Concept

Main belt — where it appears

The region between the orbits of Mars and Jupiter holding over a million asteroids larger than a kilometre. Its bodies collide at about five kilometres a second, and its families of fragments record the catastrophic collisions.

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

$A family of 276, or of 582, depending on one number. Membership of a synthetic family against the cutoff velocity used to define it, for a family of 260 genuine fragments ejected at 15 metres a second sitting in a background of 417 unrelated bodies. The clustering is single linkage in the standard proper-element metric, started from one object and grown until nothing more is within the cutoff of anything already absorbed. Three curves: the number of objects claimed, scaled to its largest value; the fraction of the real family recovered; and the fraction of the claim that is background. The shape is the whole difficulty. At low cutoff the family is fragmented and only its core is found. There is then a plateau — near 58 metres a second here, giving 276 members of which 6 per cent are background — and that plateau is what every published family list is chosen at. Past it the count runs away, because single linkage absorbs an object and then searches from the object it has just absorbed: one chance interloper bridges the family to the belt and the algorithm returns half the main belt. Completeness and contamination rise together, so there is no cutoff at which both are good and the plateau is a compromise rather than a discovery.$

A family whose size is a choice

Nothing observable distinguishes a collisional fragment from an asteroid that happens to be nearby. Membership is assigned by clustering at a cutoff velocity, and the same family has 276 members or 582 according to which cutoff is used — with completeness and contamination rising together, so no cutoff is good.

orbits · Asteroid families

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.

Asteroid family Yarkovsky effect Catastrophic disruption Collisional family Collisional lifetime Ejection velocity Hierarchical clustering Interloper Percolation Proper elements Single linkage Size distribution

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