Astronomy & Celestial Mechanics
the sky, computed
Concept

Area-to-mass ratio — where it appears

The ratio of a body's cross-sectional area to its mass, in square metres per kilogram. It sets how strongly non-gravitational forces such as air drag and radiation pressure move an orbit, so light, broad objects are moved far more than dense ones.

Named by 2 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 The three terms of the minimum disposal height. The minimum height above the geostationary ring to which a satellite should be raised at the end of its life, by the international guideline ΔH = 235 km + 1000 · Cᵣ · A/m, broken into its three terms, for reflectivity times area-to-mass ratios of 0.005, 0.01, 0.02, 0.03, 0.05 square metres per kilogram. The first 200 km is the protected zone itself; the next 35 km is the most that the Moon, the Sun and the Earth's uneven gravity lower an orbit's perigee over time; the rest is the eccentricity that sunlight raises every year, which a derivation from first principles puts at 942 km per unit of Cᵣ·A/m for an orbit started circular — the guideline's round thousand. Totals: 240 km, 245 km, 255 km, 265 km, 285 km. The term that depends on the satellite is the one sunlight sets, and for a light satellite with large solar arrays it is the largest.

A graveyard height with a term for sunlight

A geostationary satellite at the end of its life is raised about three hundred kilometres and switched off. The height is written as a formula — 235 kilometres plus a thousand times its reflectivity and area-to-mass ratio — and each term is a separate piece of orbital mechanics, the last one sunlight bending the orbit a little every year.

spaceflight · Station-keeping

Named alongside it

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

Orbital debrisBallistic coefficientBreakup modelConjunction assessmentDisposal manoeuvreEccentricity vectorGeostationary orbitGraveyard orbitHypervelocity impactKessler syndromeOrbital lifetimeProtected region

All concepts