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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.

Assumes Surface chronology and Collisional cascade.

17 min read 8 figures Measuring the unreachableSmall perturbations, large consequences

Crater counting is the only method that dates a surface anywhere in the solar system without going there. It rests on one assumption that is close to unimpeachable — objects arrive from space at a rate that is known as a function of time — and one that is not: that the holes being counted were made by those objects.

A large impact does not merely excavate a hole. It throws out a mass comparable to the mass it excavated, at speeds of hundreds of metres a second, and that material comes down again. Where it lands it makes craters, and those craters are indistinguishable from small primaries in a photograph. They are also enormously more numerous.

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.
Fig. 1 The two populations on one surface. Above about a kilometre there are no secondaries at all, because a block leaving at a few hundred metres a second cannot excavate a crater larger than that, and the count is honest. Below it the secondary branch is steeper — a slope of about −3 against the primaries’ −2 — and by fifty metres it outnumbers the primaries by hundreds to one. The two curves are the same photograph counted twice, and nothing in the image says which crater belongs to which.

The problem is not a curiosity at the edge of the method. It is the difference between a surface being one billion years old and four, on exactly the surfaces where the answer is most wanted — the young volcanic plains, the recent flows, the deposits that might record something that happened rather than something that has always been there.

Why the contamination has an edge

The saving grace of the problem is that it is confined, and the confinement follows from mechanics rather than from observation.

A block ejected from a crater on an airless body follows a ballistic arc. Its range is set by its launch speed, and its ability to make a crater when it lands is set by the same speed. A primary arrives at some tens of kilometres a second — the escape speed of the Sun at that distance, near enough — and carries kinetic energy per unit mass some four orders of magnitude larger than a block leaving at half a kilometre a second. So an impactor of a given mass makes a very much larger crater when it comes from space than when it comes from next door.

Run that backwards and it gives the edge. The largest secondary on a body is made by the largest block the largest primary threw out, at the fastest speed at which a block survives launch, and for the Moon that combination gives craters of about one kilometre. Above that diameter every crater is a primary, and a count restricted to large craters is clean by construction.

A branch that adds nothing above 4 km and everything below it. Cumulative crater counts on a 3.9-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 4 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 11532 to one. A count taken at 100 metres and read through the primary production curve returns an age of 4.60 billion years for ground that is 3.9, and it returns it with a small formal error, because the counting statistics are excellent. The error is not in the counting.
Fig. 2 An older surface with a more violent history, where the largest primaries were larger and the secondary branch therefore reaches to four kilometres rather than one. The clean part of the distribution has shrunk by a factor of four in diameter, which on a real body is a factor of sixteen in area and therefore in the number of craters available to count. That is the whole difficulty of dating ancient terrain: the diameters where the statistics are good are exactly the diameters where the population is contaminated.

The trouble is that large craters are rare. The primary production function falls steeply with diameter, so restricting a count to craters above a kilometre on a small area leaves a handful of objects and a Poisson error of tens of per cent. The temptation to go smaller is enormous, and going smaller is exactly what invites the contamination.

The arithmetic of that temptation is worth spelling out because it is what drives practice. A cumulative production function of slope −2 means that halving the diameter threshold multiplies the number of countable craters by four. Going from one kilometre to a hundred metres multiplies it by a hundred, which turns a ten per cent counting error into a one per cent one. On a target the size of a single lava flow — a few hundred square kilometres — counting above a kilometre may yield three craters, which is not a measurement at all, while counting above fifty metres yields thousands. There is no way to date a small young unit without going small, and there is no way to go small without meeting this problem. The method’s precision and its accuracy pull in opposite directions, and the pull is steep.

A further wrinkle is that the secondary branch is not a fixed feature of a body. It is a feature of the neighbourhood: a patch of ground a few crater radii from a fresh ten-kilometre impact is drowned in secondaries, and a patch on the far side of the body from every recent large impact is comparatively clean. So the contamination varies from site to site by orders of magnitude, and two counts on terrain of genuinely identical age can differ by a factor of three in the age they return.

What it does to the answer

The measurement being made is a density of craters, converted to an age through a chronology function calibrated on the Apollo and Luna samples. Inflating the density inflates the age. The interesting question is by how much, and the answer has a shape worth knowing.

One surface, one age, and an answer that depends on which craters were counted. The age returned by a crater count on 3.5-billion-year-old ground, against the diameter the count was taken at. Above 1 kilometre there are no secondaries and the answer is 3.5 exactly, at every diameter, which is the property that makes the method work at all. Below it the count is inflated — 128-fold at 100 metres — and the inferred age climbs to 4.34 billion years. Two things about the shape are worth reading. The rise is steep in the diameter and shallow in the age, because the lunar chronology function is exponential in time: a count wrong by a factor of 128 is an age wrong by 0.84 billion years, and near the top the curve flattens against the age of the solar system, so a badly contaminated count returns something ancient rather than something absurd. And the curve is monotonic, so a count taken over a range of diameters and averaged does not average the error away; it is a systematic, and it has a sign.
Fig. 3 One surface, one age, and the answer a count returns as a function of the diameter at which the count was taken. Above the secondary knee the answer is 3.50 billion years at every diameter, which is the property that makes the method work. Below it the answer climbs steeply, past four billion years by the time the count reaches a hundred metres. The rise is steep in the diameter and shallow in the age because the lunar chronology function is exponential in time: a count wrong by a factor of thirty is an age wrong by half a billion years, and the curve flattens against the age of the solar system rather than running away.

Two features of that curve matter more than its height.

It is monotonic, so averaging does not help. A count taken over a range of diameters and combined is a weighted average of a set of answers all of which are biased in the same direction. The formal error shrinks and the systematic does not.

And it saturates. Because the chronology function rises exponentially towards the early solar system, a badly contaminated count on young ground does not return an absurd number; it returns something around four billion years, which is a perfectly plausible age for a lunar surface. The failure mode is not a result that looks wrong. It is a result that looks old.

One surface, one age, and an answer that depends on which craters were counted. The age returned by a crater count on 1.2-billion-year-old ground, against the diameter the count was taken at. Above 1 kilometre there are no secondaries and the answer is 1.2 exactly, at every diameter, which is the property that makes the method work at all. Below it the count is inflated — 128-fold at 100 metres — and the inferred age climbs to 4.11 billion years. Two things about the shape are worth reading. The rise is steep in the diameter and shallow in the age, because the lunar chronology function is exponential in time: a count wrong by a factor of 128 is an age wrong by 2.91 billion years, and near the top the curve flattens against the age of the solar system, so a badly contaminated count returns something ancient rather than something absurd. And the curve is monotonic, so a count taken over a range of diameters and averaged does not average the error away; it is a systematic, and it has a sign.
Fig. 4 The same bias on much younger ground. The floor is 1.2 billion years and the small-diameter count returns something over four — a factor of more than three in age, and a much larger relative error than on old terrain, because the exponential chronology means the same multiplicative excess in the count buys far more time when the true age is low. A surface a billion years old that is counted at fifty metres can be reported as ancient, and there is no internal evidence in the count that anything has gone wrong.

This is why the discovery of the problem was so disruptive. It was not that ages were wrong by a known factor that could be divided out. It was that the ages of young surfaces, which are the ones the method is most useful for, were the ones most vulnerable.

The direction of the bias is also worth stating on its own, because a systematic with a known sign is a different object from an unknown error. Secondaries only ever add craters. There is no mechanism by which they remove any, so a contaminated count is always too high and a contaminated age is always too old. That makes every crater age a kind of upper limit, and it makes any comparison between two counts taken at the same diameter on differently contaminated terrain unreliable in a way that a comparison at large diameters is not. The relative chronology of a planet’s surface units — which came first — is the part of the method most people actually use, and it is not immune.

There is one further consequence, and it is the one that makes the problem hard to route around by being careful. Because the contamination depends on the local history of large impacts, it is correlated with the very quantity being measured. Old terrain has had more large impacts on it, so it has more secondaries; young terrain has had fewer, so it has fewer. The bias therefore does not merely add a constant offset to every age — it stretches the age scale, making old surfaces look older than they are by more than young ones do. Any attempt to calibrate the effect out by measuring it on one surface and applying the correction elsewhere runs straight into that.

The statistic that does not use a size

The size argument for identifying secondaries has an uncomfortable circularity: it assumes the production function whose slope is exactly what is in dispute. A better instrument would be one that does not use the size at all.

There is one, and it uses the fact that secondaries are not independent events. Blocks come from a single primary in a single moment, and they land in rays, clusters and chains. Primaries arrive from space independently, so their positions are a Poisson process.

A statistic that tells them apart without measuring one crater. Two fields of the same number of craters over the same area — one where every crater arrived independently and one where three quarters of them came from five parents — and the distribution of each crater's distance to its nearest neighbour. The independent field follows the closed form for a Poisson process, drawn as the dashed curve, with a median separation of 0.080 of the field's width. The clustered field's median is 0.023, and its curve rises almost vertically at small separations because most craters have a sibling a few radii away. Neither statistic uses a crater's size, which is what makes it the right instrument: the size argument for identifying secondaries assumes the production function that is in question, and this one assumes only that arrivals from space are independent events. What it cannot do is label an individual crater. It says what fraction of a field is contaminated, and that is enough to decide whether a count can be believed.
Fig. 5 Two fields of the same number of craters over the same area — one where every crater arrived independently, one where three quarters of them came from five parents — and the distribution of each crater’s distance to its nearest neighbour. The independent field follows the closed form for a Poisson process exactly. The clustered field’s median separation is a third of it, because most craters have a sibling a few radii away. Neither statistic looks at a crater’s size, which is what makes it the right instrument for a question about sizes.

The distinction being exploited is a distinction between a process with a length scale and a process without one. A Poisson field has no scale: the distribution of nearest-neighbour distances depends only on the density, and the shape of the curve is fixed. Any clustering imprints the scale of the clump, and the imprint is at small separations where the Poisson field has almost nothing. That is why the test is sensitive even when the contaminated fraction is modest — it is comparing something with something close to nothing rather than comparing two comparable numbers.

The test is old and the application is not. Nearest-neighbour statistics, two-point correlation functions and simple counts of chains and clusters are all sensitive to the same thing, and they can be computed on a crater catalogue for nothing. What they cannot do is label an individual crater; a secondary that happens to have landed alone is unidentifiable by any means. So the statistic returns a fraction, and the fraction is what decides whether a count can be believed.

A statistic that tells them apart without measuring one crater. Two fields of the same number of craters over the same area — one where every crater arrived independently and one where three quarters of them came from five parents — and the distribution of each crater's distance to its nearest neighbour. The independent field follows the closed form for a Poisson process, drawn as the dashed curve, with a median separation of 0.054 of the field's width. The clustered field's median is 0.040, and its curve rises almost vertically at small separations because most craters have a sibling a few radii away. Neither statistic uses a crater's size, which is what makes it the right instrument: the size argument for identifying secondaries assumes the production function that is in question, and this one assumes only that arrivals from space are independent events. What it cannot do is label an individual crater. It says what fraction of a field is contaminated, and that is enough to decide whether a count can be believed.
Fig. 6 A denser field in which only a third of the craters are clustered, which is closer to what a real count on moderately contaminated terrain looks like. The two curves are much nearer together and they still separate cleanly at small separations, because a clump imprints its signature at the scale of the clump and a Poisson process has no scale at all. The measurement is a difference between two curves rather than a threshold on one, and its sensitivity comes from the smallest separations where the independent field has almost nothing.

It is worth being explicit about what the statistic can and cannot deliver, because it is often quoted as though it settled the matter. It measures the excess of close pairs over what independence would give, which is a lower bound on the contaminated fraction: a secondary field that has been thoroughly stirred, or one whose parent crater is far enough away that the rays have spread, leaves no clustering signature and is counted as primary. So a clustering test that comes back clean does not certify a count. It only fails to condemn it. The asymmetry is annoying and it is the honest situation, and it is the reason the disagreement over background secondaries has stayed open for two decades — the instrument that identifies them is blind to precisely the population whose size is in dispute.

What was actually measured

The argument was made concrete on Mars, at a crater called Zunil, in 2005. Zunil is ten kilometres across, young, and surrounded by a field of small craters that can be traced to it directly: they are aligned in rays radiating from it, they are shallower than primaries of the same size, and many are in tight clusters or elongated chains. Counting them gave something like ten million secondaries above ten metres from that single impact.

There is a second observable that made the identification firm rather than suggestive: the depth-to-diameter ratio. A secondary arrives at a few hundred metres a second rather than at ten kilometres a second, so it excavates less deeply for its width, and it often arrives at an oblique angle, so it is elongated. Neither property is decisive for a single crater — primaries are sometimes shallow and sometimes oblique — but the two are measurable in bulk from a stereo image, and the population around Zunil is shallower and more elongated than the population far from it by amounts that no plausible primary distribution could produce.

Ten million is the number that mattered. The total number of primaries above ten metres expected on the whole of Mars in the time since Zunil formed is far smaller. So on the terrain around Zunil, essentially every small crater is a secondary, and a count of small craters there measures Zunil rather than the age of the ground.

The same argument was then run on the Moon and found the same thing. The most direct check is the one where the answer is independently known: several lunar surfaces have radiometric ages from returned samples, and the crater ages derived from large-diameter counts agree with them while the ages derived from small-diameter counts run systematically old.

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.
Fig. 7 The uncontaminated version of the method, for comparison: production curves for four surface ages against the empirical saturation line. Everything in this figure is what crater counting is supposed to be — parallel lines whose vertical offset is the age, and a single ceiling that says where a count stops meaning anything. The whole of the argument in this essay is about a population that is not in this diagram at all and that lands underneath the left-hand end of every one of these curves.
A 128.8-million-year-old collision, dated from the shape of a scatter plot. The Erigone family: 165 members drawn at their diameters and their proper semi-major axes, with inverse diameter up the page. The cloud is a V, and the V is a clock. Each member has been drifting in semi-major axis ever since the collision at a rate that goes as one over its diameter, with a sign set by which way it spins — prograde outward, retrograde inward — so after 130 million years the small members have moved far and the large ones have barely moved at all. Plotted against 1/D that envelope is a straight line through the family's centre, and its slope is the drift rate for a one-kilometre body multiplied by the elapsed time. Fitting the two edges of the points actually drawn here returns 128.85 million years against the 130 the members were generated from. The rounding at the bottom is not an artefact: it is the ejection velocity, some 15 metres per second, which every member got at the moment of the collision and which is the same for all sizes. The picture cannot show the interlopers — background asteroids that happen to lie inside the V and have nothing to do with the family — and it cannot show the members that have drifted into a resonance and left the belt entirely, which is the reason the oldest families have the softest edges.
Fig. 8 Where the impactors come from, on the side of the argument that is not in dispute: an asteroid family spread in semi-major axis by the size-dependent drift that follows a collision. The population arriving at the inner planets is drawn from distributions like this one, and its size-frequency slope is a measurable property of the asteroid belt rather than an assumption of the chronology. That is the reason the primary production function is the trustworthy half of the calculation and the secondary branch is not.

The controversy is not fully settled and the disagreement is quantitative rather than conceptual. Nobody disputes that secondaries exist or that they dominate the small-diameter population near a fresh large crater. What is disputed is what fraction of the background small craters, far from any identifiable source, are secondaries from impacts long ago whose rays have faded. Estimates range from a small contamination to nearly all of them, and the difference between those two positions is a factor of a few in the ages of every young surface in the solar system.

The practical protocol that has emerged from all of this is unglamorous and worth stating, because it is what the argument is for. Count at the largest diameters the area allows and report the Poisson error honestly, even when it is large. Plot the answer against the counting diameter and show the plot rather than a single number. Compute a clustering statistic on the catalogue and report the contaminated fraction. And where a small-diameter count is unavoidable, treat the result as an upper limit on the age rather than as a measurement of it. None of that recovers the precision the small craters appeared to offer; all of it replaces a precise wrong answer with an imprecise defensible one.

Where the picture stops

Three limits stand out, and the second one is the reason the problem is worse on some bodies than on others.

Saturation is a different effect and it looks similar. On very old terrain the craters are packed so tightly that each new one destroys an old one, and the count stops rising with age. That also flattens a size-frequency distribution at the small end, and it also has to be diagnosed before a count is believed. The two can be separated — saturation depletes, contamination adds — but only if the production function is trusted, which returns to the same circularity.

The escape speed decides how bad it is. On a body with a low escape speed, most ejecta leaves entirely and comes back as sporadic impacts distributed over the whole surface, or does not come back at all. On a large body almost all of it lands nearby. So the Moon and Mars are heavily affected, and a small asteroid is affected differently: a rubble pile held together by almost nothing loses its ejecta and gains a global veneer instead of local clusters.

And an atmosphere removes the small end entirely. On Mars the smallest primaries burn up or are decelerated below crater-forming speed, so the primary production function turns over at a few tens of metres while the secondary branch does not. That makes the contamination at small diameters worse than on the Moon, not better, and it is the reason the Zunil work was done on Mars.

The general shape of the trouble

The defect this essay is about has a shape that recurs throughout the collection, and it is worth naming separately from the craters.

A measurement is made by counting things. The count is converted to a physical quantity by a function that was calibrated on a population. A second population, which the calibration did not include, contributes to the count in a way that is negligible at one end of the range and dominant at the other. Because the contamination is monotonic in the counting variable, it is invisible in any single count; it shows up only as a trend — the answer depending on the range over which the count was taken, when it should not.

The same shape appears in a survey’s luminosity function, where an unrecognised second population at the faint end changes the slope; in the sizes of a debris population, where the small end is dominated by fragments rather than by original bodies; and in a collision rate estimated from a flux, where the small end of the impactor distribution is the part that is least directly observed and most heavily extrapolated. In every case the honest report is not a number but a number together with the range it was measured over.

That trend is the diagnostic, and it is nearly always available for free. If a measurement is supposed to be independent of some choice, plotting the answer against that choice costs nothing and is the most reliable single test of a systematic that a counting experiment has. A collision dated from the spread of an asteroid family is checked the same way, and so is every luminosity function in this collection.

One closing thought about why this is filed as a rung on the chronology ladder rather than as a caveat. Crater counting is the only chronometer that works on a surface nobody has visited, and it is therefore the instrument that fixes the timeline of the entire solar system beyond the handful of sampled sites. A systematic in it does not corrupt one measurement; it propagates into the ages of the Martian valley networks, the resurfacing history of Venus, the ages of the outer planets’ moons, and the impact rate that is used, in turn, to argue about the early history of the Earth. That is a very large structure resting on a distinction between two kinds of hole.

A last comparison is worth drawing, because it says what kind of statistic a crater count is. It is a count of events accumulated over time, read as a rate — the same structure as any measurement that infers a flux from a sample, and it fails in the same places. It fails where the counted objects are not independent, which is what a secondary field is; it fails where the counting is incomplete at small sizes, which a count with a knee in it describes; and it fails where the population being counted changed during the interval. A collision rate inferred without watching a collision is the same inference made on a debris population, and the arguments about correlated events are identical.

Where the ladder goes next

The rung above this one is the production function itself: where the impactor size distribution comes from, and what it would take to measure it independently of the surfaces it is used to date. The rung after that is the calibration — the handful of radiometrically dated sites that the whole chronology hangs on, and what the ages of every other surface in the solar system would do if one of them turned out to be wrong.

Where this goes next

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. A 128.8-million-year-old collision, dated from the shape of a scatter plot. The Erigone family: 165 members drawn at their diameters and their proper semi-major axes, with inverse diameter up the page. The cloud is a V, and the V is a clock. Each member has been drifting in semi-major axis ever since the collision at a rate that goes as one over its diameter, with a sign set by which way it spins — prograde outward, retrograde inward — so after 130 million years the small members have moved far and the large ones have barely moved at all. Plotted against 1/D that envelope is a straight line through the family's centre, and its slope is the drift rate for a one-kilometre body multiplied by the elapsed time. Fitting the two edges of the points actually drawn here returns 128.85 million years against the 130 the members were generated from. The rounding at the bottom is not an artefact: it is the ejection velocity, some 15 metres per second, which every member got at the moment of the collision and which is the same for all sizes. The picture cannot show the interlopers — background asteroids that happen to lie inside the V and have nothing to do with the family — and it cannot show the members that have drifted into a resonance and left the belt entirely, which is the reason the oldest families have the softest edges. A collision dated by a scatter plot Nothing in the solar system carries a date. A collisional family does — because a force that depends on a body's size has been pushing its fragments apart ever since, so the cloud is a V whose slope is an elapsed time, and one of those dates is confirmed by fossil meteorites in Swedish limestone. The 2.3-hour spin barrier, and the small bodies that are allowed through it. Rotation period against diameter for a synthetic asteroid population, both axes logarithmic, with the horizontal lines marking where a body held together by nothing but its own gravity would fly apart. That limit is P = √(3π/Gρ) and it contains only the density: 3.30 hours at 1 gram per cubic centimetre, 2.33 hours at 2 gram per cubic centimetre, 1.91 hours at 3 gram per cubic centimetre. Size does not appear in it, which is what makes the figure's shape informative rather than obvious — a barrier that depended on size would be drawn as a slope, and a horizontal line crossing five decades of diameter is a much stronger statement. The observed population respects it. Above about two hundred metres nothing rotates faster than the 2.3-hour line, and the crowding just below that line is real: bodies pile up against a limit they cannot cross. Below two hundred metres the wall stops applying and the fast rotators appear, some of them turning in minutes. Nothing about gravity changes at that size. What changes is that a body small enough is a single coherent rock with tensile strength, while a body large enough is a pile of fragments with almost none, and the barrier is a measurement of which is which. The picture is a synthetic population drawn at random from a fixed seed rather than a catalogue, so the individual points are not asteroids; what is real is the barrier, its value, and the fact that only the smallest bodies are found beyond it. A wall with no size in it Spin a body held together by nothing but its own gravity, and past a certain rate it comes apart. The rate depends on density alone — 2.3 hours for the stuff asteroids are made of — and the observed population respects the limit exactly, for every body larger than a couple of hundred metres.

What links here

Essays that link to this one from their own argument.

The objects this essay names

Each one links to every other essay that touches it.

Crater countingEjectaLunar chronologyProduction functionResurfacingSaturationSecondary craterSize frequency distributionSpatial clusteringSystematic error