Comments on the figure of the moon based on preliminary results from laser altimetry

Range measurements from the orbiting spacecraft to the lunar surface were made during the Apollo 15 mission using a laser altimeter. The measurements were made in a plane inclined at approximately 26° with respect to the lunar equator. Analysis of measurements made during one complete lunar revolution indicates that the figure of the Moon is very complex. The lunar far side appears to be considerably rougher than the near side in this plane. There appears to be a very large depression on the far side centered at approximately 180° longitude. The near-side maria are depressed with respect to surrounding terrae. These data provide some proof that there is a displacement between the center of figure and the center of mass of the Moon.     

Crater size-shape profiles for the moon and mercury: Terrain effects and interplanetary comparisons

New crater size-shape data were compiled for 221 fresh lunar craters and 152 youthful mercurian craters. Terraces and central peaks develop initially in fresh craters on the Moon in the 0–10 km diameter interval. Above a diameter of 65 km all craters are terraced and have central peaks. Swirl floor texture is most common in craters in the size range 20–30 km, but it occurs less frequently as terraces become a dominant feature of crater interiors. For the Moon there is a correlation between crater shape and geomorphic terrain type. For example, craters on the maria are more complex in terms of central peak and terrace detail at any given crater diameter than are craters in the highlands. These crater data suggest that there are significant differences in substrate and/or target properties between maria and highlands. Size-shape profiles for Mercury show that central peak and terrace onset is in the 10–20 km diameter interval; all craters are terraced at 65 km, and all have central peaks at 45 km. The crater data for Mercury show no clear cut terrain correlation. Comparison of lunar and mercurian data indicates that both central peaks and terraces are more abundant in craters in the diameter range 5–75 km on Mercury. Differences in crater shape between Mercury and the Moon may be due to differences in planetary gravitational acceleration (gMercury=2.3gMoon). Also differences between Mercury and the Moon in target and substrate and in modal impact velocity may contribute to affect crater shape.     

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.     

On the deviation of the lunar center of mass to the East. Two possible mechanisms based on evolution of the orbit and rounding off the shape of the Moon

From the observations of the gravitational field and the figure of the Moon, it is known that its center of mass (briefly COM) does not coincide with the center of figure (COF), and the line “COF/COM” is not directed to the center of the Earth, but deviates from it to the South–East. Here we study the deviation of the lunar COM to the East from the mean direction to Earth.At first, we consider the optical libration of a satellite with synchronous rotation around the planet for an observer at a point on second (empty) orbit focus. It is found that the main axis of inertia of the satellite has asymmetric nonlinear oscillations with amplitude proportional to the square of the orbit eccentricity. Given this effect, a mechanism of tidal secular evolution of the Moon’s orbit is offered that explains up to \(20\%\) of the known displacement of the lunar COM to the East. It is concluded that from the alternative—evolution of the Moon’s orbit with a decrease or increase in eccentricity—only the scenario of evolution with a monotonous increase in orbit eccentricity agrees with the displacement of lunar COM to the East. The precise calculations available confirm that now the eccentricity of the lunar orbit is actually increasing and therefore in the past it was less than its modern value, \(e = 0.0549\).To fully explain the displacement of the Moon’s COM to the East was deduced a second mechanism, which is based on the reliable effect of tidal changes in the shape of the Moon. For this purpose the differential equation which governs the process of displacement of the Moon’s COM to the East with inevitable rounding off its form in the tidal increase process of the distance between the Earth and the Moon is derived. The second mechanism not only explains the Moon’s COM displacement to the East, but it also predicts that the elongation of the lunar figure in the early epoch was significant and could reach the value \(\varepsilon\approx0.31\). Applying the theory of tidal equilibrium figures, we can estimate how close to the Earth the Moon could have formed.     

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.     

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.     

Olivine-rich exposures in the South Pole-Aitken Basin

The distribution and the geological context of the olivine-rich exposures in the South Pole-Aitken (SPA) Basin on the Moon were investigated based on the spectral data obtained from the Spectral Profiler (SP) and Multiband Imager (MI) onboard the Japanese lunar explorer Kaguya/SELENE. The olivine-rich exposures are found only in the peak rings or central peaks of the Schrödinger basin and Zeeman crater, which are located in the outer region of the SPA Basin and not in the center region. On a localized scale, the olivine-rich materials are exposed on landslide features on the crater walls or sloped wall of the central peaks or the peak rings. Another observational finding is the co-existence of olivine-rich and plagioclase-rich materials on a kilometer scale spanning most of the olivine-rich sites in the Schrödinger basin. Pyroxene-rich materials are found in fresh craters outside the peak rings or the central peaks with olivine-rich materials. Based on these results, the following scenario are proposed: (1) the impact to form the SPA Basin melted a large amount of the lunar upper mantle and crust, and distributed the melted materials to the outer region; (2) local differentiation of melted materials hid the olivine-rich materials in the center region of the SPA Basin; (3) later impacts that formed the Schrödinger and Zeeman craters excavated and exposed the olivine-rich materials to the surface again; and (4) space weathering and regolith gardening obscured the olivine-rich spectra at the exposure sites, but recent, small scale impacts or landslides on the sloped wall exposed fresh olivine-rich materials, allowing the identification of the olivine-rich exposures by spectral remote-sensing. This suggests that several, different scale events play an important role in forming the surface distributions of originally deep-seated materials on the Moon, as well as on other planetary bodies.     

Random processes as a cause of the lunar asymmetry

The offset of the center of mass of the Moon from its center of figure together with moment of inertia differences are explainable by a lunar crust of randomly varying thickness. The necessity of postulating a method of preferential material transport into a particular lunar hemisphere to explain the lunar asymmetry is eliminated.This paper represents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Differential melt scaling for oblique impacts on terrestrial planets

Analytical estimates of melt volumes produced by a given projectile and contained in a given impact crater are derived as a function of impact velocity, impact angle, planetary gravity, target and projectile densities, and specific internal energy of melting. Applications to impact events and impact craters on the Earth, Moon, and Mars are demonstrated and discussed. The most probable oblique impact (45°) produces ～1.6 times less melt volume than a vertical impact, and ～1.6 and 3.7 times more melt volume than impacts with 30° and 15° trajectories, respectively. The melt volume for a particular crater diameter increases with planetary gravity, so a crater on Earth should have more melt than similar-size craters on Mars and the Moon. The melt volume for a particular projectile diameter does not depend on gravity, but has a strong dependence on impact velocity, so the melt generated by a given projectile on the Moon is significantly larger than on Mars. Higher surface temperatures and geothermal gradients increase melt production, as do lower energies of melting. Collectively, the results imply thinner central melt sheets and a smaller proportion of melt particles in impact breccias on the Moon and Mars than on Earth. These effects are illustrated in a comparison of the Chicxulub crater on Earth, linked to the Cretaceous–Tertiary mass extinction, Gusev crater on Mars, where the Mars Exploration Rover Spirit landed, and Tsiolkovsky crater on the Moon. The results are comparable to those obtained from field and spacecraft observations, other analytical expressions, and hydrocode simulations.     

Relative and absolute ages of individual craters and the rate of infalls on the moon in the post-imbrium period

This paper contains a reasonably successful attempt to determine relative ages and then absolute ages of individual craters younger than Imbrium, and the rate of infalls onto the Moon as a function of time. After the tail of the massive premare bombardment became depleted before 3 aeons (1 aeon = 10⁹ years) ago, there was a period of minimal numbers of infalls. The rate of infalls increased rather steadily from this minimum to the present. The rate in the geologically recent past (0.3 aeon) was about two times that found for the period immediately after the last of the major lave outpourings (3.2 aeons). Absolute ages were determined for large craters (?8 km) from crater counts on the surfaces within and on the rims of the large craters. Key dates were 0 and 0.3 aeon for terrestrial meteoritic craters, 3.2, 3.5, 3.8, and 3.82 aeons for the various mare surfaces according to the determinations of D.E. Wilhelms (1980, Geologic history of the Moon, U.S. Geol. Surv. Prof. Pap.) and 3.85 aeons from the formation of Imbrium.     

Physical properties of lunar craters

The surface of the Moon is highly cratered due to impacts of meteorites, asteroids, comets and other celestial objects. The origin, size, structure, age and composition vary among craters. We study a total of 339 craters observed by the Lunar Reconnaissance Orbiter Camera(LROC). Out of these 339 craters, 214 craters are known(named craters included in the IAU Gazetteer of Planetary Nomenclature) and 125 craters are unknown(craters that are not named and objects that are absent in the IAU Gazetteer). We employ images taken by LROC at the North and South Poles and near side of the Moon. We report for the first time the study of unknown craters, while we also review the study of known craters conducted earlier by previous researchers. Our study is focused on measurements of diameter, depth, latitude and longitude of each crater for both known and unknown craters. The diameter measurements are based on considering the Moon to be a spherical body. The LROC website also provides a plot which enables us to measure the depth and diameter. We found that out of 214 known craters, 161 craters follow a linear relationship between depth(d) and diameter(D), but 53 craters do not follow this linear relationship. We study physical dimensions of these 53 craters and found that either the depth does not change significantly with diameter or the depths are extremely high relative to diameter(conical). Similarly, out of 125 unknown craters, 78 craters follow the linear relationship between depth(d) and diameter(D) but 47 craters do not follow the linear relationship.We propose that the craters following the scaling law of depth and diameter, also popularly known as the linear relationship between d and D, are formed by the impact of meteorites having heavy metals with larger dimension, while those with larger diameter but less depth are formed by meteorites/celestial objects having low density material but larger diameter. The craters with very high depth and with very small diameter are perhaps formed by the impact of meteorites that have very high density but small diameter with a conical shape. Based on analysis of the data selected for the current investigation, we further found that out of 339 craters, 100(29.5%) craters exist near the equator, 131(38.6%) are in the northern hemisphere and 108(31.80%) are in the southern hemisphere. This suggests the Moon is heavily cratered at higher latitudes and near the equatorial zone.     

Accretional heating as the major cause of compositional differences among meteorite parent bodies,the Moon,and Earth

Accretional energy can be retained with sufficient efficiency in the outer layers of the Moon due to the considerable amount of debris falling back into large craters.Heating of meteorite parent bodies occurs mainly after their accretion, by destructive collisions. The heating was generally not sufficient to differentiate the parent bodies completely so that iron meteorites would originate from the mantle, rather than from the core of a meteorite parent body. Assuming that the Earth and Moon accreted from material of similar chemical composition, we suggest that only from the outer lunar shell is there a loss of gases and volatiles due to accretional melting. The Earth melted completely and degassing was efficient for the whole mass of the Earth leading to its ≈20% higher uncompressed mean density in comparison to the Moon. Because of its lower gravitational field, gases and volatiles escaped much more easily from the lunar atmosphere than from the terrestrial one, leading to the observed depletion in volatiles of the outer parts of the Moon.     

Combined position and diameter measures for lunar craters

The note addresses the problem of simultaneously measuring positions and diameters of circular impact craters on wide-angle photographs of approximately spherical planets such as the Moon and Mercury. The method allows for situations in which the camera is not aligned on the planet's center.     

The Nature of Anomalous Formations in the Polar Regions of Mercury and the Moon

Craters located in the polar regions of Mercury and the Moon are studied. The areas of permanently shadowed zones in the polar regions of both celestial bodies are computed. In the case of the Moon, variations of the position of its rotation pole with respect to the ecliptic pole during the 18.6-year period were taken into account. In the case of Mercury, the computations were performed for a period equal to one Mercurial solar day. The variations of temperature are computed for craters coinciding with the areas of high hydrogen content for the Moon and areas with anomalous reflective properties for Mercury, including craters with anomalous areas discovered with the upgraded radio telescope of the Arecibo observatory (Harmon and Perillat, 2001). Craters that may contain deposits of water ice or other volatile compounds are identified in the polar regions of both celestial bodies.     

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.     

The Flux of Lunar Meteorites onto the Earth

Numerous new finds of lunar meteorites in Oman allow detailed constraints to be obtained on the intensity of the transfer of lunar matter to the Earth. Our estimates show that the annual flux of lunar meteorites in the mass interval from 10 to 1000 g to the entire Earth's surface should not be less than several tenths of a kilogram and is more likely equal to tens or even a few hundred kilograms, i.e., a few percent of the total meteorite flux. This corresponds to several hundred or few thousand falls of lunar meteorites on all of Earth per year. Even small impact events, which produce smaller than craters on the Moon smaller than 10 km in diameter, are capable of transferring lunar matter to the Earth. In this case, the Earth may capture between 10 to 100% of the mass of high-velocity crater ejecta leaving the Moon. Our estimates for the lunar flux imply rather optimistic prospects for the discovery of new lunar meteorites and, consequently, for the analyses of the lunar crust composition. However, the meteorite-driven flux of lunar matter did not play any significant role in the formation of the material composition of the Earth's crust, even during the stage of intense meteorite bombardment.     

Mineralogy of northern nearside mare basalts

The mineralogy of mare basalts reflects the chemical composition of the magma source, as well as the physical and chemical environment of the rocks' formation. This is significant for understanding the thermal evolution of the Moon. In this study, the spatial distribution of mineralogy on the lunar northern nearside basalts was mapped using the Moon Mineralogy Mapper(M^3) data. The study area, which is an elongated mare, Mare Frigoris and northern Mare Imbrium, was mapped and characterized into 27 units based on multi-source data, including spectrum, terrain and element abundance. We extracted 177 M^3 spectra from fresh craters. Spectral parameters such as absorption center and band area ratio(BAR)were obtained through data processing. The variation of mafic minerals in this region was acquired by analyzing these parameters. The basaltic units in eastern Mare Frigoris, which are older, have been found to be dominated by clinopyroxene with lower CaO compared to the returned lunar samples; this is similar to older basaltic units in Mare Imbrium. The basaltic units of western Mare Frigoris and Sinus Roris which are younger have been found to be rich in olivine. The late-stage basalts in Oceanus Procellarum and Mare Imbrium show the same feature. These widespread olivine-rich basalts suggest uniqueness in the evolution of the Moon. Geographically speaking, Mare Frigoris is an individual mare, but the magma source region has connections with surrounding maria in consideration of mineral differences between western and eastern Frigoris, as well as mineral similarities with maria at the same location.     

Evidence for convection in planetary interiors from first-order topography

Center of mass-center of figure offsets are known for the Earth, Moon, Mars and Venus. Such an offset requires a density distribution asymmetric about the center of mass. Observational evidence indicates that the terrestrial, lunar and Martian offsets result from crusts of variable thickness rather than lateral density inhomogeneities and that the thickness variations are more likely caused by internal convection than impact.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Constraints on the source of lunar cataclysm impactors

Multiple impact basins formed on the Moon about 3.8 Gyr ago in what is known as the lunar cataclysm or Late Heavy Bombardment. Many workers currently interpret the lunar cataclysm as an impact spike primarily caused by main-belt asteroids destabilized by delayed planetary migration. We show that morphologically fresh (class 1) craters on the lunar highlands were mostly formed during the brief tail of the cataclysm, as they have absolute crater number density similar to that of the Orientale basin and ejecta blanket. The connection between class 1 craters and the cataclysm is supported by the similarity of their size-frequency distribution to that of stratigraphically-identified Imbrian craters. Majority of lunar craters younger than the Imbrium basin (including class 1 craters) thus record the size-frequency distribution of the lunar cataclysm impactors. This distribution is much steeper than that of main-belt asteroids. We argue that the projectiles bombarding the Moon at the time of the cataclysm could not have been main-belt asteroids ejected by purely gravitational means.     

Local lunar topography from the Apollo 17 Alse radar imagery and altimetry

The Apollo 17 ALSE VHF radar provided imagery and continuous profiling data around the Moon during two revolutions. The imagery data are used to derive depth and diameter measurements of small craters (diameter <30 km). The profiling data are used to study the topography of a few large craters: the bulged floors in Hevelius, Neper, and Aitken; central peaks in Neper and Buisson; and the depressed floor of Maraldi. The same data provided accurate (better than 25 m) profiles of Mare Crisium and Mare Serenitatis.