completely different set of physics.
But the parallels can be enticing.
"As a young kid science fiction like Star Wars showed me how science was as much about exploration as it was learning formulae," Dr Duffy says. "We face challenges and solve them with technologies that I didn't even know to dream of ... By testing those ideas scientifically we can have fun exploring those worlds and also learn from what works (and what doesn't)"
And the Death Star is an awe-inspiring concept.
It's a warship the size of a small moon.
It can travel the mind-boggling distances between stars in a matter of hours.
It harnesses enough power to shatter a planet - in seconds.
It also has a gobsmacking Achilles heel (at least in the face of a scraggly, superpower charged farm-boy behind the controls of a rickety old star fighter)
But it is a weakness that actually makes perfect sense (sort of).
The more energy you use, the more heat builds up.
It's why the radiator fans on your car - and your PC - kick in when you crank up the ergs.
So how much heat would a fully armed and operational Death Star generate?
A challenging question.
But Dr Duffy has given it a try.
The Death Star housed a population of two million people. At least according to authorised official Imperial (Lucasfilm) documents.
"Energy use in the United States is 81,800 kilowatt hours (kWh) per capita in 2009 so that means two million people on board Death Star use 163.6 terawatt hours (TWh) each year. Sounds like a lot but actually it's not bad," he says.
So that doesn't explain the need for an exhaust port on a battle station that big.
But it's got a really, really big gun.
In the viral words of the "Death Star architect" responsible for the design of the exhaust ports himself (well, really just a writer for Dorkly):
"Do you understand the point of exhaust ports? Do you know HOW MUCH EXHAUST is created by this MOON-SIZED battle station? It housed a laser capable of instantly blowing up planets. It needs a LOT of ventilation - the fact that I was able to keep those exhaust ports to the size of a womp rat should earn me some credit!"
Experts in the know agree.
"It's clearly the massive issue in terms of energy," Dr Duffy says. "Informed sources reveal the minimum energy to unbind the atoms of Alderaan from one another, assuming it's the size of Earth is 2.24e32 Joules."
That's the equivalent to the entire output of the Sun for seven days.
The Death Star unleashed that energy in the space of just three seconds.
BY THE NUMBERS
Dr Duffy says storing such energy wouldn't be a problem - if you could generate and harness enough antimatter (And they can in the Star Wars universe. Just not ours). We're talking a lump roughly 5km from end-to-end.
"However, when you release that into energy there is always a loss of energy - no matter how focused the beam," he says.
"Unless the super weapon is perfect and has no losses - but there must a little otherwise we wouldn't SEE it," Dr Duffy says. "That light we can see as the green lasers show energy is escaping the beam in the form of light radiation. If light is escaping, so is heat."
The original Star Wars movie shows us it takes less than 10 seconds to power up and fire the planet killing gun.
"Now let's say that our Death Star is a marvel of engineering and it's 99.9999999999% efficient (double glazing to the max!) which means we are losing barely 1 trillionth of the energy in operating it. That means the average power loss in operating it is: 2.24e32 J * 1e-12 / 10s = 2.24e19 W (or in other words HUGE amounts)."
Somehow, the Death Star has to get rid of that excess heat - fast.
This is the nub of the problem.
Fortunately, there's an equation for that.
The power P of an object radiating (such as a star or a radiator or a fire at home) is given by the Stefan-Boltzmann law, P = A epsilon sigma T^4, Dr Duffy explains.
Epsilon is emissivity of the object (this is one for a perfect black body, 0 if perfectly reflecting). Sigma is Stefan-Boltzmann constant and is 5.67e-8 W m^-2 K^-4. T is temperature of the object with surface area A.
"So the Death Star surface area (it is a moon after all) isn't actually that big at 120km in diameter, or 60km in radius meaning the surface area is 4 * pi * r^2 = 45.22 billion square metres."
So now we find what temperature the Death Star surface would be heated up too:
T = (P / (A * sigma))**(1/4) = (2.24e19 / (45.22e9 * 5.67e-8))**0.25 = 9667K
"Basically, this is twice as hot as the surface of the Sun," he says. "This means the Death Star would be glowing WHITE hot - waaaay hotter than our Sun which is more of a mellow yellow."
Feel some sort of appreciation for Death Star exhaust port architect's challenges at this point?
There's no getting around it. That heat has to get out.
Otherwise, the Death Star would instantly turn itself into slag.
In July this year, space systems engineer Roberto Furfaro of the University of Arizona was quoted in a student research article arguing putting an exhaust port on the Death Star was a 'lazy, terrible design'.
"A good space engineer would do a thermal analysis, starting by studying the mission. Where are you going? What is the thermal environment there? Everything on the spacecraft has a minimum and maximum temperature that it can operate at, so you have to create a thermal design that allows each individual element on the spacecraft to still operate," Furfaro says.
Dr Duffy goes one step further: "The thermal exhaust port would be actually the worst solution.
"All that waste heat is going through one thermal exhaust port that's just 2m across. This means the port would have an area only 3.14 square metres. We can figure out what temperature it would be with the same equation as above:
T = (P / (A * sigma))**(1/4) = (2.24e19 / (3.14 * 5.67e-8))**0.25 = 3.3 million K
In case you're wondering, that's not white hot. That's X-ray hot. You wouldn't actually be able to see it.
"Basically that's about a third or so of the peak temperature reached at the centre of a nuclear bomb ... and this is how you're COOLING the Death Star," Dr Duffy says.
Any Imperial architect would be well within their rights to believe that would present a serious tactical challenge for attacking Rebel fighters.
"No proton torpedo is flying into that! It'd be instantly melted," Dr Duffy says.
Clearly, the Imperials didn't take into the account the power of the Force.
"Mind you so would any possible material that you would try to build the thermal exhaust port out of," he adds.
Oh. There's that.