The Expanse Will Fail if it Emulates Battlestar Galactica: A Mathematical Proof

Let’s talk about The Expanse.

Despite what you might think from the title of this post, I enjoyed the pilot episode of The Expanse. I’m happy to see contemporary science fiction trying to repatriate the interplanetary empire trope from the pie-eyed and often crackpot notions established during the Heinlein-era. The Expanse shows humanity’s colonization of Mars, Ceres, and presumably the Jovian moons, coming at the cost of our baseline humanity. Being a belter is not some romantic callback to the Jeffersonian frontier; it is a fundamental rejection of terrestrial humanity as a genetically engineered post-human.

Likewise, The Expanse comes by things like gravity in an honest way. Gravity is either the product of celestial mass, simulated through rotation, or a product of constant acceleration. There’s a bit of handwavium in terms of how humanity engineered itself to endure high/low gravity, but I’m content to let it slide. Magic gravity juice helps spacers endure 30G emergency accelerations? Okay, sure. I’ll bite. It’s an easier sell for the near-future than gravity plating a la Star Trek or inertial dampeners a la figuratively every space opera ever.

Cut to, space battles.

The Expanse’s first episode gets space battles completely, utterly, and miserably wrong. It gets space battles so wrong I might as well have been watching Star Wars. The likes of Gene Roddenberry’s Andromeda gets space battles better than The Expanse. Here comes the math.

In the pilot episode, a shuttle called “Knight” is 50,000km from its parent ship, the Canterbury. When a pirate ship appears, it is at a range of 12,00km from Knight. Put the two together and we have space battle occurring at a maximum range of 62,000km. The opening, and only, fusillade of the battle sees the pirate launch four nuclear-armed torpedoes at the Canterbury. Those torpedoes connect with the Canterbury a mere 60 seconds after launch. And this is the exact moment where I call bullshit.

Do you know how fast those torpedoes would have to be going to connect with a target 62,000km away after only 60 seconds? Very goddamn fast. Almost impossibly fast. Fast enough that the fuel they expend getting up to speed would make directed energy weapons a more cost-effective choice. But I’m getting ahead of myself.

I have no idea about the acceleration and maximum velocity of a torpedo on The Expanse. So let’s take an Earth example and do a little extrapolation. The fastest contemporary anti-ship cruise missile I could find on the internet is the experimental BrahMos-II missile. It has a maximum velocity of 2.382km/s or 2382m/s.

For the sake of argument, let’s assume the space torpedoes of the 23rd century can accelerate to 10x the speed of the BrahMos-II. In this case, that’s 23,820m/s, which is a little more than double the Earth’s escape velocity. Frankly, this seems a bit over-powered, but it’s 200 years in the future; I’m inclined to be generous.

Bearing this in mind, a torpedo launched from a ship at a velocity of 23,820m/s, assuming it launches at maximum speed – likely not possible but I don’t want to over-complicate this by factoring in an acceleration curve – would require 43.38 minutes of flight time before contacting a target 62,000,000m distant. This is also assuming the torpedo flies in a straight line, free of interference from gravity wells. It’s also not withstanding any Delta V bonus the torpedo might get from the pirate ship already being in motion. However, such a bonus would be negligible to this problem for reasons that will soon make themselves evident.

So now that science has killed the action buzz on the 60 second torpedo run, we can ask ourselves how fast those torpedoes would have to be going to have a 60 second time on target.

To cover 62,000,000 meters in 60 seconds the torpedoes would need to be travelling at approximately 1,033,333m/s. For context, the speed of light is 299,792,458m/s. Thus, The Expanses‘ torpedoes would need to be travelling at roughly 0.35% of the speed of light (C) to make the scene congruent to the laws of physics. And before you say that .35% of C is no big deal, consider that the fastest man-made thing ever was NASA’s Juno mission that hit 40,233m/s after executing a slingshot around Jupiter. Quite a ways to go before hitting 1,033,333m/s.

Given this ludicrously impossible speed, there’s really no need for a nuclear warhead on The Expanses’ torpedoes; a suitably dense piece of dog crap travelling at such speeds would have more than enough concussive force to blow up something as flimsy as a pressurized spaceship.

Now to answer the big question: what does all of this have to do with Battlestar Galactica? BSG has many strengths, but it’s depiction of warfare in space is cartoonish, at best – yes, I am talking about Ron Moore’s BSG. Vipers and Raiders engaged in dogfights driven by Newtonian physics look unbelievably cool. Likewise, fighter pilots make for accessible character archetypes. Both of these elements help make BSG an exciting and engaging piece of television (at least in the first two seasons). As a point of practicality, Vipers and Raiders are a brain dead way to wage space warfare. Recall your Douglas Adams: space is very big. Battlestars and Baseships using kinetic weapons and missiles would inevitably do better to wage war at long-range using math and thrust equations to generate shooting solutions. The ranges depicted in BSG (e.g. single digit kilometers) would result in little more than mutually assured destruction. As an audience, we forgive these things because BSG was concerned with providing spectacular looking space battles amid big political/philosophical questions. If BSG kept it real, then Adama ordering the ship to condition one would instantly cut to a team of junior officers pulling out their scientific calculators.

Unlike BSG, The Expanse is selling itself on the strength of its serious, thoughtful, and practical(ish) approach to telling a story in space. Yet in its inaugural space battle, it is very much taking the Battlestar approach. Such a choice subverts the very aesthetic the series is trying to cultivate. And frankly, I might be willing to give this utter physics fail a pass were it not for the fact that the 60 second battle becomes a setup for a broader plot arc.

The Canterbury’s navigator is about to tell something seemingly important to the ship’s XO, in command of the Knight, only to have the phone call interrupted when the Canterbury is nuked. Shenanigans!

Even if Knight and Canterbury were right next to each other when the pirate fired her torpedoes at a range of 12,000km, there should have been – working within the model explored in this post – 8.3 minutes of flight time before impact. This would be more than enough time for the navigator to say her piece and for the XO send her a final dick pic. What? He seems the type.

In no uncertain terms, the math of The Expanse’s first space battle is a joke. If the series wants to dedicate itself to showing the complexities of life in space, then it needs to abandon the Wing Commander elements of Battlestar Galactica and channel a lot more of The Martian. While I might be content to let the space battle faux pas slide once, frequent occurrences will take the shine off the series’ “hard” SF hull plating. Once that happens, they might as well give their starships FTL drives and inertial dampeners.