Possible long-term decline in impact rates: 2. Lunar impact-melt data regarding impact history

Crater counts at lunar landing sites with measured ages establish a steep decline in cratering rate during the period ∼3.8 to ∼3.1 Gyr ago. Most models of the time dependence suggest a roughly constant impact rate (within factor ∼2) after about 3 Gyr ago, but are based on sparse data. Recent dating of impact melts from lunar meteorites, and Apollo glass spherules, clarifies impact rates from ∼3.2 to ∼2 Gyr ago or less. Taken together, these data suggest a decline with roughly 700 Myr half-life around 3 Gyr ago, and a slower decline after that, dropping by a factor ∼3 from about ∼2.3 Gyr ago until the present. Planetary cratering involved several phases with different time behaviors: (1) rapid sweep-up of most primordial planetesimals into planets in the first hundred Myr, (2) possible later effects of giant planet migration with enhanced cratering, (3) longer term sweep-up of leftover planetesimals, and finally (4) the present long-term “leakage” of asteroids from reservoirs such as the main asteroid belt and Kuiper belt. In addition, at any given point on the Moon, a pattern of “spikes” (sharp maxima of relatively narrow time width) will appear in the production rate of smaller craters (?500 m?), not only from secondary debris from large primary lunar impacts at various distances from the point in question, but also from asteroid breakups dotted through Solar System history. The pattern of spikes varies according to type of sample being measured (i.e., glass spherules vs impact melts). For example, several data sets show an impact rate spike ∼470 Myr ago associated with the asteroid belt collision that produced the L chondrites (see Section 3.6 below). Such spikes should be less prominent in the production record of craters of D? few km. These phenomena affect estimates of planetary surfaces ages from crater counts, as discussed in a companion paper [Quantin, C., Mangold, N., Hartmann, W.K., Allemand, P., 2007. Icarus 186, 1-10]. Fewer impact melts and glass spherules are found at ∼3.8 Gyr than at ∼3.5 Gyr ago, even though the impact rate itself is known to have been higher at 3.8 Gyr ago than 3.5 Gyr. This disproves the assertion by Ryder [Ryder, G., 1990. EOS 71, 313, 322-323] and Cohen et al. [Cohen, B.A., Swindle, T.D., Kring, D.A., 2000. Science 290, 1754-1756] that ancient impact melts are a direct proxy for ancient impact (cf. Section 3.3). This result raises questions about how to interpret cratering history before 3.8 Gyr ago.     

Do young martian ray craters have ages consistent with the crater count system?

McEwen et al. (McEwen, A.S., Preblich, B.S., Turtle, E.P., Artemieva, N.A., Golombek, M.P., Hurst, M., Kirk, R.L., Burr, D.M., Christensen, P. [2005]. Icarus 176, 351-381) developed a useful test for the internal consistency of crater-count chronometry systems. They argued that certain multi-kilometer, fresh-looking martian craters with prominent rays should be the youngest or near-youngest craters in their size range. The “McEwen et al. test” is that the ages determined from crater densities of the smallest superimposed craters (typically diameter D ∼ 5-20 m) should thus be comparable to the expected formation intervals of the host primary. McEwen et al. concluded from MOC data that crater chronometry failed this test by factors of 700-2000. We apply HiRISE and other imagery to eight different young craters in order to re-evaluate their arguments. We use existing crater chronology systems as well as the reported observed production rate of 16 m craters (Malin, M.C., Edgett, K., Posiolova, L., McColley, S., Noe Dobrea, E. [2006]. Science 314, 1573-1557; Hartmann, W.K., Quantin, C., Mangold, N. [2007]. Icarus 186, 11-23; Kreslavsky [2007]. Seventh International Conference on Mars, 3325). Every case passes the McEwen et al. test. We conclude that the huge inconsistencies suggested by McEwen et al. are spurious. Many of these craters show evidence of impact into ice-rich material, and appear to have ice-flow features and sublimation pits on their floors. As production rate data improve, decameter-scale craters will provide a valuable way of dating these young martian geological formations and the processes that modify them.     

Nonuniform cratering of the terrestrial planets

We estimate the impact flux and cratering rate as a function of latitude on the terrestrial planets using a model distribution of planet crossing asteroids and comets [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433]. After determining the planetary impact probabilities as a function of the relative encounter velocity and encounter inclination, the impact positions are calculated analytically, assuming the projectiles follow hyperbolic paths during the encounter phase. As the source of projectiles is not isotropic, latitudinal variations of the impact flux are predicted: the calculated ratio between the pole and equator is 1.05 for Mercury, 1.00 for Venus, 0.96 for the Earth, 0.90 for the Moon, and 1.14 for Mars over its long-term obliquity variation history. By taking into account the latitudinal dependence of the impact velocity and impact angle, and by using a crater scaling law that depends on the vertical component of the impact velocity, the latitudinal variations of the cratering rate (the number of craters with a given size formed per unit time and unit area) is in general enhanced. With respect to the equator, the polar cratering rate is about 30% larger on Mars and 10% on Mercury, whereas it is 10% less on the Earth and 20% less on the Moon. The cratering rate is found to be uniform on Venus. The relative global impact fluxes on Mercury, Venus, the Earth and Mars are calculated with respect to the Moon, and we find values of 1.9, 1.8, 1.6, and 2.8, respectively. Our results show that the relative shape of the crater size-frequency distribution does not noticeably depend upon latitude for any of the terrestrial bodies in this study. Nevertheless, by neglecting the expected latitudinal variations of the cratering rate, systematic errors of 20-30% in the age of planetary surfaces could exist between equatorial and polar regions when using the crater chronology method.     

Craters on asteroids: Reconciling diverse impact records with a common impacting population

O'Brien and Greenberg [O'Brien, D.P., Greenberg, R., 2005. Icarus 178, 179-212] developed a self-consistent numerical model of the collisional and dynamical evolution of the main-belt and NEA populations that was tested against a diverse range of observational and theoretical constraints. In this paper, we use those results to update the asteroid cratering model of Greenberg et al. [Greenberg, R., Nolan, M.C., Bottke, W.F., Kolvoord, R.A., Veverka, J., 1994. Icarus 107, 84-97; Greenberg, R., Bottke, W.F., Nolan, M., Geissler, P., Petit, J., Durda, D.D., Asphaug, E., Head, J., 1996. Icarus 120, 106-118], and show that the main-belt asteroid population from the O'Brien and Greenberg collisional/dynamical evolution modeling is consistent with the crater records on Gaspra, Ida, Mathilde, and Eros, the four asteroids that have been observed by spacecraft.     

Martian cratering 9: Toward resolution of the controversy about small craters

The Malin et al. [Malin, M.C., Edgett, K., Posiolova, L., McColley, S., Noe Dobrea, E., 2006. Science 314, 1573-1577] report of ongoing production of decameter scale primary craters matches within an order of magnitude the crater production curves of Hartmann [Hartmann, W.K., 2005. Icarus 174, 294-320], and appears to contradict models that say our curves grossly overpredict primary production. Nonetheless, such models may still predict correct order-of-magnitude secondary production. The new observations, if correct, require geologically recent martian surface modification in some areas, on timescales comparable to the cycles of obliquity changes, suggesting episodic martian climatic/environmental change driven by the obliquity cycles.     

Cratering on Mars I. Cratering and obliteration history

Computerized cratering-obliteration models are developed for use in interpreting planetary surface histories in terms of the diameter-frequency relations for craters classified by morphology. An application is made to a portion of the lunar uplands, revealing several episodes of blanketing, presumably due to the formation of some of the major basins.Application to Martian craters leads to the following picture of Martian cratering and obliteration history. During a probable period of intense early bombardment, craters were degraded by two processes: a depositional-type process connected with the declining cratering rate, and a process tending to flatten the largest craters (e.g., isostatic adjustment). During late stages of the early bombardment, or subsequent to it, there occurred a major relative episode of obliteration (probably atmosphere related), but it ceased concurrently with the massive (presumably volcanic) resurfacing of the cratered plains. Subsequent resurfacing episodes have occurred in the smooth plain terrains, but obliteration processes have been virtually absent in the low-latitude cratered terrains.Recent global Martian cratering interpretations of Hartmann and Soderblom are compared. Absolute cratering chronologies are only so good as knowledge of the absolute cratering flux on Mars. The crater data of Arvidson, Mutch, and Jones do not confirm the basis, whereby Soderblom requires the dominant Martian crater obliteration process to be coincident in time with the early bombardment. If the asteroidal-cometary impact flux on Mars has averaged five times the lunar flux during post-lunar-mare epochs, then the obliterative episode lasted about half a billion years and occurred about 1.5 × 10⁹ yr ago.     

Itokawa's cratering record as observed by Hayabusa: Implications for its age and collisional history

In this paper, we study cratering and crater erasure processes and provide an age estimate for the near-Earth Asteroid (25143) Itokawa, the target of the mission Hayabusa, based on its crater history since the time when it was formed in the main belt by catastrophic disruption or experienced a global resetting event. Using a model which was applied to the study of the crater history of Gaspra, Ida, Mathilde and Eros [O'Brien, D.P., Greenberg, R., Richardson, J.E., 2006. Icarus 183, 79–92], we calculate the time needed to accumulate the craters on Itokawa's surface, taking into account several processes which can affect crater formation and crater erasure on such a low-gravity object, such as seismic shaking. We use two models of the projectile population and two scaling laws to relate crater diameter to projectile size. Both models of the projectile population provide similar results, and depending on the scaling law used, we find that the time necessary to accumulate Itokawa's craters was at least ∼75 Myr, and maybe as long as 1 Gyr. Moreover, using the same model and similar parameters (scaled accordingly), we provide a good match not only to Itokawa's craters, but also to those of Eros, which has also been imaged at high enough resolution to give crater counts in a similar size range to those on Itokawa. We show that, as for Eros, the lack of small craters on Itokawa is consistent with erasure by seismic shaking, although for Itokawa, the pronounced deficiency of the smallest craters (<10 m in diameter) requires another process or event in addition to just seismic shaking. A small body such as Itokawa is highly sensitive to specific events that may occur during its history. For example, the two parts of Itokawa, called head and body, may well have joined each other by a low-velocity impact within the last hundred thousand years [Scheeres, D.J., Abe, M., Yoshikawa, M., Nakamura, R., Gaskell, R.W., Abell, P.A., 2007. Icarus 188, 425–429]. In addition to providing an erasure mechanism for small craters, the proposed timescale of that event is consistent with the timescale necessary in our model to form the current, depleted population of just a few small (<10 m) craters on Itokawa, suggesting that it may be the explanation for the discrepancy between Itokawa's cratering record and that obtained from our equilibrium seismic shaking model. Other explanations for the depletion of the smallest craters on Itokawa, such as armoring by boulders lying on the surface, cannot be ruled out.     

The cratering history of asteroid (2867) Steins

The cratering history of main belt asteroid (2867) Steins has been investigated using OSIRIS imagery acquired during the Rosetta flyby that took place on the 5th of September 2008. For this purpose, we applied current models describing the formation and evolution of main belt asteroids, that provide the rate and velocity distributions of impactors. These models coupled with appropriate crater scaling laws, allow the cratering history to be estimated. Hence, we derive Steins’ cratering retention age, namely the time lapsed since its formation or global surface reset. We also investigate the influence of various factors—like bulk structure and crater erasing—on the estimated age, which spans from a few hundred Myrs to more than 1 Gyr, depending on the adopted scaling law and asteroid physical parameters. Moreover, a marked lack of craters smaller than about 0.6 km has been found and interpreted as a result of a peculiar evolution of Steins cratering record, possibly related either to the formation of the 2.1 km wide impact crater near the south pole or to YORP reshaping.     

Megaregolith evolution and cratering cataclysm models—Lunar cataclysm as a misconception (28 years later)

Abstract— The hypothesis of a lunar cataclysmic cratering episode between 3.8 and 3.9 Gyr ago lacks proof. Its strongest form proposes no cratering before about 4.0 Gyr, followed by catastrophic formation of most lunar craters and basins in >200 Myr. The premise that “zero impact melts implies zero impacts” is disproved by data from asteroids, on which early collisions clearly occurred, but from which early impact melts are scarce. Plausible cataclysm models imply that any cataclysm should have affected the whole inner solar system, but among available lunar and asteroid impact melt and impact age resetting data, a narrow, strong 3.8–3.9 Gyr spike in ages is seen only in the region sampled by Apollo/Luna. Reported lunar meteorite data do not show the spike. Asteroid data show a broader, milder peak, spreading from about 4.2 to 3.5 Gyr. These data suggest either that the spike in Apollo impact melt ages is associated with unique lunar front side events, or that the lunar meteorites data represent different kinds of events than the Apollo/Luna data. Here, we develop an alternate “megaregolith evolution” hypothesis to explain these data. In this hypothesis, early impact melts are absent not because there were no impacts, but because the high rate of early impacts led to their pulverization. The model estimates survival halflives of most lunar impact melts prior to 4.1 Gyr at >100 Myr. After a certain time, T_critical ?4.0 Gyr, impact melts began to survive to the present. The age distribution differences among impact melts and plutonic rocks are controlled by, and hold clues to, the history of regolith evolution and the relative depths of sequestration of impact melts versus plutonic rocks, both among lunar and asteroidal samples. Both the “zero cratering, then cataclysm” hypothesis and the “megaregolith evolution” hypothesis require further testing, especially with lunar meteorite impact melt studies.     

Variability in the small crater population on Callisto

Previous analyses of Galileo images showed the small (≈1 km and smaller) crater population on Callisto to be lower than had been expected (Moore, J.M. et al. [1999]. Icarus 140, 294-312; Bierhaus E.B. et al. [2000]. Lunar Planet. Sci. 31. Abstract #1996). In this paper we examine the small crater population using high-resolution imagery from Callisto flybys during Galileo orbits C3, C10, C21, and C30, including several C30 regions not previously analyzed. Our findings confirm that most small craters are depleted relative to a presumed equilibrium of R = 0.22, and we find that there is significant variability in the small crater counts. While some of the variability in the small crater population on Callisto can be attributed to secondary cratering, some variability also may be explained by resetting of portions of Callisto’s surface by larger impactors. This is expected where the differential size frequency distribution of the crater production population b < 3 (where b represents the exponent of a differential power-law crater-size distribution), such that large impacts affect a greater planetary surface area than smaller craters.     

39Ar‐40Ar ages of eucrites and thermal history of asteroid 4 Vesta

Abstract— Eucrite meteorites are igneous rocks that derived from a large asteroid, probably 4 Vesta. Past studies have shown that after most eucrites formed, they underwent metamorphism in temperatures up to ≥800°C. Much later, many were brecciated and heated by large impacts into the parent body surface. The less common basaltic, unbrecciated eucrites also formed near the surface but, presumably, escaped later brecciation, while the cumulate eucrites formed at depths where metamorphism may have persisted for a considerable period. To further understand the complex HED parent body thermal history, we determined new ³⁹Ar‐⁴⁰Ar ages for 9 eucrites classified as basaltic but unbrecciated, 6 eucrites classified as cumulate, and several basaltic‐brecciated eucrites. Precise Ar‐Ar ages of 2 cumulate eucrites (Moama and EET 87520) and 4 unbrecciated eucrites give a tight cluster at 4.48 ± 0.02 Gyr (not including any uncertainties in the flux monitor age). Ar‐Ar ages of 6 additional unbrecciated eucrites are consistent with this age within their relatively larger age uncertainties. By contrast, available literature data on Pb‐Pb isochron ages of 4 cumulate eucrites and 1 unbrecciated eucrite vary over 4.4–4.515 Gyr, and ¹⁴⁷Sm‐¹⁴³Nd isochron ages of 4 cumulate and 3 unbrecciated eucrites vary over 4.41–4.55 Gyr. Similar Ar‐Ar ages for cumulate and unbrecciated eucrites imply that cumulate eucrites do not have a younger formation age than basaltic eucrites, as was previously proposed. We suggest that these cumulate and unbrecciated eucrites resided at a depth where parent body temperatures were sufficiently high to cause the K‐Ar and some other chronometers to remain as open diffusion systems. From the strong clustering of Ar‐Ar ages at ?4.48 Gyr, we propose that these meteorites were excavated from depth in a single large impact event ?4.48 Gyr ago, which quickly cooled the samples and started the K‐Ar chronometer. A large (?460 km) crater postulated to exist on Vesta may be the source of these eucrites and of many smaller asteroids thought to be spectrally or physically associated with Vesta. Some Pb‐Pb and Sm‐Nd ages of cumulate and unbrecciated eucrites are consistent with the Ar‐Ar age of 4.48 Gyr, and the few older Pb‐Pb and Sm‐Nd ages may reflect an isotopic closure before the large cratering event. One cumulate eucrite gives an Ar‐Ar age of 4.25 Gyr; 3 additional cumulate eucrites give Ar‐Ar ages of 3.4–3.7 Gyr; and 2 unbrecciated eucrites give Ar‐Ar ages of ?3.55 Gyr. We attribute these younger ages to a later impact heating. Furthermore, the Ar‐Ar impact‐reset ages of several brecciated eucrites and eucritic clasts in howardites fall within the range of 3.5–4.1 Gyr. Among these, Piplia Kalan, the first eucrite to show evidence for extinct ²⁶Al, was strongly impact heated ?3.5 Gyr ago. When these data are combined with eucrite Ar‐Ar ages in the literature, they confirm that several large impact heating events occurred on Vesta between ?4.1–3.4 Gyr ago. The onset of major impact heating may have occurred at similar times for both Vesta and the moon, but impact heating appears to have persisted for a somewhat later time on Vesta.     

The chronology of Mercury's geological and geophysical evolution: The vulcanoid hypothesis

Previous discussions of Mercury's evolution have assumed that its cratering chronology is tied to that of the Moon, i.e., with Caloris forming about 3.9 Gyr ago as part of a late heavy bombardment that affected all of the terrestrial planets. That assumption requires that Mercury's core formed very early, because associated expansion features are not visible, and must have been erased before the cratering flux declined. Moreover, the modest amount of global shrinkage inferred from visible compressional features on Mercury's surface implies that the core is either largely molten at present, or had largely solidified before the end of the bombardment. The former interpretation requires a significant volatile content or implausibly large internal heat sources, while the latter raises questions about how to generate the planet's magnetic field. We have investigated whether constraints on Mercury's chronology could be relaxed by effects of a Mercury-specific bombarding population of planetesimals interior to its orbit, encountering the planet only occasionally due to secular perturbations. Such “vulcanoids” could have been a significant source of early cratering. However, those in orbits that can cross Mercury's are depleted by mutual collisions in ⪅1 Gyr, and can provide at most a modest extension of the period of heavy bombardment. Further inside Mercury's orbit, lower collisional velocities might allow survival of vulcanoids to the present. We report on a search for such bodies and on observational limits to such a population. We also review evidence that Mercury's intercrater plains are of volcanic origin and mainly predate Caloris, and that scarp formation (and global contraction) mainly postdates Caloris and has continued to recent times. If global lineaments are the product of tidal despinning, they constrain core formation to the first half of the planet's lifetime. While some questions and inconsistencies remain, the preponderance of evidence suggests that Mercury differentiated early, and at least half of its core volume is presently molten, probably due to a significant content of some light element such as sulfur.     

Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion

The main belt is believed to have originally contained an Earth mass or more of material, enough to allow the asteroids to accrete on relatively short timescales. The present-day main belt, however, only contains ∼5×¹⁰⁻⁴ Earth masses. Numerical simulations suggest that this mass loss can be explained by the dynamical depletion of main belt material via gravitational perturbations from planetary embryos and a newly-formed Jupiter. To explore this scenario, we combined dynamical results from Petit et al. [Petit, J. Morbidelli, A., Chambers, J., 2001. The primordial excitation and clearing of the asteroid belt. Icarus 153, 338-347] with a collisional evolution code capable of tracking how the main belt undergoes comminution and dynamical depletion over 4.6 Gyr [Bottke, W.F., Durda, D., Nesvorny, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H., 2005. The fossilized size distribution of the main asteroid belt. Icarus 175, 111-140]. Our results were constrained by the main belt's size-frequency distribution, the number of asteroid families produced by disruption events from diameter D>100 km parent bodies over the last 3-4 Gyr, the presence of a single large impact crater on Vesta's intact basaltic crust, and the relatively constant lunar and terrestrial impactor flux over the last 3 Gyr. We used our model to set limits on the initial size of the main belt as well as Jupiter's formation time. We find the most likely formation time for Jupiter was 3.3±2.6 Myr after the onset of fragmentation in the main belt. These results are consistent with the estimated mean disk lifetime of 3 Myr predicted by Haisch et al. [Haisch, K.E., Lada, E.A., Lada, C.J., 2001. Disk frequencies and lifetimes in young clusters. Astrophys. J. 553, L153-L156]. The post-accretion main belt population, in the form of diameter D?1000 km planetesimals, was likely to have been 160±40 times the current main belt's mass. This corresponds to 0.06-0.1 Earth masses, only a small fraction of the total mass thought to have existed in the main belt zone during planet formation. The remaining mass was most likely taken up by planetary embryos formed in the same region. Our results suggest that numerous D>200 km planetesimals disrupted early in Solar System history, but only a small fraction of their fragments survived the dynamical depletion event described above. We believe this may explain the limited presence of iron-rich M-type, olivine-rich A-type, and non-Vesta V-type asteroids in the main belt today. The collisional lifetimes determined for main belt asteroids agree with the cosmic ray exposure ages of stony meteorites and are consistent with the limited collisional evolution detected among large Koronis family members. Using the same model, we investigated the near-Earth object (NEO) population. We show the shape of the NEO size distribution is a reflection of the main belt population, with main belt asteroids driven to resonances by Yarkovsky thermal forces. We used our model of the NEO population over the last 3 Gyr, which is consistent with the current population determined by telescopic and satellite data, to explore whether the majority of small craters (D<0.1-1 km) formed on Mercury, the Moon, and Mars were produced by primary impacts or by secondary impacts generated by ejecta from large craters. Our results suggest that most small craters formed on these worlds were a by-product of secondary rather than primary impacts.     

Impact History of Eros: Craters and Boulders

Preliminary measurements of craters and boulders have been made in various locations on Eros from images acquired during the first nine months of NEAR Shoemaker's orbital mission, including the October 2000 low altitude flyover. (We offer some very preliminary, qualitative analysis of later LAF images and very high-resolution images obtained during NEAR's landing on 12 February 2001). Craters on Eros >100 m diameter closely resemble the saturated crater population of Ida; Eros is more heavily cratered than Gaspra but lacks the saturated giant craters of Mathilde. These craters and the other large-scale geological features were formed over a duration of very roughly 2 Gyr while Eros was in the main asteroid belt, between the time when its parent body was disrupted and Eros was injected into an Earth-approaching orbit (probably tens of Myr ago). Saturation equilibrium had been expected to shape Eros' crater population down to very small sizes, as on the lunar maria. However, craters <200 m diameter are instead progressively depleted toward smaller sizes and are a factor of ∼200 below empirical saturation at diameters of 4 m. Conversely, boulders and positive relief features (PRFs) rise rapidly in numbers (differential power-law index ∼−5) and those <10 m in size dominate the landscape at high resolutions. The pervasive boulders and minimal craters on Eros is radically different from the lunar surface at similar scales. This may be partly explained by a major depletion of meter-scale projectiles in the asteroid belt (due to the Yarkovsky Effect: Bell 2001), which thus form few small craters and destroy few boulders. Additionally, the small size and low gravity of Eros may result in redistribution or loss of ejecta due to seismic shaking, thus preferentially destroying small craters formed in such regolith. Possibly Eros has only a patchy, thin regolith of mobile fines; the smaller PRFs may then reflect exposures of fractured bedrock or piles of large ejecta blocks, which might further inhibit formation of craters <10 m in size. Eros may well have been largely detached dynamically and collisionally from the main asteroid belt for the past tens of Myr, in which case its cratering rate would have dropped by two orders of magnitude, perhaps enhancing the relative efficacy of other processes that would normally be negligible in competition with cratering. Such processes include thermal creep, electrostatic levitation and redistribution of fines, and space weathering (e.g., bombardment by micrometeorites and solar wind particles). Combined with other small-body responses to impact cratering (e.g., greater widespread distribution of bouldery ejecta), such processes may also help explain the unexpected small-scale character of geology on Eros. If there was a recent virtual hiatus in cratering of Eros (during which only craters <∼300 m diameter would be expected to have formed), space weathering may have reached maturity, thus explaining Eros' remarkable spectral homogeneity compared with Ida.     

Impact basin relaxation at Iapetus

We investigate impact basin relaxation on Iapetus by combining a 3D thermal evolution model (Robuchon, G., Choblet, G., Tobie, G., Cadek, O., Sotin, C., Grasset, O. [2010]. Icarus 207, 959-971) with a spherical axisymmetric viscoelastic relaxation code (Zhong, S., Paulson, A., Wahr, J. [2003]. Geophys. J. Int. 155, 679-695). Due to the progressive cooling of Iapetus, younger basins relax less than older basins. For an ice reference viscosity of 10¹⁴ Pa s, an 800 km diameter basin relaxes by 30% if it formed in the first 50 Myr but by 10% if it formed at 1.2 Gyr. Bigger basins relax more rapidly than smaller ones, because the inferred thickness of the ice shell exceeds the diameter of all but the largest basins considered. Stereo topography shows that all basins 600 km in diameter or smaller are relaxed by 25% or less. Our model can match the relaxation of all the basins considered, within error, by assuming a single basin formation age (4.36 Ga for our nominal viscosity). This result is consistent with crater counts, which show no detectable age variation between the basins examined.     

Marine‐target craters on Mars? An assessment study

Abstract— Observations of impact craters on Earth show that a water column at the target strongly influences lithology and morphology of the resultant crater. The degree of influence varies with the target water depth and impactor diameter. Morphological features detectable in satellite imagery include a concentric shape with an inner crater inset within a shallower outer crater, which is cut by gullies excavated by the resurge of water. In this study, we show that if oceans, large seas, and lakes existed on Mars for periods of time, marine‐target craters must have formed. We make an assessment of the minimum and maximum amounts of such craters based on published data on water depths, extent, and duration of putative oceans within “contacts 1 and 2,” cratering rate during the different oceanic phases, and computer modeling of minimum impactor diameters required to form long‐lasting craters in the seafloor of the oceans. We also discuss the influence of erosion and sedimentation on the preservation and exposure of the craters. For an ocean within the smaller “contact 2” with a duration of 100,000 yr and the low present crater formation rate, only ?1–2 detectable marine‐target craters would have formed. In a maximum estimate with a duration of 0.8 Gyr, as many as 1400 craters may have formed. An ocean within the larger “contact 1‐Meridiani,” with a duration of 100,000 yr, would not have received any seafloor craters despite the higher crater formation rate estimated before 3.5 Gyr. On the other hand, with a maximum duration of 0.8 Gyr, about 160 seafloor craters may have formed. However, terrestrial examples show that most marine‐target craters may be covered by thick sediments. Ground penetrating radar surveys planned for the ESA Mars Express and NASA 2005 missions may reveal buried craters, though it is uncertain if the resolution will allow the detection of diagnostic features of marine‐target craters. The implications regarding the discovery of marine‐target craters on Mars is not without significance, as such discoveries would help address the ongoing debate of whether large water bodies occupied the northern plains of Mars and would help constrain future paleoclimatic reconstructions.     

Nonuniform cratering of the Moon and a revised crater chronology of the inner Solar System

We model the cratering of the Moon and terrestrial planets from the present knowledge of the orbital and size distribution of asteroids and comets in the inner Solar System, in order to refine the crater chronology method. Impact occurrences, locations, velocities and incidence angles are calculated semi-analytically, and scaling laws are used to convert impactor sizes into crater sizes. Our approach is generalizable to other moons or planets. The lunar cratering rate varies with both latitude and longitude: with respect to the global average, it is about 25% lower at (±65°N, 90°E) and larger by the same amount at the apex of motion (0°N, 90°W) for the present Earth-Moon separation. The measured size-frequency distributions of lunar craters are reconciled with the observed population of near-Earth objects under the assumption that craters smaller than a few kilometers in diameter form in a porous megaregolith. Varying depths of this megaregolith between the mare and highlands is a plausible partial explanation for differences in previously reported measured size-frequency distributions. We give a revised analytical relationship between the number of craters and the age of a lunar surface. For the inner planets, expected size-frequency crater distributions are calculated that account for differences in impact conditions, and the age of a few key geologic units is given. We estimate the Orientale and Caloris basins to be 3.73 Ga old, and the surface of Venus to be 240 Ma old. The terrestrial cratering record is consistent with the revised chronology and a constant impact rate over the last 400 Ma. Better knowledge of the orbital dynamics, crater scaling laws and megaregolith properties are needed to confidently assess the net uncertainty of the model ages that result from the combination of numerous steps, from the observation of asteroids to the formation of craters. Our model may be inaccurate for periods prior to 3.5 Ga because of a different impactor population, or for craters smaller than a few kilometers on Mars and Mercury, due to the presence of subsurface ice and to the abundance of large secondaries, respectively. Standard parameter values allow for the first time to naturally reproduce both the size distribution and absolute number of lunar craters up to 3.5 Ga ago, and give self-consistent estimates of the planetary cratering rates relative to the Moon.     

Paleocratering of the Moon: Review of post-Apollo data

As a result of the dating of lunar samples, we are in a position to utilize the lunar surface as a recorder of environmental conditions in the Earth-Moon neighborhood in the past. Plots of crater density vs rock age at different lunar landing sites can be used to date unexplored lunar provinces. These plots also demonstrate evolution in the population of planetesimals that struck the Moon. Prior to 4.1 aeons ago, the cratering rate on the Moon was at least 10³ times the present rate, and the rate declined with a half-life less than 8×10⁷ yr. During the interval from 4.1 to 3.2 aeons ago, the number of planetesimals showed an exponential decay with a half-life about 3×10⁸ yr, corresponding to sweep-up of particles from solar orbits somewhat similar to those of Apollo asteroids. A more nearly constant cratering rate applied in the last three aeons. These data indicate that the Moon displays at least the final stages of an ancient accretion process; they also set certain conditions on possible capture processes relating to the Moon's origin. Pre-Apollo expectations that the Moon would provide a Rosetta Stone for interpreting solar system history and planet formation thus appear justified.Paper given at Philadelphia meeting of American Association for Advancement of Science, December, 1971.     

Influence of the asymmetrical cratering rate on the lunar cratering chronology

The lunar cratering rate studied over the past 1.1 Gyr, which is a foundation of the lunar cratering chronology, is a decreasing function of the angular distance from the apex of the orbital motion due to the synchronous rotation of the Moon. We here evaluate an influence of the asymmetrical rate upon the age determination.     

The volcanic history of Mars: High-resolution crater-based studies of the calderas of 20 volcanoes

Determining absolute surface ages for bodies in the Solar System is, at present, only possible for Earth and Moon with radiometric dating for both bodies and biologic proxies such as fossils for Earth. Relative ages through cratering statistics are recognized as one of the most reliable proxies for relative ages, calibrated by lunar geologic mapping and Apollo program sample returns. In this work, we have utilized the Mars Reconnaissance Orbiter’s ConTeXt Camera’s images which provide the highest resolution wide-scale coverage of Mars to systematically crater-age-date the calderas of 20 of Mars’ largest volcanoes in order to constrain the length of time over which these volcanoes - and major volcanic activity on the planet, by extension - were active. This constitutes the largest uniform and comprehensive research on these features to date, eliminating unknown uncertainties by multiple researchers analyzing different volcanoes with varied data and methods. We confirm previous results that Mars has had active volcanism throughout most of its history although it varied spatially and temporally, with the latest large-scale caldera activity ending approximately 150 ma in the Tharsis region. We find a transition from explosive to effusive eruption style occurring in the Hesperian, at approximately 3.5 Ga ago, though different regions of the planet transitioned at different times. Since we were statistically complete in our crater counts to sizes as small as ∼60 m in most cases, we also used our results to study the importance of secondary cratering and its effects on crater size-frequency distributions within the small regions of volcanic calderas. We found that there is no “golden rule” for the diameters secondaries become important in crater counts of martian surfaces, with one volcano showing a classic field of secondaries ∼2 crater diameters from the center of its primary but not affecting the size-frequency distribution, and another clearly showing an influence but from no obvious primary.