Astronomy & Celestial Mechanics
the sky, computed
Concept

Post-mission disposal — where it appears

Removing a satellite or rocket stage from a crowded orbit at the end of its working life, by lowering it to re-enter or raising it clear. Its reliability decides how fast new launches add to the long-lived debris population.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

A quadratic and a linear, crossing at 149 objects. The two rates that decide whether a shell at 900 km is stable, against how many objects are in it. Production goes as N² — every collision needs two objects, so the number of collisions is proportional to the square of the population, and each one is taken here to make 1600 trackable fragments. Removal goes as N, because drag acts on each object independently and takes 1,195 years to do it at this altitude. A quadratic and a linear cross exactly once, at 149 objects in this shell, and above that crossing the population grows with nothing launched. The shell presently holds about 2,280, which is 15 times the crossing. Every number on the production side is uncertain by a factor of a few — the fragment yield most of all, and the cross-section is calibrated against an observed collision rate rather than measured — so the position of the crossing carries that uncertainty with it. The shape does not, and the shape is the argument: a quadratic overtakes a linear once and never comes back, the crossing falls as the altitude rises because the lifetime is in the denominator, and what results is a threshold rather than a trend.

A collision rate that needs no collision

The flux through an orbital shell is a gas-kinetic calculation with no orbits in it. Production goes as the square of the population and removal goes as the first power, so a quadratic overtakes a linear once and never comes back — and which side of that a shell is on is decided by its altitude.

spaceflight · Orbital debris How much future debris each removal prevents. The share of the derelict population's expected future fragment production removed, against the number of objects removed, out of 1858, for three orders of removal: by the ranking weight — collision rate times fragments times fragment lifetime — by mass alone, and at random. Removing the 200 top-ranked objects removes 70 per cent; the top fifty alone, 45 per cent; the top ten, 19. Removing by mass does nearly as well at first and falls behind, because mass is most of the weight and altitude the rest. Removing at random, fifty objects remove 3.5 per cent. The population is synthetic, built to the published inventory's broad shape; the concentration of risk in a few tens of heavy upper stages is the finding the real analyses also make.

Fifty objects that hold most of the future

Low Earth orbit holds thousands of dead satellites and spent rocket stages, and the debris of the future will come mostly from their collisions. But not in equal shares. A derelict's contribution is the chance it is hit, times the fragments it would make, times how long they would stay up — and all three favour the heaviest objects in the most crowded, highest orbits. Ranked that way, a few tens of rocket bodies near 850 kilometres carry nearly half the risk, and the arithmetic of cleaning space becomes the arithmetic of choosing them.

spaceflight · Orbital debris Removals a year, set almost entirely by one percentage. The number of derelicts that must be removed each year to hold a shell at 50 per cent of its critical count, against the fraction of disposals that fail, for a 650-satellite constellation at 800, 1000, 1200 km. Because a dead satellite at these heights stays up for centuries, almost every failure has to be removed by hand, and the removal rate is very nearly the failure rate: at 1200 km, 13 a year if ninety per cent of disposals succeed and 1.3 if ninety-nine do. The removal budget is therefore set by an engineering reliability rather than by the orbital environment, and a percentage point of reliability is worth a fixed number of removal missions a year for as long as the constellation flies. Five removals a year is enough for this shell only above 96.2 per cent reliability.

A removal rate set by one percentage

How many dead satellites have to be taken out of a high orbit each year is decided less by the orbit than by how often a satellite fails to dispose of itself. Above eight hundred kilometres a derelict stays for centuries, so the removal rate needed to keep a shell stable is very nearly the failure rate, and moving disposal reliability from ninety per cent to ninety-nine cuts the work tenfold.

spaceflight · Orbital debris

Named alongside it

The objects these essays reach for when they reach for this one.

Kessler syndromeOrbital debrisOrbital lifetimeActive debris removalAtmospheric dragBallistic coefficientBreakup modelCollision cross-sectionCollision probabilityCollision rateConjunction analysisCritical density

All concepts