Astronomy & Celestial Mechanics
the sky, computed
Concept

Secondary craters — where it appears

Craters made not by impactors from space but by the debris thrown out of a larger impact. They are numerous at small sizes and cluster round their parent crater, so they contaminate crater counts used to date surfaces.

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

The age a handful of craters allows. The probability of each age for a 100 square-kilometre surface on Mars, given a count of 0, 3, 10, 30, 100 craters 50 metres across or larger, per unit of the logarithm of age, with a uniform prior on age. No craters: younger than 45 Myr at 95 per cent, and nothing more; 3: 55 Myr, from 31 Myr to 88 Myr; 10: 158 Myr, from 116 Myr to 212 Myr; 30: 457 Myr, from 382 Myr to 547 Myr; 100: 1,502 Myr, from 1,359 Myr to 1,660 Myr. Each tenfold increase in the count narrows the range by about the square root of ten, from a factor of 2.8 with three craters to 1.22 with a hundred. The counting error is only part of the story: the chronology converting a crater density into an age is uncertain by a factor of about 1.6 on Mars before any crater is counted.

A young surface dated by a handful of holes

The surfaces that decide whether a planet is still geologically alive — the freshest lava on Mars, the smoothest ice on Europa — are the ones with fewest craters to count. Their ages are Poisson estimates from a few dozen holes, they cannot be younger than the area and crater size allow, and a fraction of a per cent of older ground in the counting area can double them. What survives best is not when a surface formed but which of two surfaces formed first.

orbits · Surface chronology Craters forming on Mars now, against the rate the clock assumes. The rate at which craters larger than a given diameter form on Mars, per square kilometre per year, against that diameter, both on logarithmic scales. The black curve is the production function scaled from the Moon, the rate every crater-count age on Mars assumes. The red curve and its points are the craters found forming between successive orbital images — 248 above 3.9 metres over the survey's coverage, 1.65 × 10⁻⁶ per square kilometre per year, with a cumulative slope of −2.2, shallower than the scaled function's −3. At 4 metres the scaled function predicts 6.4 times what is seen; the two cross near 42 metres; above that the survey has found too few craters to say. Bars are the counts' Poisson errors.

A clock checked by the craters it is making now

Every young age on Mars is a crater count divided by a rate borrowed from the Moon. Since 2006 the orbiting cameras have been watching that rate happen: hundreds of fresh craters, metres across, that were not there in the previous image. They form several times less often than the borrowed rate predicts at the smallest sizes, and more often than it at a few tens of metres — and the youngest surfaces on Mars are dated from exactly the sizes where the two disagree most.

orbits · Surface chronology

Named alongside it

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

Chronology functionCrater countingImpact fluxMarsPoisson statisticsProduction functionAtmospheric entryResurfacingSurface chronology

All concepts