Orbital debris cascade

Why can a single collision in orbit make a whole altitude band unusable for decades?

Two spacecraft, each a few metres across, touch once, somewhere above the North Pole. The natural expectation is a local mess — an expensive accident, a cloud of wreckage, and in due course the sky closing over it. Instead the accepted worry is that one such event can degrade an entire shell of orbits for longer than a career.

The usual explanation is that space is getting crowded. That is worth checking, because if crowding were the mechanism the numbers ought to show it.

So check. Take a shell a hundred kilometres thick around an altitude of 800 kilometres. Its radius from Earth's centre is about 7,170 kilometres, so its volume is roughly six times ten to the nineteenth cubic metres. Now be maximally unfair to the sky and cram every one of the roughly thirty thousand tracked objects in all of Earth orbit into that single shell. You would have one object per cube about 130 kilometres on a side. Whatever this is, it is not a crowd. Dropping that intuition is what makes room for the real mechanism.

If not density, then what? Speed. At 800 kilometres a satellite moves at about 7.5 kilometres per second, and two objects on crossing orbits meet at closing speeds of order 10 — head-on, nearer 15. At that speed material strength stops being relevant: the impact pressure vastly exceeds any solid's ability to hold itself together, so both bodies partly vaporise and the target is not dented but disassembled. A one-centimetre aluminium sphere weighs about 1.4 grams, and at 10 kilometres per second carries around 70 kilojoules — about what a 200-kilogram motorcycle carries at highway speed. That fragment is too small to track from the ground, and it will destroy a tonne of satellite.

Now the step that turns an accident into a mechanism. What does a collision do to the number of objects? Not add one. The 2007 Chinese anti-satellite test against Fengyun-1C, at about 865 kilometres, produced more than three thousand catalogued fragments and far more too small to catalogue; the 2009 collision between Iridium 33 and Cosmos 2251, near 789 kilometres, produced roughly two thousand. Each event multiplies the population.

And how does risk scale with population? Collisions require pairs, and the number of pairs among n objects is about n squared over two. Double the population and you roughly quadruple the encounter rate. So we have a loop with the wrong sign.

Two questions remain, and they set the timescale. Why should a collision over the Pole endanger orbits everywhere in the band? Because fragments do not stay a cloud. They depart with a spread of velocities, acquiring a spread of orbital periods and slightly different orbital planes — and Earth's equatorial bulge makes each plane precess at a rate depending on altitude and inclination. Orbits that begin nearly together drift apart in orientation, and within months to a few years the cloud is smeared into a shell wrapped round the planet. A single event contaminates every orbit in its altitude range.

And why decades? Because only one process removes debris — atmospheric drag — and the atmosphere thins nearly exponentially with height. Below about 400 kilometres, drag clears things in months to a couple of years, which is why the Space Station must be reboosted. Near 800 kilometres, lifetimes run to decades and beyond. Above roughly 1,000 kilometres, removal is effectively absent on any human timescale. The sink is not a constant to be compared against the source; it collapses as you climb.

Put the two together and Donald Kessler and Burton Cour-Palais's 1978 result appears. Compare production, growing as n squared, with removal, roughly n divided by the drag lifetime. Below some critical population the sink wins and the band recovers. Above it, the population grows on its own even if every launch stopped tomorrow. That is why the word is cascade and not congestion: crossing the threshold changes the sign of the trend, not the size of the problem. It also explains why altitude matters so much, since the drag lifetime sits inside the criterion — the critical population near 1,000 kilometres is far smaller than near 400.

Whether parts of low orbit have already crossed that line is genuinely argued. NASA analyses have concluded the population around 900 to 1,000 kilometres would grow even with no further launches; other assessments make the answer depend heavily on how reliably operators actually deorbit spent hardware.

Three refinements connect those steps. First, "unusable" is a statement about economics and risk tolerance, not physics. Nothing forbids flying through a debris shell; what changes is that shielding cannot stop centimetre fragments, tracking cannot see them, and the expected loss rate makes the orbit not worth insuring or occupying.

Second, the cascade is slow — not a chain reaction on the scale of hours but a population trend playing out over decades, which is why it is so easy to discount and so hard to reverse.

Third, mitigation follows from the criterion rather than from sentiment. Deorbit rules shorten the effective lifetime and so raise the critical population; flying constellations low — around 550 kilometres, where drag genuinely bites — keeps the sink strong; and removing whole intact objects matters more than removing fragments, since a derelict rocket body is a large target whose destruction would supply thousands of new fragments at once.

• How conjunction warnings are computed, and why most predicted close approaches are never manoeuvred against.
• Why active debris removal targets a handful of large derelicts rather than the far more numerous fragments.
• What the atmosphere does with thousands of tonnes of re-entering aluminium.

Every term the collection defines is gathered in the glossary.