Fifty objects that hold most of the future

The population of objects in low Earth orbit has a feedback built into it. Collisions produce fragments at a rate that goes as the square of the population, and the atmosphere removes them at a rate that goes as the first power, so above a critical density the fragments multiply faster than drag can clear them. In the band between about 750 and 1000 kilometres, where the air is thin and the objects are many, the population has probably already crossed that line: even if nothing more were launched, collisions among what is already there would make the debris grow over the next two centuries.

Stopping that growth requires taking objects out of orbit, and the question is which. There are several thousand intact derelicts — dead satellites and the upper stages of the rockets that launched them — and several hundred thousand fragments too small to track. Removing any one of them costs a dedicated spacecraft, a rendezvous with a tumbling, uncooperative target, and a controlled descent. Removing them all is out of the question. The value of each removal is the debris it prevents, and that value is not evenly spread.

Three factors, all favouring the same objects #

A derelict’s contribution to the future debris population is a product of three things.

The first is how likely it is to be struck. The collision rate on one object is the flux of other objects through its cross-section: the density of objects at its altitude, times their relative speed of about ten kilometres a second, times its area. The area grows as the two-thirds power of mass for objects of similar density.

The second is how much debris the collision would make. The standard breakup model, fitted to laboratory impacts and one deliberate test in orbit, gives the number of fragments larger than a given size in a catastrophic collision as proportional to the colliding mass to the power 0.75. A nine-tonne rocket stage makes roughly five times as many fragments as a one-tonne satellite.

The third is how long those fragments stay. A fragment’s drag lifetime depends steeply on its altitude, because the density of the thermosphere falls by a factor of ten for every hundred kilometres or so.

Put together, the weight goes as the object’s mass to the power $\tfrac23 + \tfrac34 = \tfrac{17}{12}$, times a function of altitude that combines the local density of objects with the lifetime of fragments made there. Heavier objects win twice: they are bigger targets and bigger sources. Higher objects, in the crowded bands, win twice as well: they are hit more often and their fragments last longer.

That separation matters for policy. The rapid growth in the number of satellites has happened mostly around 550 kilometres, where a failed satellite or a collision’s fragments are cleared by the atmosphere within about five years. The long-term hazard sits higher, in orbits where derelicts launched decades ago will stay for centuries, and the objects that dominate it were put there before anyone was worried.

Who is on the list #

Ranked by that weight, the population sorts itself sharply.

The real inventory has the same shape, and the real rankings, made by several groups with different weightings and different models, agree on its core. The heaviest intact objects in low orbit are about twenty upper stages of a Soviet and later Ukrainian launcher, each about nine tonnes and eleven metres long, left between 830 and 850 kilometres from the late 1980s onward. Around them, at 750 to 1000 kilometres, sit a few hundred smaller upper stages of about 1.4 tonnes from the most-launched rocket of the Soviet era. A handful of large dead satellites, including an eight-tonne European Earth-observation satellite at 770 kilometres, complete the top of every list. A published ranking of the fifty statistically most concerning objects in low orbit, in 2021, was dominated by exactly these classes.

What makes them dangerous is not only their mass but their company. The upper stages were placed in the same few orbital shells, crossing each other’s paths repeatedly, and several near-misses between them have been recorded at distances of tens of metres. A collision between two nine-tonne stages would roughly double the tracked debris in their band in one event — a single collision comparable to everything that has happened there in sixty years.

One collision on the list #

It is worth running the breakup model once for the worst case on the list, because the number is what gives the ranking its urgency. The standard model gives the number of fragments larger than a size $L$, in metres, from a catastrophic collision involving a total mass $M$ in kilograms, as about $0.1\,M^{0.75} L^{-1.71}$. For two of the nine-tonne stages colliding, $M$ is about 18,000 kilograms. Fragments larger than ten centimetres — the size the tracking network catalogues — come to about eight thousand. Fragments larger than a centimetre, the ones that can disable a spacecraft and cannot be tracked, come to about four hundred thousand.

The whole catalogue of tracked objects in low orbit today is some tens of thousands. One collision between two objects on the list would add a quarter as many again, concentrated in the band that already carries the most risk, with a fragment lifetime of a century and a half. Those fragments would then join the population that produces the next collisions, which is the feedback the removal is meant to break. The ranking puts at the top the objects whose collision would do this, and the arithmetic of the breakup model is why removing a single nine-tonne stage is worth removing dozens of small satellites.

Mass, but not only mass #

A simple rule — remove the heaviest objects first — captures much of this, as the first figure shows: the mass-ordered removal tracks the ranked removal closely for the first twenty objects, which in both orderings are the nine-tonne stages. After that the two part company, because the next-heaviest objects are not all in the dangerous band. A three-tonne stage at 650 kilometres ranks above a 1.4-tonne stage at 850 by mass and far below it by risk.

The bow is the whole case for targeting. A removal campaign budgeted by tonnes should spend them where a tonne is worth most, and the ranking says where that is. It also says something about diminishing returns: after the first few tens of objects the curve flattens, and each further removal buys less. Simulations of the whole environment by the space agencies found that removing about five of the highest-ranked objects a year, beginning soon and continuing for decades, together with near-universal disposal of new satellites at the end of their lives, is enough to stabilise the population in the critical band. Fewer removals leave it growing; many more buy little extra.

The first twenty removals #

The ranked curve in the first figure rises steeply for its first twenty objects and then bends, and the bend has a simple cause.

That structure suggests a plan in two parts. The first part is a short, specific list — fewer than twenty objects, all of one type, in one narrow band of altitude and inclination — which could in principle be handled by one design of removal spacecraft, launched repeatedly into nearly the same orbit. The second part is a longer and more varied list, spread across more orbits and object types, where each removal buys less and the campaign would have to decide whether the marginal object is worth a mission. The arithmetic makes the first part obviously worthwhile and leaves the second to be argued.

Why the heavy stages are where they are #

The dangerous objects were not placed carelessly by the standards of their time; they were left where the physics of launch put them. A satellite launched into a sun-synchronous or high-inclination orbit near 800 kilometres is carried there by an upper stage that ends its burn in nearly the same orbit. Removing the stage afterwards requires it to restart its engine and lower its perigee into the atmosphere, and the upper stages of the 1970s and 1980s mostly could not restart. They were left in orbit next to their payloads, in the altitudes and inclinations that Earth-observation and navigation satellites favoured, and those orbits are exactly the ones in which drag is too weak to clear anything within centuries.

The concentration by inclination makes the problem worse. Many of the heavy stages share a handful of inclinations, near 71, 74 and 83 degrees, so their orbits cross each other frequently and at high relative speeds, near the poles where the orbits converge. A population spread evenly over all inclinations would collide less often than one bunched into a few orbital planes that intersect at the same latitudes every orbit. The ranking used here treats the density of objects as a function of altitude alone; the real analyses, which follow each pair of orbits, find the bunching raises the risk among the listed objects further.

What makes a removal hard #

Every one of these targets is uncooperative. A derelict upper stage has no docking fixture, no working attitude control and no lights; it is usually tumbling, spun up over decades by the slow torques of sunlight, gravity gradient and the magnetic field, sometimes at several degrees a second. A removal spacecraft has to catch up with it in its own orbit — which, at 850 kilometres and near-polar inclination, is a launch of its own — close to within metres, match its tumble or stop it, attach, and then lower both into the atmosphere in a controlled way, so that a nine-tonne object whose dense parts can survive re-entry falls into an empty ocean.

The first steps have been flown. A commercial inspection spacecraft rendezvoused in 2024 with a Japanese upper stage in low orbit, approached to within tens of metres and photographed it in detail — the kind of close inspection a capture mission needs first. Capture of a real derelict has not yet been done; a European mission planned to capture a small adapter left in orbit by a launch is scheduled for the coming years. Each removal of a nine-tonne stage will cost a large fraction of a small launch vehicle’s capacity and an unproven capture system, which is why the question of which stage to remove first is worth this much arithmetic.

There is also a subtler cost. Every removal mission is itself a spacecraft in the most crowded band, approaching a large object closely, and a failed capture could produce the collision it was sent to prevent. The ranking weights the benefit; the risk of the operation has to be weighed against it, and for the heaviest objects both are largest.

Letting the air finish the job #

A removal does not have to carry its target all the way down. The lifetime curve shows why: an object whose perigee is lowered to about 300 kilometres meets air dense enough to bring it down within weeks to months, whatever its apogee. A removal spacecraft that attaches to a derelict and lowers its perigee from 850 kilometres to 300 needs a velocity change of about 150 metres per second, a small fraction of what a fully controlled descent needs. The atmosphere then does the rest.

The catch is where the object falls. An uncontrolled re-entry puts the landing point anywhere under the orbit’s ground track, and a nine-tonne upper stage carries dense parts — engine components, propellant tanks of titanium and steel — that survive re-entry heating and reach the ground. The accepted threshold is that no uncontrolled re-entry should carry more than a one-in-ten-thousand chance of injuring someone, and the heaviest stages exceed it. For them, the removal spacecraft must stay attached and steer the final burn so that the debris falls into the empty South Pacific, which roughly doubles the velocity change and requires the combined vehicle to be controllable to the end. For the smaller objects on the list, a partial lowering and an uncontrolled fall may be acceptable, and the cheaper method is what makes the longer tail of the list worth considering at all.

Drag-enhancement devices — sails or inflatable balloons attached to a derelict to increase its area — work on the same principle without any propulsion, by raising the drag at the object’s existing altitude. At 850 kilometres they are of limited use, because even a large increase in area turns a thousand-year lifetime into a few decades; in the lower bands they are effective, and they are increasingly fitted to new satellites before launch as a guaranteed way down.

What the ranking leaves out #

The weight used here is a product of three factors, each simplified. The density of objects is an illustrative profile shaped like the catalogue’s; the real one has more structure, and it changes as constellations are deployed and old satellites decay. The fragment count uses the standard breakup model’s mass law, which was fitted to impacts far smaller than a collision of two nine-tonne stages and may not extrapolate. The lifetime is a drag lifetime for typical fragments in a mean atmosphere; the real thermosphere swells and shrinks with the solar cycle by a factor of ten in density at these heights, and models of it are wrong by factors of two. None of these changes which class of object tops the list, because all three factors point the same way.

The population itself is synthetic in the figures: built to the real inventory’s classes and numbers — the eighteen heavy stages, the few hundred smaller ones, the dead satellites — but with invented positions within the bands. The real rankings use each object’s actual orbit, and they depend in addition on how often each pair of orbits intersects, which can make particular pairs of objects far more dangerous than their individual weights suggest. The published lists of concerning objects weight exactly those encounters.

And the ranking is a snapshot. As derelicts decay, new satellites are launched and some are removed, the weights change. A removal campaign lasting decades would re-rank its targets as it went.

A problem with a short list #

The general point is that a problem that looks hopelessly large — hundreds of thousands of objects, most of them invisible — has a structure that makes a small part of it decisive. The fragments do most of the damage but are made by collisions among a few thousand intact objects, and among those a few tens dominate, because the factors that make an object dangerous all multiply and all favour the same kind of object. It is the same kind of concentration that makes a mass-and-light budget top-heavy in a debris disc: the quantity that matters scales faster than the count, and the tail of the distribution carries it.

That structure is also why prevention is so much cheaper than cure. Paying to keep an orbit or dispose of a satellite at the end of its life costs a few per cent of its propellant; removing it afterwards costs another mission. Every satellite now launched to the critical band without a reliable way down is a candidate for next century’s list.

Still open: whether five a year is enough, and who pays #

The simulations that found five removals a year sufficient assumed that almost every new satellite would be disposed of properly, and that the population’s growth came mostly from collisions among existing derelicts. Both assumptions are being tested by the large constellations, which have added more satellites to orbit in five years than in the previous sixty, most of them low enough to fall quickly but some in the critical band. Whether the removal rate needed is five objects a year or fifteen depends on the disposal reliability those constellations achieve and on how many of their failures happen in orbits that last for centuries. And the removals themselves serve every operator in the band while costing whoever flies them. How a service whose benefit is the absence of a future collision is to be paid for is not a question celestial mechanics answers, but the ranking says exactly which fifty objects the answer has to reach.