Astronomy & Celestial Mechanics
the sky, computed
Concept

Impact flux — where it appears

The rate at which impactors of a given size strike a surface, per unit area and time. It is measured on the Moon by counting craters on radiometrically dated units, and transferred to other bodies through a modelled ratio that is not measured anywhere.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

A clock that is a straight line for three billion years and then is not. The lunar chronology function: craters of a kilometre or more per square kilometre against the age of the surface, with the count logarithmic and time not. The dashed line is the present impact rate extrapolated backwards, and it accounts for the whole curve up to 3.1 billion years — over that entire range, dating a surface is dividing a crater count by a constant. The rate itself, read off the slope of the drawn curve at the present day, is 8.4·10⁻⁴ craters per square kilometre per billion years, which over the whole Moon is about 32 new craters of a kilometre or more per million years. Past three and a half billion years the exponential term takes over and the curve turns almost vertical: ground that is 4.1 billion years old carries 26 times the crater density of ground 3.5 billion years old, for a difference in age of six hundred million years. Most of the craters on the Moon were made in a small fraction of its life, and nothing that happened after them is recorded anything like as densely. The six marked ages are laboratory measurements on returned rock, and they are what makes the curve a chronology rather than a shape — the Moon is the only body whose crater counts and whose radiometric ages have ever been measured on the same square kilometre.

A surface dated by counting holes in it

Every age quoted for a surface in the solar system outside the Earth — a Martian lava flow, a crater on Mercury, the ice of Europa — comes from counting craters and passing the count through one curve. That curve was calibrated on nine square kilometres of the Moon, and it is nearly a straight line for three billion years and then is not.

orbits · Surface chronology Nine dates, and a gap from 0.8 to 3.1 billion years. The lunar crater chronology and the samples that fix it: crater density per square kilometre against age, the density axis logarithmic. Every point is a laboratory measurement on returned rock — six mare and highland units dated by crystallisation, four young craters dated by how long their ejecta has been exposed to cosmic rays. The curve is a fit of N(T) = A(e^(λT) − 1) + BT with the exponential rate swept over 6 to 7.9 per billion years and the two amplitudes refitted at each; the best fit lands at λ = 6.95, against the 6.93 the published chronology uses, which is a check on the fitting rather than an input to it. What the figure exists to show is where the calibrating samples fall in time. Six of them lie between 3.15 and 3.92 billion years, four between 0.026 and 0.80, and there is nothing whatever between 0.8 and 3.1 — a gap covering half the age of the solar system. The consequence is drawn as the spread of the acceptable curves: a surface whose crater density says 3.5 billion years is dated to ±0.03 billion by this family, and a surface at 2 billion to ±0.13. The chronology is a measurement where the astronauts landed and an interpolation everywhere else.

Nine dates for every surface in the solar system

Every absolute age quoted for a planetary surface — Martian volcanism, Mercury's plains, the resurfacing of Europa — descends from radiometric dates on rocks returned from nine landing sites on one body. Six of them fall between 3.15 and 3.92 billion years, and there is nothing at all between 0.8 and 3.1.

orbits · Surface chronology 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.

Crater countingProduction functionChronology functionLate heavy bombardmentMarsPoisson statisticsResurfacingSecondary cratersAtmospheric entryCalibrationCrater chronologyCratering rate

All concepts