Astronomy & Celestial Mechanics
the sky, computed
Concept

Collisional lifetime — where it appears

The expected time before a body is shattered by an impact from a projectile large enough to disrupt it. In the asteroid belt it is under a billion years for kilometre bodies and tens of billions for the largest, which are mostly primordial.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Debris discs of very different masses, fading to one line. The fractional luminosity of a debris belt at 50 AU — the share of its star's light the dust absorbs and re-radiates — against age, from a million to ten billion years, for belts that start with 1, 10, 100, 1000 Earth masses of planetesimals up to 60 km across. Each stays near its starting brightness until its largest bodies have had time to collide, 16.5 billion years, 1.7 billion years, 165 million years, 17 million years respectively, and then fades as one over the age. A heavier belt starts brighter and grinds itself down faster, and the two effects cancel: after their collisional times all belts lie on the same line, the dashed maximum, whatever their mass. At ten billion years the two heaviest differ by 1 per cent.

A ceiling that forgets how much there was

A belt of planetesimals around a star shows itself only through its dust, and the dust is ground from the belt's largest bodies by collisions. Give the belt more mass and it makes more dust — but it also collides more often, and grinds itself away faster. At late times the two effects cancel exactly, and every belt at a given distance and age lies on the same line of maximum brightness whatever it started with. A disc above that line cannot be a steady cascade, and it is telling of a recent catastrophe.

orbits · Collisional cascade How many families four billion years should have made. The expected number of catastrophic disruptions in four billion years of parents larger than a diameter, in today's belt, for the basalt strength law and for strengths half and twice as large. With the standard law, 23 parents above 100 km, 69 above 50 km, 609 above 20 km. Halving the strength raises the count above 100 km to 31; doubling it lowers it to 18. About twenty families from parents above 100 km have been identified (dot), which the present belt can account for without an earlier, busier one — but only if the strength is near the standard law, and only because the large-parent families are the ones that do not fade.

How often the belt breaks, counted from its own collisions

An asteroid family is the wreckage of one catastrophic collision, and the belt's own collision rate says how many there should be. Combine the chance that two asteroids meet, the number of projectiles big enough to shatter each target, and the energy shattering takes, and today's belt predicts about twenty disruptions of bodies larger than a hundred kilometres in four billion years — close to the twenty families of that size that have been found. The same arithmetic makes the youngest large family a one-in-eighteen event.

orbits · Asteroid families

Named alongside it

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

Catastrophic disruptionAsteroid familyCollisional cascadeDebris discFractional luminosityGiant impactMain beltPlanetesimalSize distributionSpecific energySteady stateYarkovsky effect

All concepts