How Much Antimatter Was Needed To Blow Up Alderaan?

In Star Wars Episode IV the peaceful planet of Alderaan was blown up by the the Death Star using a superlaser.

That was quite the feat and in this post I am going to figure out how much energy was needed to do that, how much antimatter you would need to power the superlaser and some implications of the situation.

Gravitational Binding Energy

If you assemble a large mass like a planet it is kind of like dropping a whole bunch of matter down a self-assembling gravity well.

The matter will speed up as it falls down the well losing its original potential energy and gaining kinetic energy. The kinetic energy will be converted into heat energy on impact with the surface and this newly formed planet will glow red hot and be a molten hell planet for a long time until it cools off.

This energy that was dissipated is known as the gravitational binding energy and to disassemble that planet bit-by-bit you would have to input the same amount of energy all over again.

Or you could just use a massive superlaser and do it all at once.

The gravitational binding energy has been worked out for us and it is given by:

where,
U is the binding energy in joules,
G is the gravitational constant = 6.67 x 10^-11 N·m²·kg^-2
M is the mass of the planet in kg and
R is the radius of the planet in m.

For the case of the Earth M = 5.97 x 10²⁴ kg and R = 6370 km = 6,370,000 m.

Plugging in the numbers for Earth we get a binding energy of 2.24 x 10²⁴ joules. That is a lot of energy and it explains why it took so long for the Earth and the other rocky planets to cool down after they formed.

If Alderaan was similar to the Earth in mass then the Death Star would have had to impart this much energy into it to cause it to "disassemble".

How Much Antimatter?

Let's assume the Death Star's superlaser was 100% efficient. Not realistic but it is a good start for a calculation.

We know that mass and energy are equivalent and the relation is given by E = mc². For a more detailed explanation of this please see an earlier post of mine One Gram Killed Hiroshima.

Re-arranging the equation to solve for m we get m = E/c² where c is the speed of light in metres per second (c = 300,000,000 m/s).

The binding energy U for Earth is 2.24 x 10²⁴ joules (which is 'E' in the case of the m = E/c² equation).

Solving this simple equation gives us a mass equivalence of 2.5 x 10¹⁵ kg. If you take one half of that amount in antimatter (1.25 x 10¹⁵ kg) and reacted it with the same amount of matter then 2.24 x 10²⁴ joules of energy would appear, rapidly and violently in case you were wondering.

If the Death Star superlaser were powered by antimatter and 100% efficient it would have had to store this much antimatter just to get one shot off to kill a planet.

A Big Ball Of Anti-Water

So just how would you store this much antimatter?

Maybe if you took two anti-hydrogen atoms and chemically combined it with an atom of anti-oxygen to make anti-water then you could store it as a great big ball of anti-water. React this anti-water with an equivalent large ball of water to make your energy.

How would you keep this giant ball of anti-water from touching and destroying the Death Star? The Force of course (duh).

Just how large would this giant ball of water be? We know the density of water is 1000 kg per cubic metre and the equation for the volume of a sphere is:

A ball of anti-water with a radius of about 6,665 m = 6.7 km will have a mass of 1.25 x 10¹⁵kg.

That is a lot of antimatter.

Of course you would need much more than that if you wanted to blow up more than one planet. The Death Star #1 had a diameter of about 100 km to 160 km so there was plenty of room for that.

Many, many small reaction chambers reacting 1 kg each would be needed to combine the matter and anti-matter to power the laser. One reaction chamber alone would have been enough to destroy Jedah in Rogue One.

Blowing Up The Death Star Is Somewhat Problematic (Understatement of the Century)

The movie's hero Luke Skywalker fired a proton torpedo into a thermal exhaust port, hitting the main reactor and destroyed the Death Star.

If the Death Star were powered by antimatter then the ensuing explosion would have converted 1.25 x 10¹⁵ kg of antimatter with 1.25 x 10¹⁵ kg of matter into energy within a second or so.

For arguments sake let's say the reaction was exactly one second long, this would be a temporary power output of 2.24 x 10²⁴ joules of energy within one second and this equals 2.24 x 10²⁴ W of power .

A yottawatt is 10²⁴ and the Sun is estimated to put out a power of 385 yottawatts.

This means that the power output of the destruction of the Death Star was about 2.24/385 = 0.6 percent of the power output of the Sun. Mostly in the form of brain and body-frying gamma rays.

The ships of the rebel force were only a few thousand kilometres away from this massive gamma ray burst so it is very doubtful that they survived. Most likely their brains and eyeballs would have exploded from the quick energy input to be followed very shortly thereafter by being reduced to a pile of carbon and exploding steam.

Buh bye Luke.

The nearby rebel base on the fourth moon of Yavin would not have fared that well either. The immense gamma ray burst would have destroyed the ozone layer and set the forests on fire. Any life forms exposed to the sky at the time would receive the sunburn of a lifetime and then they would have died.

The life on the other side of this moon would live, for a short while only as the environmental catastrophe would create a global firestorm and a nuclear winter.

Buh bye fourth moon of Yavin.

Closing Words

After doing the math, it seems unlikely that any machine would have the power to rapidly disassemble (i.e. blow up) a planet.

It also seems unlikely that the Death Star would have been powered by antimatter as it would be a quite frightening task to keep a 12 km diameter ball of anti-water floating around in your super weapon.

Instead of antimatter, maybe the Empire scientists knew how to tap into the zero point energy of the vacuum or even into the energy from the spacetime expansion of the Universe itself. Who knows?

In any event, I doubt blowing up a machine like the Death Star is something you can survive unless you are in the next solar system about 10 light years away.

Thank you for reading my post.

Post Sources

https://en.wikipedia.org/wiki/Alderaan
https://en.wikipedia.org/wiki/Death_Star
https://en.wikipedia.org/wiki/Gravitational_binding_energy
https://en.wikipedia.org/wiki/Gravitational_constant
https://en.wikipedia.org/wiki/TNT_equivalent
https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
https://en.wikipedia.org/wiki/History_of_Earth
https://en.wikipedia.org/wiki/Orders_of_magnitude_(power)#Yottawatt_(1024_watts)
https://en.wikipedia.org/wiki/Yavin
https://en.wikipedia.org/wiki/Zero-point_energy
https://en.wikipedia.org/wiki/Rogue_One#Plot