Purple vs Green: The Battle of the Spherical Space-cows


In the last article I talked about the situation in Gundam Wing, where Earth is in an armed standoff with her off-world colonies placed at the LaGrange points. As I said at the end, although both sides in the anime are acting like idiots, there are options both sides could pursue that could bring a decisive result. This article is quite long, so I advise settling down with your favourite beverage and a snack. But before we start learning about space wars, I need to talk about cows.


How do you work out the mass of a cow? You can’t ask, that would be rude. And it wouldn’t be any better if you sauntered up innocently with a set of scales. Fortunately, basic maths will help us out here. We know that cows float, but not very high in the water, so their density must be a bit less than 1 – let’s call it 80kg per cubic metre for now. If we could figure out the volume of the cow, that would let us work out its mass.

Well then, what’s the volume of a cow? In the absence of Archimedes and a handy bath, we don’t have a definite answer. We could work it out using a measuring tape, but that might give away what we’re up to. Instead, we know that cows are about three metres long. Let’s assume they have a radius of 1.5m. The formula

volume = 4/3 x π x radius³

gives us a spherical cow with a volume of about 14 cubic metres. Multiplying the volume by the density tells us that Bessie weighs about 1120kg. Which is pretty close to reality, if you look into average bovine masses, and also a pretty good effort considering we didn’t start with any measurements at all.


As you have probably gathered from all this, we are now in physics-experiment-land! Physics-experiment-land is a wonderful place, full of spherical frictionless cows of uniform density, which delight in helping us reduce complex problems into simpler forms. And that is pretty much what we’re going to be doing in this discussion – there are simply too many details to all be considered, so we’re going to make extensive use of approximations and what us technical types refer to as SWAGs (Scientific Wild-Assed Guesses).

The answers this process gives us are unlikely to be completely correct – apart from anything else, most cows aren’t spherical (or frictionless). But they will give us a “good-enough” idea of the answer, and if we need more exact results at least we know where to start. Now, back to our space war. In order to avoid bias by using more ideologically-charged terms, I’m going to label the combatants Purple – the space colonies – and Green (Earth).


This image was in the last article, and it shows the Lagrange points (named for the French astronomer) in the Earth-Moon system. L1, L2 and L3 are all unstable – objects placed at them will tend to wander away. But L4 and L5 are dynamically stable – objects placed there can orbit the point, and will tend to remain there. In this situation there are large space colonies at all of the Lagrange points, which tells us that the colonies have at least a limited ability to stabilise themselves. For purposes of this article I’m going to focus on the Earth-Moon system shown in this image – yes, the rest of the solar system does exist, but the war will be won or lost here.

When I’m considering a military situation I always like to start by looking at a map. Spatial relationships are often very important and besides, the colours look nice. In this particular case, however, the map tells us two critical facts straight away. Take another look at that map of Lagrange points, and see if anything jumps out at you.


The uniforms are optional.

The first thing the map tells us is that Purple has an advantage in terms of surveillance. There is a space colony in direct line of sight to every part of Earth’s surface at all times, so Green cannot launch anything without it being spotted more or less immediately. The same is true in reverse, of course – Green can see anything Purple might launch from those colonies. But since Purple is already in space while Green has to get there before they can do anything else, this is on balance an advantage for Purple.

In fact, it’s a bigger advantage than it might seem at first. The amount of energy needed to change orbit, or even change direction entirely, is not huge. As the saying goes, once you’re in orbit you’re half-way to anywhere! And Purple is already there. Green, however, is not. It takes a lot of energy to get from Earth’s surface to a low orbit, and spacecraft doing this are very vulnerable. Purple probably can’t prevent Green from launching ships, but it’s a complex undertaking. Putting a spaceship in orbit will be significantly more difficult for Green than for Purple.

The geometry of the L2 colony also poses a problem for both sides. It is permanently shielded by the Moon, which means on the one hand that it is an excellent place to do things that Purple doesn’t want Green to know about. It also means, however, that it relies on communication links for warning of anything Green might be doing. And the travel times pose a problem too. If either side wants to do something either to or using all the space colonies simultaneously, whatever is launched to/from L2 will have to leave first (thus warning the other side that shit is about to get real). This makes sudden ‘Pearl Harbour’ disabling strikes more or less impossible for Green to conduct, but it also means that Purple can’t drop giant space robots from all of the colonies at once and have them arrive on Earth at the same time. Hypothetically speaking.


In theory, theory and practice are the same. In practice, however…

After looking at a map, the next thing we’ll need to do is to size up the resources available to each side. At first it looks like no contest: Green is at best a Type I civilisation on the Kardashev scale, Purple theoretically has all the resources of the entire solar system available and is verging on Type II. But in actual fact Green has a major advantage here.

Energy is about the only resource where Green doesn’t have an overwhelming advantage, in fact. Purple can build solar panels more or less as large as they like, and without any pesky atmosphere to get in the way. Against that Green has a wide variety of energy sources, from renewables to nuclear power, and can spread them over a large part of the planet’s surface. It’s tough to call, but I think Purple might have an edge here. Unfortunately that’s about where Purple’s luck runs out as far as resources go.

Purple is already in space, yes, and Green can’t get to resources in space without at the very least being seen by Purple (and probably having to fight their way there and back again). But getting at space resources requires spaceships, and most of the propulsion systems we know of either require gobsmackingly huge quantities of fuel or are very slow. The exceptions fall into a category best described as ‘radiation spewing atomic rockets’, which (surprise!) depend on radioactive materials. If you want either lots of fuel or radioactives, the best place we know of to get them is Earth. This means Green will not be short of high-power propulsion systems, and Purple will have a great deal of trouble matching them.

But it gets worse. Building military forces requires other resources too – steel, aluminium, silicon, rare earths, and so on. Some of those can be found in space – the asteroid belt is a good place to look, and the moon has some too – but without plenty of powerful engines it will be extremely slow for Purple to get them. Green, on the other hand, has a great deal of those substances right at hand. If they want more, they know where to go. Green is practically swimming in militarily significant resources right from the start, while Purple will be struggling to scrape them together.

And it gets worse again! Green also has a huge population base (along with an equally huge life support system to take care of them), a huge industrial base, and can link its research centres together relatively easily (and undetectably, thanks to cables) to increase their advantage even further. Purple has none of those things, which gives us our first clue about the strategies of both sides: Purple has to either win so fast that Green’s resources can’t come into play, or they have to compete in a way that renders those resources meaningless. Because if quantity ever becomes important, Green will crush them so fast it isn’t even remotely funny.


Weapons and Defences
There are three main classes of weaponry available to Purple and Green – lasers; kinetic energy projectiles; and missiles. These apply to any combat that takes place, whether they’re small versions mounted on drones or huge versions mounted on colonies. I’ll discuss each of them in turn, along with what might be useful as a defence against them. The one thing I won’t discuss is ‘weapons of mass destruction’. This is because, when we’re talking about conflicts like this, simply killing everyone is relatively easy. But that isn’t a war, it’s a kind of horrible spasm. In this setting military forces are the arm of restraint – they’re what you use when you want to have graduations of frightfulness, with the possibility of escalation or de-escalation. They’re more expensive than mutual suicide, but they also give you a lot more options. The weapons they use will fall into those three categories I mentioned earlier.

Lasers are your directed energy weapons. I’m using the term here to include microwave beams, as well as the exotic x-ray and gamma-ray lasers. They strike with the speed of light, and as long as you have the power to run them they can operate for long periods of time. On the other hand they lose effectiveness quickly and at long ranges can only reliably destroy fragile targets. They’re fine as anti-missile defences, but they will not be cutting enemy spaceships in half.

In terms of defences, conventional armour is your best bet against lasers. This is heavy, however, and has a big effect on the manoeuvrability of your spacecraft (another reason those high-power propulsion systems are important). Lasers also don’t work well through an atmosphere, thanks to thermal blooming and all that water vapour. This, oddly enough, is an advantage for Green – Green is not short of power and has plenty of capacity to sink the waste heat generated, so they can simply pump more energy through their lasers until the low-orbital realm becomes a very risky place for Purple spacecraft.


Kinetic energy weapons are guns. They probably aren’t using conventional propellants – coil guns or rail guns are far more likely due to the higher velocities they can create – but they do their damage the same way, by slamming something into you real hard. In space, this is lethal. Something the size of a golf ball can strike with the energy of a small nuclear weapon. A bucket of ball bearings dropped in somethings orbital path is all it takes to destroy it, and the fragments thrown out by the impact will just make matters worse for everyone (which is, incidentally, a not-insignificant danger to spacecraft in the future).

Small kinetic weapons are likely to be the short-range smashers carried by warships in this setting. They are only accurate at the shortest of ranges, but getting hit by one is guaranteed to ruin someone’s day. It also pays to be careful where you point them, because they just keep going until they hit something. Throwing big kinetic weapons (technically referred to as ‘rocks’) from the surface of the Moon is one of the nastier options for Purple to strike at Green. It would be a big escalation of the conflict, but they would hit very hard and there’s not much that can be done to stop them once they’re on their way.

Defending spacecraft is much easier, however. The kinetic energy of a projectile depends on its velocity much more than its mass (Kinetic energy = ½ mass x velocity2, for anyone interested). Which means the projectiles fired by spaceships are likely to be small and moving very fast. Lasers might be able to destroy or deflect them, but there’s an even easier way to stop them: simply put a thin skin of metal a bit above the main hull of your spacecraft. The projectiles will release their energy when they hit that, which is bad news for the patch they hit but much better than having them strike the hull.


We all know what missiles are, right? Self-powered, possibly self-guided weapons that deliver a payload to a target. Drones (or Autonomous Kill Vehicles, whichever we’re making a show about anthropomorphic versions of today) do more or less the same thing but might be reusable. Missiles are the only really effective long-range weapons available here, and they are deadly dangerous. Unless they are shot down or decoyed missiles will hit their targets. Given the above about the dangers of kinetic energy in space, they might not even bother with a warhead – the damage caused by a tonne of metal crashing into your spaceship is so great that even a nuke won’t add much to the devastation. The exception is bomb-pumped x-ray lasers – all they have to do is get ‘close enough’ in order to send a beam of ravening death through their target.

Lasers are the point-defence weapons of choice against missiles, but if the missile designer is willing to build big ones then they can be armoured enough to survive the terminal phases of their flight. The big disadvantage of missiles is their size, mass, and expense – each missile is basically a small spaceship, after all, and although launching enough missiles will saturate a point-defence system it doesn’t take long before you’re expending a greater mass of missiles than the target weighs itself.


Stealth and Concealment
There isn’t any.

No, seriously – there ain’t no stealth in space, ok? You can shape your spacecraft to deflect radar waves or use radar-absorbent materials, but we already track chips of paint less than an inch long out to geostationary orbit and the only reason we don’t look further than that is because we don’t need to. Besides, anything other than a solid lump of rock is going to need at the very least some electronics and a power source and that inevitably also means there will be some waste heat to get rid of. This is actually a major problem for spacecraft (and presumably Purple’s space colonies as well), but for us it means that the temperature of your spacecraft is always going to be higher than the average background temperature of space. Which in turn means that it will stick out like dogs balls to anyone with an infrared scanner. Electronic warfare and decoys might be able to confuse people about your exact location, but there’s no hiding that you’re out there or even roughly where you are.

However, all that being said there are two major exceptions to the “no stealth” rule. Firstly, remember how L2 is behind the Moon all the time? Green cannot see what is happening at L2 without getting some sort of sensor platform out there, so if Purple wants to prepare a nasty surprise for Green this is an obvious place to do it. And secondly, there is stealth on a planet’s surface. Green has a multitude of potential hiding places and options for camouflage, and if Purple wants a good look at any of them they will have to get into a low orbit. That makes them vulnerable to more or less anything, from lasers to buckets of BBs lofted on sub-orbital trajectories. Unfortunately this only applies as long as whatever-it-is stays on Earth. As I mentioned earlier, Purple will immediately see anything Green launches. On balance this is still an advantage for Green, but no matter what they build it will still be difficult to actually use it without Purple noticing.


We all like to think our strategy is like this.

So, putting all this together, what does this tell us about the options for our belligerent bovines?

For starters, Green is going to want to use their resource advantage. They will tend to build big, capable spacecraft that can take a beating and dish one out. This limits their manoeuvrability, so expect either high-speed slashing attacks or slower-paced slugging matches (both of which Green will expect to win). Green cannot afford to lose control of the lower orbits, so they might easily try to put up a defensive array of satellites or perhaps even orbital battlestations. Alternatively, they might make use of their concealment options and keep their defences on the ground until they are needed. Aircraft or submarines launching missiles as well as ground-based lasers are the most likely for this.

In terms of strategy, most of Purple’s resources are going to be coming from the Moon and any asteroids they manage to mine. Expect the colony at L1 to take the brunt of Green’s attacks, as they seek to cut Purple off from their resource base. Green is also highly likely to want to actually invade the colonies – for one thing this gives them a foothold in space, for another Green already has the resources they need so this is a war about control from their point of view. Green’s forces will include infantry, and they will be willing to take casualties in order to occupy any colonies they can reach. But they will also be willing to take a reasonably long view – a war of attrition works in their favour, after all, and they might also try to lure Purple into ruinous ‘victories’ that end up weakening the space colonies.

Naval-minded commanders might also try a ‘fleet-in-being’ strategy: Purple cannot ignore a sizable Green force in space, but by skilfully denying them a battle Green can tie down their fleet and make them expend precious resources sustaining it. Green however has enough numbers to do this and deploy another significant force elsewhere. The primary advantage of superior numbers is greater freedom to pursue multiple avenues of attack, after all, and it doesn’t take a genius to realise the advantages of holding someone down before you pound them.


In reality, it’s probably more like this.

Purple, on the other hand, will be desperate to avoid going toe-to-toe as much as they can. They simply do not have the resources to expend in that sort of contest, and due to their much lower population every crew they lose is a significant blow to the quality of their forces. I expect their ships to be smaller and less heavily armed, but significantly more manoeuvrable on average. They are also likely to make more use of drones and AKVs, which they will be quite willing to risk in both attack and defence. Typical tactics will probably be to dance around at the edges of the battle area, deploying swarms of AKVs, and then leaving as fast as possible in the fervent hope Green doesn’t slap them with a missile volley.

The colonies themselves will probably have large laser arrays to defend themselves with, and Purple will have no compunctions about trying to sneak kinetics or bomb-pumped mines into Green’s orbital space – the chances of a hit may be low, but the investment is equally small and it makes Green nervous about using those orbits.

Purple’s strategic situation is more complex than Green’s. Purple theoretically has all the resources of the solar system available, but will need a couple of hundred years of uninterrupted development to really make use of this – time which Green is unlikely to grant them. The spectre of orbital bombardment will be rising behind every choice Purple makes. How easy it would be to simply redirect an asteroid or two and turn Earth into an artistic collection of craters! Unfortunately, given the time involved this would not even work very well as a deterrent: Green would see it coming months away, and have ample opportunity to ensure that Purple didn’t survive their victory.

However, at the same time the rest of the solar system offers Purple its best chance of winning in the long run. Once self-sustaining colonies are established elsewhere it simply becomes too difficult to conquer or destroy all of them. In the meantime, Purple will have to keep Green at arms length – use harassment and raids to distract Green and keep them from focusing their power. Dropping special-ops groups to Earth to wreak havoc is a good way of doing that. In general, Purple will be trying to follow an ‘anti-access’ strategy. But Purple absolutely cannot afford to lose their position and surveillance advantages. L3 is the weak point there, a long way from the support of the other colonies.


I expect their meetings will look EXACTLY like this.

The key to this contest, like so many others throughout history, will be the leadership on both sides. If Purple can provoke and distract Green into frittering away their forces on activities which are ultimately meaningless, they have a good chance of neutralising Greens resource advantage. Alternatively, if they make it difficult, dangerous, and annoying enough to get at space, Green might just get sick of the whole business and seek an accommodation.

On the other hand, if Green manages to keep its focus and accept the costs, they will be able to simply roll right over Purple long before Purple is in any shape to stop them. If Green’s leaders want to be more subtle, they might also be able to win without firing a shot simply by goading Purple into wasting its limited resources. Perhaps their biggest advantage, however, is that Green can afford to make mistakes. Losing a major battle would be unfortunate for Green. It would be a disaster for Purple, though, and the Purple fleet commander is the only person who could lose the war in an afternoon. They wouldn’t even have to lose the battle to do it, either!

On balance, then, Green has the best chance of winning the battle of the spherical space-cows. It might be expensive for them, but God is on the side of the big bovines.

Question of the post: This whole post is based on plausible extrapolations of what we know today. But sci-fi often uses a “one impossible thing” rule, in which a single impossibility (often technological) is used as the basis for a setting. What single impossibility would change this situation around? Or alternatively, which single impossibility would you like to see included in a setting like this?

About Dr. J.H. Watson

I’m a New Zealander, in my 30s, and until recently I lived in rural Japan. I have interests in history, pop culture, video games, and the clever use of language.
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4 Responses to Purple vs Green: The Battle of the Spherical Space-cows

  1. Ged Maybury says:

    Hmmm… Well to balance the game, I’d introduce some sort of matter-transfer/stargate thingy, but with one limiting factor: it cannot work within severe gravity gradients (i.e. Earth’s surface, maybe the Moon.) If the device was ‘single-ended’ rather than needing a gate at both ends (or if *some* of them could thus be configured – maybe as a disposable option), that would add extra frisson.


    • Some sort of matter transporter, especially a single-ended one, would absolutely change things around. Depending on where the terminii could be located it could turn the whole thing into a walkover for Green, Purple, or an unholy mass of factional bickering.


  2. fgfdfh says:

    You want implausible tech? Let’s go with something from the gundam series itself: Minovsky particle. I briefly commented about it in the last article, but here’s more details from Wiki:

    “When the Minovsky particle is spread in large numbers in the open air or in open space, the particles disrupt low-frequency electromagnetic radiation, such as microwaves and radio waves. The Minovsky particle also interferes with the operations of electronic circuitry and destroys unprotected circuits due to the particles’ high electrical charge which act like a continuous electromagnetic pulse on metal objects. Because of the way Minovsky particles react with other types of radiation, radar systems and long-range wireless communication systems become useless, infra-red signals are defracted and their accuracy decreases, and visible light is fogged”

    With this, stealth is possible, giving Purple an advantage. They can do a lot resource gathering and fleet hiding now. On the other hand, it’s only useful when the war already happened, because the rise in Minovsky particle density signals everyone that something fishy is going on. Close combat and dogfight are more useful now, as long-range weapons are useless. Space battleship and space fighters become much bulkier due to the need of better shielding for electronic circuit. This means the return of 20th-esque dogfight and aircraft carrier. This element actually give advantage to Green, which has more readily available resources.

    Mecha, unfortunately, is still useless.

    Liked by 1 person

    • Good analysis! I think you’re right, bringing everything down to short range is an advantage for Green. I disagree about the carriers, though – a fighter spacecraft needs more complex electronics than a missile or AKV, plus it needs enough fuel to not only get to the target and deliver its weapons but also make it back to the carrier. Even under these circumstances missiles and drones make more sense.

      And as you say, mecha are still useless.


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