Comparison of the crater morphology-size relationship for Mars,Moon, and Mercury

New central peak-crater size data for Mars shows that a higher percentage of relatively unmodified Martian craters have central peaks than do fresh lunar craters below a diameter of 30 km. For example, in the diameter range 10 to 20 km, 60% of studied Martian craters have central peaks compared to 26% for the Moon. Gault et al. (1975, J. Geophys. Res.80, 2444–2460) have demonstrated that central peaks occur in smaller craters on Mercury than on the Moon, and that this effect is due to the different gravity fields in which the craters formed. Similar differences when comparing Mars and the Moon show that gravity has affected the diameter at which central peaks form on Mars. Erosion on Mars, therefore, does not completely mask differences in crater interior structure that are caused by differences in gravity. Effects of Mars' higher surface gravity when compared to the Moon are not detected when comparing terrace and crater shape data. The morphology-crater size statistics also show that a full range of crater shapes occur on Mars, and craters tend to become more morphologically complex with increasing diameter. Comparisons of Martian and Mercurian crater data show differences which may be related to the greater efficacy of erosion on Mars.     

Martian cratering revisited: Implications for early geologic evolution

Improved crater statistics from varied Martian terrains are compared to lunar crater populations. The distribution functions for the average Martian cratered terrain and the average lunar highlands over the diameter range 8–2000 km are quite similar. The Martian population is less dense by approximately 0.70 from 8 to 256 km diameter and diverges to proportionally lower densities at greater diameters. Crater densities on Martian “pure” terra give a lower limit to the Mars/Moon integrated crater flux of 0.75 since the last stabilization of the respective planetary crusts. The crater population >8 km diameter postdating the Martian northern plains is statistically indistinguishable from that population postdating the lunar maria. Monte Carlo simulations were performed to constrain plausible mechanisms of crater obliteration. The models demonstrate that if the crater density difference between the lunar and Martian terra has been due to resurfacing processes, random intercrater plains formation cannot be the sole process. If plains preferentially form in and obliterate larger craters, then the observed Martian distribution retains its “shape” as the crater density decreases. This result is consistent with the morphology of Martian intercrater plains.     

Lunar crater arcs

An analysis has been made of the tendency of large lunar craters to lie along circles. A catalog of the craters ? 50 km in diameter was prepared first, noting position, diameter, rim sharpness and completion, nature of underlying surface, and geological age. The subset of those craters 50–400 km in diameter was then used as input to computer programs which identified each ‘family’ of four or more craters, of selected geological age, lying on a circular arc. For comparison, families were also identified for randomized crater models in which the crater spatial density was matched to that on the Moon, either overall or, separately, for mare and highland areas. The observed frequency of lunar arcuate families was statistically highly significantly greater than for the randomized models, for craters classified as either late pre-Imbrian (Nectarian), middle pre-Imbrian, or early pre-Imbrian, as well as for a number of larger age-classes. The lunar families tend to center in specific areas of the Moon: these lie in highlands rather than maria and are different for families of Nectarian craters than for pre-Nectarian. The origin of the arcuate crater groupings is not understood.     

Mercury's albedo from Mariner 10: Implications for the presence of ferrous iron

Mariner 10 clear filter (490 nm) images of Mercury were recalibrated and photometrically normalized to produce a mosaic of nearly an entire hemisphere of the planet. Albedo contrasts are slightly larger than seen in the lunar highlands (excluding maria). Variegations indicative of compositional differences include diffuse low albedo units often overlain by smooth plains, the high albedo smooth plains of Borealis Planitia, and high-albedo enigmatic crater floor deposits. A higher level of contrast between immature crater ejecta and average mature material on Mercury compared to the Moon is consistent with a more intense space weathering environment on Mercury that results in a more mature regolith. Immature lunar highlands materials are ∼1.5 times higher in reflectance than analogous immature mercurian materials. Immature materials of the same composition would have the same reflectance on both bodies, thus this observation requires that Mercury's crust contains a significant darkening agent, either opaque minerals or ferrous iron bearing silicates, in abundances significantly higher than those of the lunar highlands. If the darkening agent is opaque minerals (e.g. ilmenite or ulvospinel) Mercury's crust may contain significant ferrous iron and yet not exhibit a 1-μm absorption band.     

Floor-fractured lunar craters

Numerous lunar craters (206 examples, mean diameter = 40km) contain pronounced floor rilles (fractures) and evidence for volcanic processes. Seven morphologic classes have been defined according to floor depth and the appearance of the floor, wall, and rim zones. Such craters containing central peaks exhibit peak heights (approximately 1km) comparable to those within well-preserved impact craters but exhibit smaller rim-peak elevation differences (generally 0–1.5km) than those (2.4km) within impact craters. In addition, the morphology, spatial distribution, and floor elevation data reveal a probable genetic association with the maria and suggest that a large number of floor-fractured craters represent pre-mare impact craters whose floors have been lifted tectonically and modified volcanically during the epochs of mare flooding. Floor uplift is envisioned as floating on an intruded sill, and estimates of the buoyed floor thickness are consistent with the inferred depth of brecciation beneath impact craters, a zone interpreted as a trap for the intruding magma. The derived model of crater modification accounts for (1) the large differences in affected crater size and age; (2) the small peak-rim elevation differences; (3) remnant central peaks within mare-flooded craters and ringed plains; (4) ridged and flat-topped rim profiles of heavily modified craters and ringed plains; and (5) the absence of positive gravity anomalies in most floor-fractured craters and some large mare-filled craters. One of the seven morphologic classes, however, displays a significantly smaller mean size, larger distances from the maria, and distinctive morphology relative to the other six classes. The distinctive morphology is attributed, in part, to the relatively small size of the affected crater, but certain members of this class represent a style of volcanism unrelated to the maria - perhaps triggered by the last major basin-forming impacts.     

Mineralogy of the lunar crust: Results from Clementine

Abstract— The central peaks of 109 impact craters across the Moon are examined with Clementine ultraviolet-visible (UVVIS) camera multispectral data. The craters range in diameter from 40 to 180 km and are believed to have exhumed material from 5–30 km beneath the surface to form the peaks, including both upper and lower crustal rocks depending on whether craters have impacted into highlands or basins. Representative five-color spectra from spectrally and spatially distinct areas within the peaks are classified using spectral parameters, including “key ratio” (which is related to mafic mineral abundance) and “spectral curvature” (linked to absorption band shape, which distinguishes between low- and high-Ca pyroxene and olivine). The spectral parameters are correlated to mineralogical abundances, related in turn to highland plutonic rock compositions. The derived rock compositions for the various central peaks are presented in a global map. From these results, it is evident that the lunar crust is compositionally diverse, both globally and at local 100 m scales found within individual sets of central peaks. Although the central peaks compositions imply a crust that is generally consistent with previous models of crustal structure, they also indicate a more anorthositic crust than generally assumed, with a bulk plagioclase content of ～81%, evolving from “pure” anorthosite near the surface towards more mafic, low-Ca pyroxene-rich compositions with depth (comparable to anorthositic norite). Evidence for mafic plutons occurs in both highlands and basins and represent all mafic highland rock types. However, the lower crust is more compositionally diverse than the highlands, with both a greater range of rock types and more diversity within individual sets of central peaks.     

Geology of the lunar farside crater Necho

The lunar farside crater Necho (30 km diameter) displays intricate morphological and structural characteristics. The highland setting provides a complex impact site when compared with the relatively uniform setting of mare craters. Therefore, the effects of pre-impact topography and structure play a dominant role in Necho's formation and modification. Necho's bright ejecta, extensive rays, fresh morphology, and lack of superposed craters indicate that it is extremely young. The asymmetric distribution of ejecta materials may be due to substrate effects, topographic shalowing, or oblique impact.Necho's interior is divided into five physiographic units based on morphologic differences: three floor units (Necho does not display a true flat floor), one hilly central unit, and the wall unit which includes terraces and smooth walls. The interior of the crater also exhibits an unusual asymmetry in the prevalence of terraced units on the western wall. Interior morphology and terrace orientations are probably the result of pre-impact effects. Structural and topographic orientations associated with three large pre-existing degraded craters dominate the impact site.     

Floor-fractured crater models of the Sudbury Structure,Canada: Implications for initial crater size and crater modification

Abstract The pattern of radial and concentric offset dikes at Sudbury strongly resembles fracture patterns in certain volcanically modified craters on the Moon. Since the Sudbury dikes apparently formed shortly after the impact event, this resemblance suggests that early endogenic modification at Sudbury was comparable to deformation in lunar floor-fractured craters. Although regional deformation has obscured many details of the Sudbury Structure, such a comparison of Sudbury with lunar floor-fractured craters provides two alternative models for the original size and surface structures of the Sudbury basin. First, the Sudbury date pattern can be correlated with fractures in the central peak crater Haldane (36 km in diameter). This comparison indicates an initial Sudbury diameter of between 100 and 140 km but requires loss of a central peak complex for which there is little evidence. Alternatively, comparison of the Sudbury dikes with fractures in the two-ring basin Schrödinger indicates an initial Sudbury diameter of at least ～ 180 km, which is in agreement with other recent estimates for the size of the Sudbury Structure. In addition to constraining the size and structure of the original Sudbury crater, these comparisons also suggest that crater modification may reflect different deformation mechanisms at different sizes. Most lunar floor-fractured craters are attributed to deformation over a shallow, crater-centered intrusion; however, there is no evidence for such an intrusion at Sudbury. Instead, melts from the evolving impact melt sheet probably entered fractures formed by isostatically-induced flexure of the crater floor. Since most of the lunar floor-fractured craters are too small (<100-km diameter) to induce significant isostatic adjustment, crater modification by isostatic uplift apparently is limited to only the largest of craters, whereas deformation over igneous intrusions dominates the modification of smaller craters.     

The effect of target properties on crater morphology: Comparison of central peak craters on the Moon and Ganymede

Abstract— We examine the morphology of central peak craters on the Moon and Ganymede in order to investigate differences in the near‐surface properties of these bodies. We have extracted topographic profiles across craters on Ganymede using Galileo images, and use these data to compile scaling trends. Comparisons between lunar and Ganymede craters show that crater depth, wall slope and amount of central uplift are all affected by material properties. We observe no major differences between similar‐sized craters in the dark and bright terrain of Ganymede, suggesting that dark terrain does not contain enough silicate material to significantly increase the strength of the surface ice. Below crater diameters of ?12 km, central peak craters on Ganymede and simple craters on the Moon have similar rim heights, indicating comparable amounts of rim collapse. This suggests that the formation of central peaks at smaller crater diameters on Ganymede than the Moon is dominated by enhanced central floor uplift rather than rim collapse. Crater wall slope trends are similar on the Moon and Ganymede, indicating that there is a similar trend in material weakening with increasing crater size, and possibly that the mechanism of weakening during impact is analogous in icy and rocky targets. We have run a suite of numerical models to simulate the formation of central peak craters on Ganymede and the Moon. Our modeling shows that the same styles of strength model can be applied to ice and rock, and that the strength model parameters do not differ significantly between materials.     

Crater dimensions from apollo data and supplemental sources

A catalog of crater dimensions that were compiled mostly from the new Apollo-based Lunar Topographic Orthophotomaps is presented in its entirety. Values of crater diameter, depth, rim height, flank width, circularity, and floor diameter (where applicable) are tabulated for a sample of 484 craters on the Moon and 22 craters on Earth. Systematic techniques of mensuration are detailed. The lunar craters range in size from 400 m to 300 km across and include primary impact craters of the main sequence, secondary impact craters, craterlets atop domes and cones, and dark-halo craters. The terrestrial craters are between 10 m and 22.5 km in diameter and were formed by meteorite impact.     

Transitional impact craters on the Moon: Insight into the effect of target lithology on the impact cratering process

We studied a data set of 28 well‐preserved lunar craters in the transitional (simple‐to‐complex) regime with the aim of investigating the underlying cause(s) for morphological differences of these craters in mare versus highland terrains. These transitional craters range from 15 to 42 km in diameter, demonstrating that the transition from simple to complex craters is not abrupt and occurs over a broad diameter range. We examined and measured the following crater attributes: depth (d), diameter (D), floor diameter (D_f), rim height (h), and wall width (w), as well as the number and onset of terraces and rock slides. The number of terraces increases with increasing crater size and, in general, mare craters possess more terraces than highland craters of the same diameter. There are also clear differences in the d/D ratio of mare versus highland craters, with transitional craters in mare targets being noticeably shallower than similarly sized highland craters. We propose that layering in mare targets is a major driver for these differences. Layering provides pre‐existing planes of weakness that facilitate crater collapse, thus explaining the overall shallower depths of mare craters and the onset of crater collapse (i.e., the transition from simple to complex crater morphology) at smaller diameters as compared to highland craters. This suggests that layering and its interplay with target strength and porosity may play a more significant role than previously considered.     

Blocky craters: Implications about the lunar megaregolith

Radar, infrared, and photogeologic properties of lunar craters have been studied to determine whether there is a systematic difference in blocky craters between the maria and terrae and whether this difference may be due to a deep megaregolith of pulverized material forming the terra surface, as opposed to a layer of semi-coherent basalt flows forming the mare surface. Some 1310 craters from about 4 to 100 km diameter have been catalogued as radar and/or infrared anomalies. In addition, a study of Apollo Orbital Photography confirmed that the radar and infrared anomalies are correlated with blocky rubble around the crater.Analysis of the radar and infrared data indicated systematic terra—mare differences. Fresh terra craters smaller than 12 km were less likely to be infrared and radar anomalies than comparable mare craters: but terra and mare craters larger than 12 km had similar infrared and radar signatures. Also, there are many terra craters which are radar bright but not infrared anomalies.Our interpretation of these data is that while the maria are rock layers (basaltic flow units) where craters eject boulder fields, the terrae are covered by relatively pulverized megaregolith at least 2 km deep, where craters eject less rocky rubble. Blocky rubble, either in the form of actual rocks or partly consolidated blocks, contributes to the radar and infrared signatures of the crater. However, aging by impacts rapidly destroys these effects, possibly through burial by secondary debris or by disintegration of the blocks themselves, especially in terra regions.PSI Contribution No. 110.     

Simultaneous impact and lunar craters

The existence of large terrestrial impact crater doublets and Martian crater doublets that have been inferred to be impact craters demonstrates that simultaneous impact of two or more bodies occurs at nearly the same point on planetary surfaces. An experimental study of simultaneous impact of two projectiles near one another shows that doublet craters with ridges perpendicular to the bilateral axis of symmetry result when separation between impact points relative to individual crater diameter is large. When separation is progressively less, elliptical craters with central ridges and central peaks, circular craters with flat floors containing ridges and peaks, and circular craters with deep round bottoms are produced. These craters are similar in structure to many of the large lunar craters. Results suggest that the simultaneous impact of meteoroids near one another may be an important mechanism for the production of central peaks in large lunar craters.     

Tektites: Size estimates of their source craters and implications for their origin

From estimates of the total masses of tektites in three strewnfields, calculations by Orphal et al. (1980) of the amount of melt that could be ejected from impact craters, and equations relating kinetic energy of impact to crater diameter, it is possible to calculate minimum diameters of lunar craters capable of ejecting the liquid masses that could have formed the various tektite strewnfields. No lunar craters of the requisite sizes have been found that are young enough to correlate with the dates of formations of the strewnfields and it seems clear that the Moon must be eliminated as a source of tektites on the Earth. It is concluded that the associations of the Ivory Coast tektites with the Bosumtwi crater and the moldavites with the Rieskessel are real and the tektites are of terrestrial origin. It follows that if the Ivory Coast tektites came from the 10.5-km-wide Bosumtwi crater, the larger masses in the Australasian and North American strewnfields came from craters 17 km in diameter and between 33 and 65 km in diameter, respectively. No crater has yet been proven to be the parent of the Australisian tektites. The large crater that formed the North American tektites may not yet have been found, although the Mistastin Lake Crater may eventually be proven to be the source.     

On the depths and shapes of the freshest kilometer-scale simple craters on the lunar maria: A new crater shape model

Recent work on the shapes of small, simple impact craters on the Moon has shown that the parabolic ideal does not well represent the vast majority of these craters. They are hyperbolic in shape and usually resemble a cone more than a parabola. A parabolic shape also does not fit the most commonly held archetype for simple craters in general (Linné), which is also hyperbolic. In addition, Linné itself may not be the best model for fresh simple craters, in terms of cross-sectional shape, although shape data to compare it to have heretofore been lacking. Here, the “free shadowfront method” for determining the shapes of simple craters is used to measure 64 fresh simple craters on five lunar maria to test both assumptions. Laser altimetry cross sections, available for many of the craters measured herein, are used to complement and spot-check the shadow measurement results, and thereby demonstrate the efficacy of the free shadowfront method. A new shape model is established, and two craters that better fit this model than Linné are identified. These are located at 24.45° N/328.12° E and 31.35° N/296.46° E and have diameters of 1.40 and 2.73 km, respectively. An apparent dichotomy between fresh simple craters smaller than 2.5 km and those larger than this is observed. Flat floors are found to be ubiquitous among the larger craters, but rare and small in extent in smaller ones. A slide in one crater which appears to be an incipient flat floor suggests a major mode of formation for these flat floors.     

A description of the crater Tsiolkovsky on the lunar far side

Although researchers in the last decade have been primarily concerned with the exotic findings of the more distant planets and moons in our solar system, as given by the Voyager series, there is still much work to be done on our nearer neighbours, including the Moon. This paper summarizes some basic age dating of a portion of the lunar surface, namely the mare in the crater Tsiolkovsky on the lunar far side.Using the Apollo 15 panoramic camera photographs, the cumulative crater frequency (N km^-2) relative to crater diameter (D) distribution has been obtained for the mare in the crater Tsiolkovsky. The diameter size range sampled was 0.07 km < D < 1 km. A total of 12 604 craters were counted and their average apparent diameters measured. There were 85 sample areas on the mare surface which were chosen at random, after exclusion of blanketed, volcanic or secondary cratered areas. It was found that a large proportion of the crater floor contains endogenic features, especially volcanic vents at approximately D = 0.3 km. An additional 7 areas of interest were also examined in detail for comparison with areas of purely primary impact craters. Evidence for up to 8 lava floodings can be detected from the size-frequency distributions although no visual data, e.g., flow lobes, can be seen on the mare surface.The total size-frequency distribution for all the areas is coincident with Neukum et al. (1975a and b) Calibration Distribution in the size range 0.25 km < D < 1 km which is at the smallest crater diameters that they obtained. Neukum et al. (1975a and b) give their distribution as a polynomial of 7th degree. However, in this present study a variation is indicated in the steepening of the curve for D < 0.1 km.The results also approximate (but only for D < 0.6 km) the distribution obtained by Shoemaker et al. (1970) in the range 100 m < D < 3 km where N ~ D ^-2.9. The best fit line reached for the data given here is N ~ D ^-2.682.Comparison of the distribution with plots for the maria at Apollo 11, 12, and 15 landing sites show that Tsiolkovsky mare is 3.51 ± 0.1 × 10⁹ yr old. This agrees with other workers (see Gornitz, 1973) who place it between Mare Tranquillitatis (Apollo 11 radiometric dating: 3.5 to 3.9 aeons) and Oceanus Procellarum (Apollo 12: 3.5 to 3.4 aeons). There are no rock samples from Tsiolkovsky to given an absolute age.This places Tsiolkovsky mare within the weighted mean of the age range (1.0 to 4.3 × 10⁹ yr old) of the maria on the Moon. From this it can be concluded that the processes producing the vast basalt outpourings seen on the Moon's face apply for the far side also and that there is a linking factor for the whole Moon.     

Pluto—The ninth planet's golden year: A meeting held at New Mexico State University,Las Cruces,New Mexico

The simple-to-complex transition for impact craters on Mars occurs at diameters between about 3 and 8 km. Ballistically emplaced ejecta surround primarily those craters that have a simple interior morphology, whereas ejecta displaying features attributable to fluid flow are mostly restricted to complex craters. Size-dependent characteristics of 73 relatively fresh Martian craters, emphasizing the new depth/diameter (d/D) data of D. W. G. Arthur (1980, to be submitted for publication), test two hypotheses for the mode of formation of central peaks in complex craters. In particular, five features appear sequentially with increasing crater size: first flat floors (3–4 km), then central peaks and shallower depths (4–5 km), next scalloped rims (? km), and lastly terraced walls (～8 km). This relative order indicates that a shallow depth of excavation and an unspecified rebound mechanism, not centripetal collapse and deep sliding, have produced central peaks and in turn have facilitated failure of the rim. The mechanism of formation of a shallow crater remains elusive, but probably operates only at the excavation stage of impact. This interpretation is consistent with two separate and complementary lines of evidence. First, field data have documented only shallow subsurface deformation and a shallow transient cavity in complex terrestrial meteorite craters and in certain surface-burst explosion craters; thus the shallow transient cavities of complex craters never were geometrically similar to the deep cavities of simple craters. Second, the average depths of complex craters and the diameters marking the transition from simple to complex craters on Mars and on three other terrestrial planets vary inversely with gravitational acceleration at the planetary surface, g, a variable more important in the excavation of a crater than in any subsequent modification of its geometry. The new interpretation is summarized diagrammatically for complex craters on all planets.     

Moon: Central peak heights and crater origins

The heights of central peaks in lunar craters are directly proportional to crater diameters, implying that peak height is a function of crater-forming energy. A similar relationship exists for terrestrial meteorite and TNT craters whose uplifts are of rebound origin. A rebound origin for lunar central peaks implies an impact origin for central peak craters. Correlation of peak heights and crater depths provides direct evidence for lava filling of crater floors.     

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.     

Lunar craters evolution and meteoroidal flux in pre-mare and post-mare times

In order to study the geomorphic evolution and lifetimes of lunar craters, data were collected from (i) 32mare andterra provinces of the nearside of the Moon using the L.P.L. catalog; (ii) amare area in Sinus Medii, using direct observations of Lunar Orbiter photos, and (iii) aterra area on the farside using direct observations of Zond-8 photos. The theory presented in a previous publication is expanded and applied to the data.The following conclusions are obtained. (1) Steady-state conditions occur on the studiedmare surfaces for craters of diameter up to approximately 220 m, and on the studiedterra surfaces for craters of diameter up to at least 50 km. (2) The average lifetime of a crater, in addition of being a function of the meteoroidal flux, is a steep function of the diameter of the crater. (3) The correlation is good between a geomorphic classification of craters based on visual comparison with standard craters and a classification of craters based on their depth-diameter ratio, resulting in a coefficient of rank correlation of 0.64. (4) When craters are classified as young, mature, and old, the length of time spent as young is less than a few percent of the total lifetime of the crater; the time spent as mature is 10 to 30%; and as much as 80% is spent as an old crater. Within the error of the calculations, these values are independent of crater diameter and apply to both pre-mare and post-mare craters, indicating that they are also independent of the intensity of the meteoroidal flux. (5) The average lifetime of a 50 km crater in pre-mare times is estimated to be less than 0.3×10⁹ years. (6) The average lifetime of a 50 km crater in post-mare times is estimated to be between 3×10¹¹ and 10¹⁴ years. (7) The average meteoroidal flux in pre-mare times is estimated to be three to six orders of magnitude more intense than in post-mare times.