What does "orbital carrying capacity" even mean?
How far can we stretch analogies to terrestrial resources?
I’m in London this week for the Summit for Space Sustainability, where I’m supposed to say something about “orbital carrying capacity”. I wanted to reflect and write a bit on how I’m thinking about the term and this question before the event, where I’ll likely reconsider many of these notions.
I think the question behind the term “orbital carrying capacity” is something like “what’s the biggest number of satellites that can be in an orbit together?” Maybe there are modifiers like “safely” thrown in there somewhere.
(Edited to add) Why does this matter? Over the next decade or so, folks are planning to launch a lot of satellites — tens to hundreds of thousands, depending on which plans materialize, and maybe more. If we don’t want to end up accidentally overfilling (and maybe trashing) valuable regions of orbital space, we should get a sense of the limits to how much we can put up there. (Thanks @patwater for suggesting this edit!)
I think there are two ways to think about this question with analogy to terrestrial resources: a mechanical sense of “packing” objects into a box, and a biological sense of “sustaining” a population in a region. Both, I think, have serious limitations for thinking about orbits. Instead, I want to point to a third way to think about the concept: an economic sense of choosing the number of satellites that’s worth keeping in orbit. I’ll explain the first two ways of thinking about the term, then why I think they’re lacking, then explain the economic way of thinking about it. Buckle up, this one’s a bit long.
TL,DR: to an economist many things are ultimately about “willingness/ability to pay”, and “orbital carrying capacity” is one of those things.
Filling a box, or “packing capacity”
Let’s start with the mechanical notion. Say you’re moving and you need to fill a box with stuff. There’s a limit to how much stuff that box can hold. Let’s call this the “mechanical” definition of the box’s carrying capacity: the amount of stuff you can fit in the box. You could just as well label this the “packing capacity” of the box. The packing capacity of a box is a number in volumetric units describing the total amount of stuff that can fit in the box.
Clearly, the packing capacity number is informative. But it does take a bit more translation to be really usable. The packing capacity may be in units like cubic meters, while your stuff is in units like “25 books and a kettle”. That’s not a showstopper. You can do unit conversions, or (more likely) just try to pack things in until they fit as well as they can. At some point you’ll notice how you pack matters: different configurations of stuff fit different quantities of stuff in the box. For the packing capacity number to be useful, you also need a notion of how the stuff is configured in the box. Some stuff (books) can pack tightly, but other stuff (kettle) can’t pack so tightly. So in addition to the configuration of the stuff, you also need to know something about the shape of the stuff. The number of “slots” an object takes up in your box depends on these things.
Orbital packing capacity
This is somewhat transferable to thinking about orbits and orbital slotting. Certainly configurations matter — some configurations make it easier to figure out slotting than others. It gets a bit complicated because while a box just has three static dimensions and positions are known with certainty, orbits have three dynamic dimensions. Well, that’s what math is for. You can calculate a “volume” in six dimensions just like you could in three. “Aha,” you say, “but there are error bars on object positions, you don’t know them exactly.” Not to worry. We can add some buffer around the objects to account for our inability to exactly predict or measure their positions. Ok, what about shapes — satellites aren’t all similarly shaped. Still not a huge problem. We can draw a tight sphere around each satellite and put the error bars (“error spheres”) on those spheres.
If you carry out this exercise you can calculate a “maximum orbital packing capacity” which tells you the absolute maximum number of objects which could orbit around the Earth in a given orbital shell (or whatever shape you please) under a specified configuration. Even with very generous limits, you can get an astronomically (ha) large number for low-Earth orbit (LEO), easily on the order of hundreds of millions or even billions of objects.
So is “packing capacity” a useful notion in orbit?
It depends. If you take the positions of objects currently in orbit (both active satellites and debris) as given, you can use this type of exercise to calculate how much more stuff could be packed into orbit (given a configuration) before the objects were guaranteed to collide. That could be useful if you just want to know what the outer physical limits are.
But the box-packing analogy starts to wear thin here. When a box gets filled, no more stuff can be put in. When an orbit gets “filled” (in the packing capacity sense), putting in one more thing guarantees a collision. Bad things happen when orbiting objects collide, the resulting fragments occupy a whole bunch of slots, and the whole delicately balanced system eventually turns into one giant orbiting garbage heap. “Ok,” you say, “then just don’t exceed the packing capacity, maybe even leave some extra buffer.” I’m not sure how exactly we enforce that, but sure, let’s pretend we can do it. We come to smaller but still large number — maybe just a few million or so objects under the highest-tetris-score configuration. I’m ignoring lethal non-trackable debris — tiny fragments we can’t observe but which still pack a punch — so let’s add some buffer for that. Maybe a scant million or so? Let’s call this “buffered packing capacity.”
At this point we’ve come pretty far from the maximum packing capacity number we calculated. Maybe we can rigorously justify these calculations without appealing to arbitrary value judgements. More likely there will be some arbitrary safety factor that sneaks in, something like “let’s only accept an x% risk of collision.” In the near future we’re looking at maybe tens to hundreds of thousands of satellites being in orbit, so we’re either far away from the buffered packing capacity or right at the edge or blowing past it, depending on possibly-arbitrary assumptions and configurations.
Anyway as object dimensions change the packing capacity numbers will change too. So if it is a useful notion it’s one that will need constant updating. Perhaps the most useful thing about it is it highlights the importance of configurations.
Cows in a field, or “carrying capacity”
Astute readers will have noticed that I started talking about something called “orbital packing capacity” instead of “orbital carrying capacity,” ostensibly what this piece is about. Let’s talk about “carrying capacity,” then.
In biological sciences, “carrying capacity” usually refers to the number of organisms an environment can sustain before the organisms die out from too few resources. The calculation usually goes something like this. Say we want to figure out how many cows can sustainably graze a field. Let’s say one cow needs to eat one ton of grass per month or it dies. Suppose the field grows 100 tons of grass per month, and to keep things simple it starts off with 100 tons of grass. So if we put 100 cows in the field for a month, they’ll eat all the grass, but it’s ok since by the start of the next month there’ll be another 100 tons for them to graze. The carrying capacity of the field is 100 cows. (The packing capacity is likely much larger, but also useless to us since we need to keep the cows alive.)
What happens if we put 101 cows in the field? Well, there’s only 100 tons of grass to start. So one cow is going to starve to death. What if the field had 101 tons of grass to start with? The 101 cows will be fine in month 1, but when month 2 rolls around, we’re back to having one dead cow. Whoops.
When a resource consumer exceeds the carrying capacity of its environment, its population typically declines and the resource regenerates until the two reach a stable equilibrium (a “steady state”) where both are constant over time. Or not, and the resource deteriorates and the population declines and we’re left with a barren wasteland littered with dead cows.
A biological notion for an artificial population
At a surface level it seems like you could define a similar notion for orbits: the maximum number of satellites you can put into an orbital volume such that none of them experience a catastrophic collision. The resource here is clean orbital space, the consumer is active satellites. Maybe there’s even an analogy between predators hunting prey and debris “hunting” satellites. But I think these biological analogies don’t really work for (at least) two reasons.
First, debris are not really like biological predators. In a typical predator-prey system, the size of the predator population depends on the size of the prey population. Overpredation causes the prey population to collapse, leading to a collapse in the predator population soon after. In some cases, the prey population rebounds, the predators rebound soon after, and the process repeats. Or not, and we get extinction of both predators and prey. This is effectively the cows and grass story. But debris isn’t like that. Debris objects can collide with each other and create more debris. The process can continue until drag pulls them down or until they reduce themselves to a fine mist. Either way, it’ll take a while after the “prey” (satellite) population collapses for the “predator” population to collapse. In higher orbits, “a while” can be decades or centuries. So debris are more like zombie fish that can feed on each other and reproduce for a long time than typical biological predators.1 Also, since debris also use orbital space, it would be as if cows ate soil and grass. Zombie predators that eat each other, and the prey species, and the prey’s food. Zombie pests, perhaps.
Second, satellites are not like biological prey. Prey species (like all species) reproduce. Given enough time and provided they haven’t fallen below a minimum threshold, their population will rebound from a low level until they reach (or oscillate around) some steady state with the relevant resources and predators. So when we harvest them, we can be assured that they’ll bounce back. Artificial populations like satellites aren’t like this. We don’t harvest them; we create them. They don’t reproduce; we launch satellites to replenish their population. And we can launch satellites even as the skies get so cluttered that the satellites live shorter and more congested lives, at least until they get so cluttered no rocket can deliver its payload. If you believe very low-Earth orbit is self-cleaning, there will always be a region where we can always replenish the satellite population. Will we? That’s a different and interesting question. Let’s come back to that.
I think these two differences make analogies to biological carrying capacity notions less than apt. The “predator” population can grow on its own, (eventually) untethered from the “prey” population. We can’t really define a “sustainable harvest” level that links what we can take to an orbit’s carrying capacity.2 And debris and satellites both “compete” for clean orbital space, so the debris are less a predator and more a pest species.
But the fundamental difference is that we can launch as many satellites as we’d like. They won’t all live out their full design lifetimes. Eventually most will live very short lives, and the more we launch the shorter their lives will be. The real limiting factor here isn’t “what can the environment sustain?”; it’s “when do the expected benefits from launching satellites no longer exceed the costs?”
“Orbital carrying capacity” is a cost-benefit test
Let’s come back to the initial question behind the concept. What’s the biggest number of satellites that can be in an orbit together? As many as we want, as long as it’s (a) physically possible, and (b) worth our while to place and keep the satellites there. The physical constraints of maximum packing capacity apply to any configuration, but that’s likely to be such a large number it’s not really the binding constraint. The binding constraint is our willingness to keep launching satellites to orbit. Put differently: the relevant notion of orbital carrying capacity is an economic notion of willingness to use an orbit.
While our willingness to shoot stuff into the sky is limited by maximum packing capacity, buffered packing capacity notions aren’t so relevant. Biological notions of carrying capacity may be relevant, but they need to incorporate our willingness to launch satellites as the key factor driving satellite population growth. Debris “predation” on satellites in an orbit matters, but again only insofar as it affects our willingness to launch satellites to that orbit.
What does this mean for the coming rush of megaconstellations? I’m not sure yet. This is already long and I’m still thinking it through. But here’s where I’m at right now:
Hard or soft, capacity thresholds are not likely to reflect the reality of what people are willing to pack into an orbit. If it’s a maximum packing capacity, it’ll be so large as to be useless. If it’s a buffered packing capacity, the necessary assumptions will be inherently contestable. Regardless, they’ll form some kind of Schelling point for coordination.
Satellite operators may face incentives to encourage or deter others to/from operating “near” them, at least partly through their choice of configuration.3 That is, the “carrying capacity” will be at least partly an economic choice variable for the operators in an orbit, not entirely an exogenous constraint from physics and economics.
That’s all for now! I’m looking forward to the Summit, and to developing my thoughts on “orbital carrying capacity” further there.
A fisheries scientist once told me there’s a fish that does something like this, but I can’t recall the name of the fish.
Sébastien Rouillon has done some work on a related notion for a “maximum sustainable launch rate”, but the notion doesn’t quite capture the “zombie predator” nature of debris. In ongoing work, we’ve defined a notion of “orbital carrying capacity” that incorporates debris growth. But even that notion on its own doesn’t capture the fact that we can launch as many satellites as we’d like.
What does “near” mean in LEO? Let’s go with “two satellites are near each other if they will regularly pass within 5 km of each other.” You can adapt this conjunction-based definition to any approach threshold, and it allows for all kinds of exotic orbital paths. It’s similar to the graph-theoretic definition Hugh Lewis and coauthors developed to analyze debris removal.