Generator

The crater-chronology generator

Below 410 metres the oldest surface stops counting

Below 410 metres the oldest surface stops counting. Cumulative crater counts — the number of craters at least as large as D, per square kilometre — for four lunar surfaces of different ages, with both axes logarithmic. The production curves are parallel straight lines of slope −2.00, one above the other in proportion to how long each surface has been exposed: age enters as a vertical shift and nothing else. The heavy line crossing them is the empirical saturation density, of slope −1.83, which is where craters are packed so tightly that each new one destroys about one old one and the count stops rising. Because production is the steeper of the two, saturation is reached first at the small diameters, and it is reached at all only on ancient ground: the 3.9 Gyr surface saturates below 410 metres while the 0.5 Gyr surface does not saturate anywhere on this plot. So a count that includes small craters on old terrain is measuring the strength of the regolith rather than the age of the ground, and the diameter at which the measured distribution bends away from the production slope is where a count has to stop being believed.

Cumulative crater counts — the number of craters at least as large as D, per square kilometre — for four lunar surfaces of different ages, with both axes logarithmic. The production curves are parallel straight lines of slope −2.00, one above the other in proportion to how long each surface has been exposed: age enters as a vertical shift and nothing else. The heavy line crossing them is the empirical saturation density, of slope −1.83, which is where craters are packed so tightly that each new one destroys about one old one and the count stops rising. Because production is the steeper of the two, saturation is reached first at the small diameters, and it is reached at all only on ancient ground: the 3.9 Gyr surface saturates below 410 metres while the 0.5 Gyr surface does not saturate anywhere on this plot. So a count that includes small craters on old terrain is measuring the strength of the regolith rather than the age of the ground, and the diameter at which the measured distribution bends away from the production slope is where a count has to stop being believed.

3 essays call crater-chronology. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Every figure listed here is the same construction drawn at different numbers, so a correction to one is a correction to all of them.

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

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.

A branch that adds nothing above 1 km and everything below it. Cumulative crater counts on a 3.5-billion-year-old surface, with the population split into the craters made by objects arriving from outside and the craters made by blocks thrown out of larger ones on the same surface. The two are indistinguishable in a photograph and completely different as a statistic. Secondaries stop at about 1 kilometre, because that is the largest crater a block leaving at a few hundred metres a second can excavate, so the upper half of the plot is unaffected. Below it they are steeper — slope -3.2 against the primaries' -2 — and by the smallest diameter drawn they outnumber the primaries 292 to one. A count taken at 100 metres and read through the primary production curve returns an age of 4.34 billion years for ground that is 3.5, and it returns it with a small formal error, because the counting statistics are excellent. The error is not in the counting.

The craters that were not primary

Counting craters dates a surface, and the method works because impacts from space arrive at a known rate. Some of the holes were not made from space. They were made by rock thrown out of the larger holes on the same surface, and they are far more numerous than anything that arrived.

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 anchors 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.

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