The accurate definition of the lunar cratering chronology is important for deriving absolute model ages across the lunar surface and throughout the Solar System. Images from the Lunar Reconnaissance Orbiter Narrow Angle Cameras and Wide-Angle Camera and the SELENE/Kaguya Terrain Camera provide new opportunities to investigate crater size-frequency distributions (CSFDs) on individual geological units at lunar impact craters. We report new CSFD measurements for the Copernican-aged craters North Ray, Tycho, and Copernicus, which are crucial anchor points for the lunar cratering chronology. We also discuss possible reasons for an age discrepancy observed between the impact melt and ejecta units. Our CSFDs for North Ray and Tycho crater ejecta deposits are consistent with earlier measurements. However, for Copernicus crater and one of its rays, we find significantly lower cumulative crater frequencies than previous studies. Our new results for Copernicus crater fit the existing lunar absolute chronologies significantly better than the previous counts. Our derived model ages of the ejecta blankets of North Ray, Tycho, and Copernicus agree well with radiometric and exposure ages of the Apollo 16, 17, and 12 landing sites, respectively, and are generally consistent with a constant impact rate over the last 3 Ga. However, small variations of the impact rate cannot be resolved in our data and require further investigations.
 Radiometric and exposure ages from returned Apollo 11, 12, 14, 15, 16, and 17 and Luna 16 and 24 samples were correlated with crater size-frequency distribution (CSFD) measurements or the cumulative number of craters of a certain reference diameter (usually ≥1 km in diameter or Ncum(D ≥ 1 km)) at the landing sites to anchor the lunar cratering chronology (Figure 1) [e.g., Basaltic Volcanism Study Project (BVSP), 1981; Neukum, 1983; Neukum and Ivanov, 1994; Stöffler and Ryder, 2001, Le Feuvre and Wieczorek, 2011]. This is not a trivial task and led to several chronologies [e.g., Neukum, 1983; BVSP, 1981; Neukum and Ivanov, 1994; Stöffler and Ryder, 2001; Stöffler et al., 2006, and references therein], which all agree to within a factor of 2–3 with each other [Neukum and Ivanov, 1994]. All chronologies are only constrained by a few data points over the last 1 Ga, i.e., Copernicus, Tycho, North Ray, and Cone craters, and there are no calibration data available between 1 and 3 Ga and beyond 3.9 Ga [Stöffler and Ryder, 2001]. On the basis of these four young craters, a constant lunar impact rate for the last 3 Ga was postulated [e.g., Neukum, 1983; Neukum et al., 2001]. Hence Copernicus, Tycho, North Ray, and Cone craters are crucial for the determination of an accurate lunar cratering chronology and our understanding of the impact rate in the inner Solar System (including Earth) over the last 1 Ga. In all of the previously published chronologies, the data point for Copernicus lies above the derived lunar cratering chronology. Either existing CSFD measurements for Copernicus have significantly higher Ncum(D ≥ 1 km) than expected from the chronology or the radiometric and exposure ages derived from materials thought to have originated from Copernicus are too young and thus represent a different event (Figure 1).
Stöffler and Ryder  carefully reviewed the radiometric and exposure ages determined from returned samples; that is, they revisited the x axis of the lunar cratering chronology. Here, using images from the Lunar Reconnaissance Orbiter (LRO) Narrow Angle Cameras (NAC; 0.5 to 2.0 m/pixel) and Wide-angle Camera (WAC; ≤100 m/pixel) [Robinson et al., 2010], as well as the SELENE/Kaguya Terrain Camera (TC; 10 m/pixel) [Haruyama et al., 2008], we update CSFD measurements for young craters North Ray, Tycho, and Copernicus, which represent the y axis of the chronology.
 The well-established technique of CSFD measurements is described elsewhere [e.g., Hartmann, 1966; Crater Analysis Techniques Working Group, 1979; Neukum, 1983; Hiesinger et al., 2000]. In short, to obtain the relative or absolute age of a photogeological unit, one must (1) measure the surface area of the unit and (2) measure the diameters of each primary impact crater within this unit. Obtained crater diameters are sorted into 18 bins per diameter decade, (i.e., in the interval 1 ≤ D ≤ 10 we have the steps 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0) and plotted as cumulative distributions [e.g., Crater Analysis Techniques Working Group, 1979], which give the number of craters larger than or equal to a certain diameter per area measured, typically either 1 km2 or 106 km2.
 The cumulative crater density of a geologic unit taken at a fixed reference diameter (usually 1 or 10 km) is directly related to the time the unit has been exposed to the meteorite flux and therefore gives a relative age of this unit. The production function of Neukum et al.  is only valid for craters with diameters >10 m and <100 km; in the current study, absolute model ages (AMAs) were derived only for lunar craters in this diameter range, despite the fact that the NAC resolution allows the recognition of smaller craters.
Morota et al.  found that the crater density near the apex of the Moon is 1.5–1.8 times higher than around the antapex. Gallant et al.  reported that the cratering rate of an area within 30° of the apex is 1.28 ± 0.01 times higher than of an area of equal size near the antapex. Le Feuvre and Wieczorek  argued that compared with the global average, the cratering rate is about 25% higher at the apex and about 25% lower at the antapex. To correct for this spatial variation of impact craters, they developed a new lunar chronology, which is very similar to the chronology of Neukum et al.  for ages younger than 3 Ga. However, significant differences between the two chronologies occur at model ages older than 3 Ga. Because the differences are rather small for young surface ages, we use the well-established chronology of Neukum et al. .
 For our crater counts of North Ray crater, we used LRO NAC image pair M129187331 (Table 1). For Tycho crater, we used four pairs of LRO NAC images: M104570590, M104584909, M104599198, and M109312132. Crater counts of the landslide, thought to have been triggered by secondary impacts from Tycho at the Apollo 17 landing site [Wolfe et al., 1975; Lucchitta, 1977], were performed on NAC image pair M104318871. For Copernicus crater, we used five LRO NAC image pairs: M102300677, M102271998, M102279188, M102293451, and M122360312. The Apollo 12 landing site, which provides exposure ages potentially linked to Copernicus [e.g., Meyer et al., 1971; Silver, 1971; Eberhardt et al., 1973; Alexander et al., 1976; Bogard et al., 1994; Stöffler and Ryder, 2001], was studied in NAC image pair M104662862. Pixel scales of the NAC images used in our study vary from 0.5 to 1.4 m; incidence angles are between 43 and 81 degrees, with one image having an incidence angle of 27 degrees (Table 1). This image of Copernicus was chosen because at the time of counting this was the highest incidence angle NAC image available for this portion of the Copernicus ejecta blanket. Most of the Tycho NAC counts were performed on images with incidence angles of 62 degrees, and most of the Copernicus NAC counts were done on images with incidence angles of 77–78 degrees. Whenever possible, we selected images with similar incidence angles to minimize the possible effect of differing incidence angles on the crater size-frequency measurements [Soderblom, 1970; Young, 1975; Wilcox et al., 2005; Ostrach et al., 2011].
Table 1. Key Parameters of LROC NAC and LROC WAC Images Used for Crater Size-Frequency Distribution Measurements
Day of Year
Incidence Angle (°)
North Ray Crater
Apollo 17 Landslide
Apollo 12 Landing Site
 To test the validity of using NAC images to perform crater counts at small crater diameters (e.g., ≪100 m) and with small counting areas (e.g., <25 km2), we also performed measurements on the continuous ejecta blankets of Tycho and Copernicus using LRO WAC images and mosaics to study craters >300 m to several kilometers in diameter (M104584833, M104599125, M117561446, M117616709, M117630271, and M117637067). The WAC images have a pixel scale of 56–84 m and incidence angles of 62–84 degrees (Table 1). For Tycho, two WAC images had an incidence angle of 62 degrees, consistent with that of most of the NAC images we used. For Copernicus, all WAC images had incidence angles of 81 degrees, which was very similar to the NAC data. A compilation of important image parameters is given in Table 1. In addition, for our CSFD measurements of Copernicus crater we used portions of the SELENE/Kaguya Terrain Camera (TC) mosaic [Haruyama et al., 2008], which has an intermediate spatial resolution (10 m/pixel) compared to NAC and WAC.
 For North Ray crater, we used exactly the same four count areas as defined in the doctoral thesis of König , also referred to in the work of Neukum , Neukum et al. , and Stöffler and Ryder  (Figure 2a and Table 2). The North Ray crater areas were counted independently by two of the current authors to test the reproducibility of data collection. Fits to the lunar production function produced identical ages within the standard errors for both data sets.
Table 2. Size of Counting Areas, Number of Craters Counted, Ncum(D ≥ 1 km), Absolute Model Ages (AMAs), and Errors for Each Unit
Number of Craters
Ncum(D ≥ 1 km) (× 10−5)
AMA Error (Ma)
North Ray Crater
4.10 × 10−1
8.37 × 10−1
4.37 × 10−1
4.36 × 10−1
2.12 × 100
4.10 × 10−1
8.37 × 10−1
4.37 × 10−1
4.36 × 10−1
2.12 × 100
1.09 × 10−1
1.24 × 100
2.17 × 10−1
8.11 × 10−2
1.65 × 100
8.58 × 10−1
1.53 × 100
9.03 × 10−1
1.35 × 100
2.61 × 10−1
3.72 × 10−2
4.07 × 100
6.71 × 103
Apollo 17 Landslide
8.97 × 10−1
1.12 × 100
9.59 × 10−1
2.98 × 100
1.60 × 101
1.31 × 100
9.66 × 100
1.69 × 101
1.80 × 101
4.02 × 100
2.31 × 101
1.63 × 101
1.57 × 101
1.21 × 102
4.81 × 10−1
1.64 × 100
2.01 × 10−1
9.30 × 10−2
1.01 × 100
2.92 × 10−1
7.22 × 102
9.92 × 102
9.12 × 102
SUM WAC CE1–3
2.63 × 103
1.61 × 103
Apollo 12 Landing Site
1.19 × 100
1.19 × 100
 The individual count areas measured by author 1 gave Ncum(D ≥ 1 km) of 5.06 × 10−5 (NR1), 4.19 × 10−5 (NR2), 3.72 × 10−5 (NR3), and 3.54 × 10−5 (NR4). Applying the lunar cratering chronology of Neukum et al. , we derived AMAs of ∼60, ∼50, ∼44, and ∼42 Ma, respectively. An average crater frequency was derived by summing all craters in all four count areas to give an average CSFD and then determining the Ncum(D ≥ 1 km) for this combined data set (Figure 2b). This case yields an average Ncum(D ≥ 1 km) of 3.90 × 10−5, with an AMA of ∼47 Ma. Crater counts by author 2 indicate Ncum(D ≥ 1 km) of 5.09 × 10−5 (NR1), 4.24 × 10−5 (NR2), 3.71 × 10−5 (NR3), and 3.24 × 10−5 (NR4), with respective absolute model ages of ∼61, ∼51, ∼44, and ∼39 Ma. The sum of the four count areas yields an absolute model age of ∼46 Ma (Ncum(D ≥ 1 km) of 3.84 × 10−5) for North Ray crater (Figure 2c).
 Using NAC images, we collected data for ten areas at Tycho crater (Figures 3 and 4a–4d and Table 2), including four individual smooth impact melt pools just outside the eastern and western rims. We also measured two areas on the floor of Tycho, including one impact melt pool adjacent to the central peak and a hummocky portion of the floor, and four areas on the continuous ejecta blanket. For comparison, two count areas on the continuous ejecta were also measured using WAC images. AMAs were also determined for three areas on the landslide deposit at the Apollo 17 landing site (Table 2).
 For the exterior impact melt pools we derived model ages of ∼74 Ma (TM1; Ncum(D ≥ 1 km) = 6.19 × 10−5), ∼38 (TM2; Ncum(D ≥ 1 km) = 3.19 × 10−5), ∼35 (TM4; Ncum(D ≥ 1 km) = 2.93 × 10−5), and ∼29 (TM5; Ncum(D ≥ 1 km) = 2.43 × 10−5). The average model age is ∼32 Ma (Ncum(D ≥ 1 km) = 2.72 × 10−5). The AMA of the interior melt pool (TM3) is ∼36 Ma (Ncum(D ≥ 1 km) = 3.01 × 10−5). The hummocky area on the Tycho floor, which yielded an AMA of ∼33 Ma (TF1; Ncum(D ≥ 1 km) = 2.74 × 10−5), appears to be contemporaneous with the impact melt pool ages. In summary, all but one of the investigated impact melt pools at Tycho, as well as the floor of Tycho, show similar model ages of ∼32–38 Ma (Figures 4a–4d).
 Crater counts performed using NAC images in four areas on the continuous ejecta blanket revealed significantly older ages compared to the ages of the melt ponds and the hummocky floor. Our results indicate that ejecta area TE1 is ∼108 Ma old (Ncum(D ≥ 1 km) = 9.09 × 10−5), TE2 is ∼106 Ma old (Ncum(D ≥ 1 km) = 8.90 × 10−5), TE3 is ∼84 Ma old (Ncum(D ≥ 1 km) = 7.01 × 10−5), and TE4 is ∼68 Ma old (Ncum(D ≥ 1 km) = 5.66 × 10−5). The average absolute model age of all four continuous ejecta counts is ∼85 Ma (Ncum(D ≥ 1 km) = 7.12 × 10−5) (Figure 5 and Table 2). The absolute model ages derived from counts on WAC images are on the order of ∼124 Ma (+12/−12 Ma), somewhat older than the average AMA of ∼85 Ma (+15/−18 Ma) from the NAC images (Figure 6 and Table 2).
 Our crater counts for the three areas on the Apollo 17 landslide gave ages of ∼93 (LS1; Ncum(D ≥ 1 km) = 7.78 × 10−5), ∼91 (LS2; Ncum(D ≥ 1 km) = 7.66 × 10−5), and ∼71 Ma (LS3; Ncum(D ≥ 1 km) = 5.91 × 10−5). Overall, these data yield an average age of 85 Ma, with Ncum(D ≥ 1 km) = 7.16 × 10−5 (Figures 7a and 7b and Table 2).
 The AMAs of the interior melt pools CIM1, CIM2, and CIM3 are ∼195 Ma (Ncum(D ≥ 1 km) = 1.64 × 10−4), ∼144 Ma (Ncum(D ≥ 1 km) = 1.20 × 10−4), and ∼112 Ma (Ncum(D ≥ 1 km) = 9.35 × 10−5), respectively. The AMA of the exterior melt pool CEM1 is ∼223 Ma (Ncum(D ≥ 1 km) = 1.87 × 10−4). We calculated an AMA of ∼478 Ma (Ncum(D ≥ 1 km) = 4.01 × 10−4) for floor unit CF1 and ∼341 Ma (Ncum(D ≥ 1 km) = 2.86 × 10−4) for unit CF2. Floor unit CF2 shows evidence for resurfacing at ∼89 Ma ago (Ncum(D ≥ 1 km) = 7.45 × 10−5). Our crater counts for nine ejecta regions indicate ages of ∼1210 Ma (CE1, Ncum(D ≥ 1 km) = 1.01 × 10−3), ∼1190 Ma (CE2, Ncum(D ≥ 1 km) = 1.0 × 10−3), ∼841 Ma (CE3, Ncum(D ≥ 1 km) = 7.05 × 10−4), ∼808 Ma (CE4, Ncum(D ≥ 1 km) = 6.77 × 10−4), ∼790 Ma (CE5, Ncum(D ≥ 1 km) = 6.26 × 10−4), ∼708 Ma (CE6, Ncum(D ≥ 1 km) = 5.93 × 10−4), ∼624 Ma (CE7, Ncum(D ≥ 1 km) = 5.23 × 10−4), ∼598 Ma (CE8, Ncum(D ≥ 1 km) = 5.01 × 10−4), and ∼519 Ma (CE9, Ncum(D ≥ 1 km) = 4.35 × 10−4). Summing up all the craters of the NAC ejecta counts gave an average model age of ∼797 Ma (Ncum(D ≥ 1 km) = 6.68 × 10−4) (Figure 10 and Table 2). Crater counts on a bright ray area north of the Apollo 12 (NAP12) landing site indicate an AMA of ∼678 Ma (Ncum(D ≥ 1 km) = 5.56 × 10−4), which is consistent with the results for the continuous ejecta counts (Figures 11a and 11b and Table 2). The count area that includes the Apollo 12 landing site itself (AP12) is in an equilibrium condition, thus an absolute model age cannot be fit to the CSFD.
 For comparison, we also performed crater counts for the Copernicus ejecta blanket on a WAC mosaic. We selected three areas in the east-southeast, southwest, and northwest. For the area in the northwest we calculated an absolute model age of ∼797 Ma (Ncum(D ≥ 1 km) = 6.68 × 10−4), for the area in the southwest the AMA is ∼736 Ma (Ncum(D ≥ 1 km) = 6.17 × 10−4), and for the area in the east-southeast it is ∼567 Ma (Ncum(D ≥ 1 km) = 4.75 × 10−4). Summing up all WAC counts for the continuous ejecta, we derived an absolute model age of ∼779 Ma (Ncum(D ≥ 1 km) = 6.53 × 10−4), which is in good agreement with our counts on NAC images (Figure 12 and Table 2).
 Finally, we performed crater counts for the east-southeastern and northwestern WAC areas using SELENE/Kaguya Terrain Camera (TC) images, which have a resolution of about 10 m/pixel, intermediate in spatial resolution to the NAC and WAC images. On the basis of counts on TC images, we derived an absolute model age of ∼678 Ma (Ncum(D ≥ 1 km) = 5.68 × 10−4) for the Copernicus ejecta blanket, which is similar to and within the standard error of our NAC and WAC data. Figure 12 summarizes the results of our counts of the ejecta blanket on NAC, WAC, and TC. Shown are three curves, each of which represents the summed CSFDs of the count areas in each data set, as described above.
 Multiphase volcanism is an unlikely explanation for the observed discrepancy because it would require the Moon to remain hot enough to produce eruptions extremely late in its geologic history, i.e., within the last few tens of millions of years. This timing is inconsistent with thermal modeling showing that by 100 Ma, the interior had cooled enough and the lithosphere was thick enough to hinder volcanic activity [e.g., Ziethe et al., 2009]. Ivanov and Melosh  pointed out that an impact of a 20 km object hitting the target at 15 km−1 would form a 250–300 km large crater with 10,000 km3 of impact melt. However, their numerical simulations showed that even a crater of this size would not raise the mantle material above the peridotite solidus by decompression, necessary for volcanic eruptions. Consequently, they concluded that impacts do not initiate volcanic eruptions [Ivanov and Melosh, 2003]. In addition, the pools are relatively small, whereas models of the ascent of lunar magmas predict that late-stage volcanic eruptions should have large volumes [Head and Wilson, 1992]. Furthermore, the location of numerous ponds at high elevations near the crater rim and flow features into the pools without evidence of source craters suggests that these pools formed by impact melt accumulation rather than volcanic eruptions.
Shoemaker et al.  suggested that observed differences in crater densities between Tycho ejecta and “smooth deposits” (interpreted to be impact melt ponds) resulted from the formation of self-secondary craters on the ejecta prior to the emplacement of the smooth deposits. They pointed out that obvious self-secondary craters are also present at the Sedan test site and are concentrated just outside the crater rim. Plescia et al.  also reported a nonuniform distribution of craters on the Giordano Bruno ejecta blanket that may be indicative of a population of self-secondary craters. CSFDs with steeper slopes than the production function might also be due to self-secondary craters at Cone and South Ray craters [Plescia and Robinson, 2011], as well as at Giordano Bruno [Plescia et al., 2010]. Craters on the ejecta blanket of Giordano Bruno that do not have pristine morphologies, lack ejecta blankets, and hence may be partly covered by continuous ejecta deposits and/or discrete ejecta blocks, were interpreted as self-secondary craters [Plescia et al., 2010]. Similar to Shoemaker et al. , Plescia et al. , and Plescia and Robinson  proposed that such craters might have formed from self-secondary impacts when blocks from the primary crater were ejected in near-vertical high-velocity trajectories to such high altitudes that their fallback time was greater than the emplacement of most of the primary ejecta material, including the melt ponds. However, Oberbeck and Morrison  argued that deposits near Tycho crater only show few secondary craters, while at greater distances subdued secondary craters were observed on the continuous ejecta blanket. According to Oberbeck and Morrison , these craters were partly filled by debris surge deposits emplaced after secondary crater formation. Oberbeck and Morrison  proposed that the sequence of secondary cratering followed by mantling with a debris surge is characteristic for all Tycho ejecta deposits. If this is the case, it seems unlikely that small-scale self-secondary craters with sizes relevant for our crater counts on NAC images survived this debris surge. Significant self-secondary cratering at Copernicus and Tycho is also not supported by our crater counts because the continuous ejecta data do not show strong deviations indicative of a large population of secondary craters when fitted with the lunar production function of Neukum et al. .
 Small-diameter secondary craters from subsequent nearby impacts are also negligible, because the crater counts on NAC, TC, and WAC images are reasonably well fitted with one isochron over a wide diameter range. The absence of close-by young impact craters large enough to produce a significant number of secondary craters on the ejecta blanket supports our interpretation, at least for Tycho. For Copernicus we avoided areas with obvious secondary craters from Kepler and Aristarchus.
 The material properties of the target are one of the factors that affect the final diameter of an impact crater [e.g., Holsapple and Schmidt, 1982; Holsapple, 1993; Ivanov and Hartmann, 2007; Ivanov, 2008; Wünnemann et al., 2011; Le Feuvre and Wieczorek, 2011]. In general, for impactors with the same characteristics, stronger targets will yield smaller craters than weaker targets, whereas more porous targets yield smaller craters relative to less porous targets [e.g., Wünnemann et al., 2011]. This effect can be quite significant, leading to differences in crater diameters, for example, on the order of 50 m for craters less than 100 m in diameter in models presented by Dundas et al.  to explain differences in CSFDs on two different surface types on young Martian lava flows. Thus, target strength can have a significant effect on resulting absolute model ages, such that geologically contemporaneous units appear to have formed at different times. At lunar impact craters, CSFDs on weaker but more porous ejecta deposits give higher AMAs than those measured on stronger but more competent impact melt deposits (this work, van der Bogert et al. , and Ashley et al. ). For example, van der Bogert et al.  calculated a 70 Ma difference in model ages for a simple comparison postulating a 20% difference in crater diameters between the two units at Jackson crater.
 Because work is still underway to understand the possible effects of self-secondary cratering and target properties on CSFDs, we use the CSFDs we derived from the continuous ejecta blanket for comparison with previous studies, which also made measurements on ejecta units. Traditionally, the ejecta blankets of major impact events have been considered as stratigraphic marker horizons, e.g., Nectaris, Imbrium, Copernicus, and Eratosthenes [e.g., Wilhelms, 1987]. In addition, for the calibration of the lunar impact chronology, crater size-frequency distributions of discrete ejecta blankets have often been correlated with the returned samples of various landing sites, e.g., the ejecta blanket of North Ray crater with exposure ages of Apollo 16, or the Copernicus ray with the exposure ages of Apollo 12 samples. For this reason, we compare our ages of the studied ejecta blankets, rather than for other types of units, to the exposure ages of the Apollo samples.
 Crater counts of four areas around North Ray crater by König  revealed an average Ncum(D ≥ 1 km) of these areas of 3.9 ± 1.0 × 10−5 and a model age of 48.9 ± 1.7 Ma. Neukum  reported the average Ncum(D ≥ 1 km) of these areas as 4.4 ± 1.1 × 10−5 (Ncum(D ≥ 10) = 1.1 × 10−7), with a corresponding model age of 50 ± 1.4 Ma. Stöffler and Ryder  in their review paper adopted the Ncum(D ≥ 1 km) of Neukum . Moore et al.  published an Ncum(D ≥ 0.01) = 1.82 × 10−4 and a formation age of North Ray crater of 50.3 ± 0.8 Ma, based on work by Drozd et al. . Plescia and Robinson  derived a model age of 92.1 Ma (Ncum(D ≥ 0.01) = 382) from their crater counts. Our new AMAs agree well with the exposure ages of North Ray crater and are consistent with and confirm previous Ncum(D ≥ 1 km) ages [e.g., König, 1977; Neukum, 1983; Neukum et al., 2001]. However, the result of Plescia and Robinson  is neither consistent with our model ages nor the exposure ages of Apollo 16 samples.
 Secondary craters from Tycho crater are suggested to have triggered a landslide on the north slope of the South Massif about 2200 km away at the Apollo 17 landing site [Wolfe et al., 1975; Lucchitta, 1977]. König  and Neukum and König  counted craters on the landslide and in the area of a cluster of secondary craters (Central Cluster) on the Taurus-Littrow floor and compared these counts with their counts made at Tycho. They found the counts agreed well and concluded that the landslide and the Central Cluster likely resulted from Tycho ejecta. Analyses of the samples returned from the landslide revealed exposure ages of about ∼100 Ma. Consequently, this age has been interpreted to represent the formation age of Tycho crater [e.g., Arvidson et al., 1976; Lucchitta, 1977; Drozd et al., 1977; Guinness and Arvidson, 1977]. The Central Cluster also has exposure ages of ∼100 Ma [Wolfe et al., 1975; Lucchitta, 1977], consistent with the idea that Tycho is a young, Copernican-aged crater. From the exposure ages, Drozd et al.  concluded that Tycho is 109 ± 4 Ma old. This age is identical to that of Guinness and Arvidson  and is similar to an exposure age of 96 ± 5 Ma for the landslide and Central Cluster materials derived by Arvidson et al. . However, Stöffler and Ryder  point out that the geological evidence for the formation of the South Massif landslide and the secondary crater cluster due to distal ejecta from Tycho is equivocal.
 Crater counts on the floor and the continuous ejecta blanket of Tycho revealed an average Ncum(D ≥ 1 km) = (6.0 ± 1.7) × 10−5 for these areas [König, 1977]. Neukum  reported a Ncum(D ≥ 1 km) = (9.0 ± 1.8) × 10−5; the same Ncum(D ≥ 1 km) is also found in the work of Stöffler and Ryder . Our new crater counts for the Tycho ejecta blanket are in agreement with these earlier crater counts.
 Our measurements performed for the Apollo 17 landslide exhibit a systematic increase of model ages of the landslide count areas with increasing distance from South Massif. This trend may either be an effect of the gradual decrease in slope toward the edge of the landslide, the decrease in thickness of the landslide, or may reflect shielding of areas closer to the massif. Steep slopes may affect CSFDs because the downslope movement of regolith and crater materials obscures craters faster than on a flat surface. Depending on the thickness of a superposed geologic unit, CSFD measurements might include craters from the older surface beneath, thus affecting the model age of the younger surface. Also, fewer craters might form in areas immediately adjacent to a topographic high, which serves as a shield. Nevertheless, the summation of the CSFDs for the three areas yielded an AMA of ∼86 Ma, which is within the error for the summed NAC Tycho ejecta AMA (Figure 6) and slightly younger than the ages derived from counts using WAC images. In addition, our absolute model ages for the landslide agree well with the exposure ages of both the Apollo 17 landslide and the Central Cluster. In summary, for Tycho, our crater counts are consistent with and confirm previous Ncum(D ≥ 1 km) ages [e.g., Neukum et al., 2001; Neukum and König, 1976].
 The Apollo 12 landing site is covered with Copernicus ray material, which led Meyer et al.  to propose that KREEP glass in the Apollo 12 samples was actually ejected by Copernicus and could be used to date the impact. Exposure ages of samples 12032 and 12033 collected at Head crater have an age of 800–850 Ma [Eberhardt et al., 1973; Alexander et al., 1976; Silver, 1971]. Radiometric ages of these samples, including degassing ages of felsite clasts within the ropy glasses also support an age of 800 ± 15 Ma [Bogard et al., 1992; Bogard et al., 1994; Wentworth et al., 1994]. Recent analyses of 21 Apollo 12 regolith samples, including additional analyses of samples 12032 and 12033, show degassing ages of 700–800 Ma, which give an estimated 782 ± 21 Ma age for the Copernicus impact event [Barra et al., 2006].
 While these ages are generally accepted to reflect the age of the Copernicus impact event, Stöffler and Ryder  pointed out problems with this interpretation. They argued that not all KREEP material at the Apollo 12 site comes from Copernicus; it may have come from different sources [Korotev et al., 2000], as Copernicus did not primarily excavate KREEP material. In addition, the glass samples were only found at Head crater; they are not widely distributed at the Apollo landing site. As the Copernicus ray is clearly visible from orbit, it is reasonable to assume that the ray material should be widely distributed at the landing site, not only at Head crater. From these considerations, Stöffler and Ryder  concluded that the age of Copernicus is either well known at 800 ± 15 Ma or it can only be inferred to be younger than ∼2 Ga.
 Assuming a constant flux of impactors for the last 3 Ga [e.g., König, 1977; BVSP, 1981; Neukum, 1983; Neukum and Ivanov, 1994; Hartmann and Neukum, 2001; Neukum et al., 2001; Stöffler and Ryder, 2001] and using the radiometric age of North Ray crater (50.3 ± 0.8 Ma) as a calibration point [e.g., Stöffler and Ryder, 2001; Drozd et al., 1977], previous absolute model ages derived from crater size-frequency distribution (CSFD) measurements for the floor of Copernicus and its continuous ejecta blanket are significantly older than the exposure ages. For example, Neukum  determined an absolute model age of 1.5 Ga (Ncum(D ≥ 1 km) = 1.3 × 10−3) and König  determined a model age of 1320 ± 310 Ma (Ncum(D ≥ 1 km) = (1.0 ± 0.3) × 10−3). While exposure ages and CSFDs of Tycho, North Ray, and Cone crater are consistent with a constant cratering rate over the last 3 Ga, cumulative crater frequencies at Copernicus crater were too high [e.g., König, 1977; BVSP, 1981; Neukum, 1983; Neukum and Ivanov, 1994; Hartmann and Neukum, 2001; Neukum et al., 2001; Stöffler and Ryder, 2001]. Neukum and König  argued that either their counts were affected by a large number of secondary craters or the radiometric ages of the Apollo 12 samples do not date the Copernicus event [Neukum and König, 1976]. Indeed, at least two of the three count areas shown in the work of König , particularly on the continuous ejecta blanket close to the northeastern rim and the northeastern discontinuous ejecta blanket, appear to be influenced by secondary or self-secondary craters, thus leading to higher Ncum(D ≥ 1 km) values. Compared to those count areas, our count areas appear smoother, less hummocky and show fewer, less pronounced radially oriented grooves, which were likely formed by secondary impacts. In fact, high-resolution LRO NAC and Kaguya TC images allow for a more careful selection of count areas to minimize effects from secondary craters and areas that more likely represent individual ejecta units, rather than mixtures of different geological units, while WAC images provide the wider geological context. This combination of images with different spatial resolutions is an improvement over previous studies of Copernicus because it is a large, geologically complex crater.
 Our new crater counts for the ejecta blanket on NAC images yielded ages between ∼519 Ma (Ncum(D ≥ 1 km) = 4.35 × 10−4) and ∼1210 Ma (Ncum(D ≥ 1 km) = 1.01 × 10−3). Figure 1 shows the new Ncum(D ≥ 1 km) ages (in red) of Copernicus fit the lunar cratering chronology much better than previous ages [e.g., König, 1977; BVSP, 1981; Neukum, 1983; Neukum and Ivanov, 1994; Hartmann and Neukum, 2001; Neukum et al., 2001; Stöffler and Ryder, 2001]. Because the crater counts on NAC, TC, and WAC images are reasonably well-fitted with one isochron over a wide diameter range, we argue that secondary cratering at small diameters is also negligible. Alternatively, secondary craters of varying sizes might have equally affected all three counts, which seems rather unlikely. Because NAC and WAC crater counts of the Tycho ejecta blanket are similarly well-fitted with one isochron, we argue that secondary cratering for Tycho is also negligible. The absence of close-by young impact craters large enough to produce a significant number of secondary craters on the ejecta blanket of at least Tycho is consistent with our interpretation. Self-secondary cratering at Copernicus and Tycho is also not supported by our crater counts because the data do not show strong deviations when fitted with the lunar production function of Neukum et al. , assuming that the production function is free of self-secondaries and secondary craters.
 Crater counts of a bright ray area north of the Apollo 12 (NAP12) landing site revealed an AMA of ∼678 Ma (Ncum(D ≥ 1 km) = 5.56 × 10−4), roughly consistent with the Copernicus ejecta ages. For the Apollo 12 site, craters smaller than ∼30 m fall just below equilibrium, whereas craters between ∼30 m and ∼300 m are in equilibrium condition (Figure 11b). It is not clear whether the emplacement of the Copernicus ray caused this erasure of small craters, as rays from smaller nearby craters also intersect at the Apollo 12 site. However, the deflection from equilibrium in the CSFD (black arrow in Figure 11b) is roughly consistent with the age of the Copernicus ray and ejecta units. Because the age of the Copernicus ray north of the Apollo 12 landing site is similar to that of the Copernicus ejecta, it is likely that Apollo 12 samples indeed date the Copernicus event. These data also suggest that ray formation discontinuously resets the age of the underlying surface. In some locations, the effects of the ray are negligible, for example at the Apollo 12 landing site; in other locations, ray formation effects seem to be significant enough to reset the surface age, e.g., north of the Apollo 12 landing site. Indeed, the albedo of the ray is higher at the NAP12 count area than at the Apollo 12 landing site.
5.5. The Lunar Chronology
 The lunar cratering chronology has been used to date unsampled surfaces throughout the Solar System [e.g., Strom and Neukum, 1988; Hartmann and Neukum, 2001; Ivanov, 2001]. Thus it is beneficial to determine the lunar impact rate as accurately as possible to minimize the propagation of errors from the Moon to other Solar System bodies.
 Our new counts for North Ray, Tycho, and Copernicus craters fit, and thus support, the lunar chronology of Neukum et al.  at young ages. Our data are also generally consistent with a constant impact rate, although with only three data points we cannot exclude small episodic variations in the cratering rate. Variations in impact rate caused by cometary showers were suggested to occur periodically due to perturbation of the Oort cloud by galactic tides, the passage of the Solar System near a molecular cloud, or an unseen star [e.g., Rampino and Stothers, 1984; Davis et al., 1984; Napier, 1998; Gardner et al., 2011]. Vertical oscillations of the Sun about the galactic midplane with a period of 52–74 Ma were also suggested to cause variations in the impact rate [e.g., Rampino and Stothers, 1984; Napier, 1998, 2006]. However, Bailer-Jones  systematically reinvestigated the available data and found no periodicity, similar to results of Grieve  and Jetsu and Pelt . Bailer-Jones  argued that most studies that claim a periodicity in the impact rate suffer from problems in their methodology, including misinterpretations of statistical probabilities (p values), overestimating the significance of periodogram peaks, or failing to consider a sufficient set of models.
 From our CSFD measurements performed on North Ray, Tycho, and Copernicus craters, we conclude that (1) despite being geologically contemporaneous with the ejecta blanket, the impact melt pools have younger apparent absolute model ages, which might be related to different target properties and/or self-secondaries; (2) our derived model ages of the ejecta blankets agree well with radiometric and exposure ages of the Apollo 16, 17, and 12 landing sites, respectively; (3) our new crater counts for the Copernicus ejecta blanket better fit the lunar chronology than previous counts; (4) the new counts are generally consistent with a constant impact rate over the last 3 Ga; small variations cannot be resolved in our data and require further investigations.
 We gratefully acknowledge the superb work of the LROC design, engineering, operations, and science team. We thank NASA and the German Aerospace Center (DLR) for support of this investigation. We also thank D. A. Kring, M. Le Feuvre, an anonymous reviewer, and team members (J. B. Plescia, A. S. McEwen, B. R. Hawke, M. Banks, L. Gaddis, and T. Watters) for their helpful comments on this and a previous version of the manuscript.