Astronomy & Celestial Mechanics
the sky, computed
Concept

Breakup model — where it appears

An empirical rule for how many fragments of each size a collision or explosion in orbit produces. For a catastrophic collision the count above a size L goes as the colliding mass to the power 0.75 times L to the power −1.71.

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

1,236 fragments anybody can see, and 63,397 that can kill. The cumulative fragment size distribution from the standard breakup model, for a catastrophic collision involving 1500 kilograms and for an explosion of the same object, both axes logarithmic. The exponents are −1.71 and −1.60, measured off the drawn curves; they are empirical, fitted to ground tests and to the observed clouds of real events, and they are steep. What follows is the reason a catalogue of tracked objects is not a catalogue of the hazard. Above ten centimetres — the size a ground radar can follow in low orbit — the collision makes about 1,236 pieces. Above one centimetre, which is the size that goes through a spacecraft at ten kilometres a second and cannot be shielded against, it makes 63,397. Above a millimetre, which shielding does stop but which erodes a surface, 3,251,385. The tracked population is under two per cent of the lethal one, and the difference is not a gap in the catalogue that better radars will close — objects of a centimetre at a thousand kilometres are beyond any sensor that has been proposed. An explosion makes fewer large pieces than a collision and a comparable number of small ones, because an explosion divides one object and a collision destroys two.

The fragments nobody can see and cannot shield against

A catastrophic collision in low orbit makes about a thousand pieces big enough to track and sixty thousand big enough to destroy a spacecraft. The catalogue is under two per cent of the hazard, the gap is not one better radars will close, and the fragments' lifetimes span a factor of twenty-five within a single event.

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 Too slow to shatter. The kinetic energy a projectile brings per gram of a 2,000 kg satellite, against the impact speed on logarithmic axes, for projectiles of 1, 10, 100 kg. Above 40 joules per gram (dashed) the standard breakup model counts the collision as catastrophic — the whole target is shattered; below it, only a crater is made. The speeds needed are 12.6, 4.0, 1.3 km/s respectively. In the geostationary ring, where nothing crosses faster than about 0.8 km/s (shaded), only a projectile of hundreds of kilograms — another satellite — can shatter a satellite; in low orbit, at ten kilometres a second, a kilogram can.

A ring where nothing leaves and little shatters

Every argument about orbital debris in low orbit ends in the atmosphere, which pulls fragments down in years or centuries. The geostationary ring has no atmosphere, so its removal term is exactly zero and anything left there stays for millions of years. It is saved by a second fact of the same geometry. Everything in the ring moves at nearly the same speed in nearly the same direction, so collisions there are slow, and a slow collision usually leaves a crater where a fast one leaves a cloud.

spaceflight · Orbital debris

Named alongside it

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

Orbital debrisKessler syndromeOrbital lifetimeActive debris removalArea-to-mass ratioBallistic coefficientCatastrophic breakupCollision probabilityCollision velocityConjunction assessmentGeostationary orbitGraveyard orbit

All concepts