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.     

Lunar velocity structure and compositional and thermal inferences

Seismic data from the Apollo Passive Seismic Network stations are analyzed to determine the velocity structure and to infer the composition and physical properties of the lunar interior. Data from artificial impacts (S-IVB booster and LM ascent stage) cover a distance range of 70–1100 km. Travel times and amplitudes, as well as theoretical seismograms, are used to derive a velocity model for the outer 150 km of the Moon. TheP wave velocity model confirms our earlier report of a lunar crust in the eastern part of Oceanus Procellarum.The crust is about 60 km thick and may consist of two layers in the mare regions. Possible values for theP-wave velocity in the uppermost mantle are between 7.7 km s^–1 and 9.0 km s^–1. The 9 km s^–1 velocity cannot extend below a depth of about 100 km and must decrease below this depth. The elastic properties of the deep interior as inferred from the seismograms of natural events (meteoroid impacts and moonquakes) occurring at great distance indicate that there is an increase in attenuation and a possible decrease of velocity at depths below about 1000 km. This verifies the high temperatures calculated for the deep lunar interior by thermal history models.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Integration and Comparison of Clementine and Lunar Prospector Data: Global Scale Multielement Analysis1 (Fe,Ti, and Th) of the Lunar Surface

In this paper, we present (1) a statistical analysis, based on a systematic clustering method, of a dataset integrating the global abundance maps of the three elements iron, titanium, and thorium derived from Clementine and Lunar Prospector and (2) a comparison of iron abundances between Clementine and Lunar Prospector. Homogeneous geologic units are compositionally characterized and spatially defined in relation to the major rock types sampled on the Moon. With the lowest abundances of Fe, Ti, and Th found on the Moon, the lunar highland terrains are quite homogeneous with two major large feldspathic units, one being slightly more mafic than the other. Two distinct regions with unique compositions are unambiguously identified: the Procellarum KREEP Terrane (PKT) and the South Pole–Aitken (SPA). The PKT, which includes all the units with Th abundances higher than 3.5 ppm (KREEP-rich materials), is delimited by an almost continuous ringlike unit. In particular, it includes the western nearside maria, except for Mare Humorum. With concentrations in Fe, Ti, and Th enhanced relative to the surrounding highlands, the South Pole–Aitken basin floor represents a large mafic anomaly on the far side, suggesting wide deposits of lower crust and possible mantle materials. However, due to indirect residual latitude effects in the CSR (Clementine spectral reflectance) measurements, iron abundances might have been overestimated in SPA, thus implying that crustal materials, rather than mantle materials, might represent the dominant contributor to the mafic component exposed on the basin floor.     

Lunar Dust: Properties and Investigation Techniques

Physical conditions in the near-surface layer of the Moon are overviewed. This medium is formed in the course of the permanent micrometeoroid bombardment of the lunar regolith and due to the exposure of the regolith to solar radiation and high-energy charged particles of solar and galactic origin. During a considerable part of a lunar day (more than 20%), the Moon is passing through the Earth’s magnetosphere, where the conditions strongly differ from those in the interplanetary space. The external effects on the lunar regolith form the plasma-dusty medium above the lunar surface, the so-called lunar exosphere, whose characteristic altitude may reach several tens of kilometers. Observations of the near-surface dusty exosphere were carried out with the TV cameras onboard the landers Surveyor 5, 6, and 7 (1967–1968) and with the astrophotometer of Lunokhod-2 (1973). Their results showed that the near-surface layer glows above the sunlit surface of the Moon. This was interpreted as the scattering of solar light by dust particles. Direct detection of particles on the lunar surface was made by the Lunar Ejects and Meteorite (LEAM) instrument deployed by the Apollo 17 astronauts. Recently, the investigations of dust particles were performed by the Lunar Atmosphere and Dust Environment Explorer (LADEE) instrument at an altitude of several tens of kilometers. These observations urged forward the development of theoretical models for the lunar exosphere formation, and these models are being continuously improved. However, to date, many issues related to the dynamics of dust and the near-surface electric fields remain unresolved. Further investigations of the lunar exosphere are planned to be performed onboard the Russian landers Luna-Glob and Luna-Resurs.     

Photometric Stability of the Lunar Surface

The rate at which cratering events currently occur on the Moon is considered in light of their influence on the use of the Moon as a radiometric standard. The radiometric effect of small impact events is determined empirically from the study of Clementine images. Events that would change the integral brightness of the moon by 1% are expected once per 1.4 Gyr. Events that cause a 1% shift in one pixel for low Earth-orbiting instruments with a 1-km nadir field of view are expected approximately once each 43 Myr. Events discernible at 1% radiometric resolution with a 5 arc-sec telescope resolution correspond to crater diameters of approximately 210 m and are expected once every 200 years. These rates are uncertain by a factor of two. For a fixed illumination and observation geometry, the Moon can be considered photometrically stable to 1 × 10⁻⁸per annum for irradiance, and 1 × 10⁻⁷per annum for radiance at a resolution common for spacecraft imaging instruments, exceeding reasonable instrument goals by six orders of magnitude.     

Lunar paleotides and the origin of the Earth-Moon system

A new method for determining the early history of the Earth-Moon system is described. Called the study of lunar paleotides, it describes a method for explaining features of the remnant lunar gravity field, and the generation of the lunar mascons. A method for the determination of Earth-Moon distances compared with the radiometric ages of the maria is developed. It is shown that the Moon underwent strong anomalous gravitational tidal forces, for a durationt<10⁶yr, prior to the formation of the mascon surfaces. As these tidal forces had not been present at the time of the formation of the Moon, this shows that the Moon could not have been formed in orbit about the Earth.There are tides in the affairs of men which, taken at the flood, lead on to fortune... William Shakespeare 1564–1616     

Analytical Approach to the Motion of a Lunar Artificial Satellite

The canonical equations of motion of an artificial lunar satellite are formulated including the effects of the asphericity of the Moon comprising the harmonics J ₂, J ₂₂, J ₃, J ₃₁, J ₄ andJ ₅, the oblateness of the Earth up to the second zonal harmonic, as well as the disturbing function due to the attractions of the Earth and of the Sun (terms are retained up to order 10^-6 for the higher orbits and 10^-8 for the lower orbits). This revised version was published online in July 2006 with corrections to the Cover Date.     

The stress state of Venusian crust and variations of its thickness: Implication for tectonics and geodynamics

The data obtained for the heights of the relief and the external gravitational field of Venus for spherical harmonics with degree and order up to 18 allow one to start theoretical analysis of the crust-mantle boundary (Venusian Moho) and stress state of the planetary interior. We suppose that Venusian convection is confined by floating massive crust. Apparently the convection in the upper mantle of Venus is separated from that one in the lower mantle and its lateral scale must be essentially smaller than on Earth. So, the convection is reflected to a larger degree of the gravitational field of the planet than for Earth. The spherical harmonic expansion of the topography for Venus correlates with corresponding expansion of the non-equilibrium part of the gravitational potential for n = 3–18. At the same time the relief of Venus is significantly compensated. It is reasonable to suppose that the gravity field for these harmonics is due to crustal thickness variations and, probably, to variations of crustal density. Thus, in the proposed scheme the Moho's relief causes the partial isostatic compensation of the topography.All calculations are carried out for the series of realistic models of Venus taking into consideration an asthenosphere. The asthenosphere is modeled either by a weakened (shear modulus is reduced), or by a liquid inviscid layer. We also suppose that the asthenosphere extends from the base of crust to a depth of 418 km, and the density contrast across the Moho boundary is –0.4 g * cm^–3. If the actual density contrast across the Moho is less than the supposed one by some factor, then one must increase the amplitudes of the roots and inverse roots by the same factor. The results for the Moho's relief and stresses in the crust are presented for the case of the mean thickness of the crust of 50 km, which satisfies the probable upper (connected with phase transitions in waterless basalts) and lower (appearing in the framework of our interpretation) limits.On the whole, the crust-mantle boundary on Venus is evidently smooth, and the stress level in the crust is appreciably smaller than the crustal stresses on the Earth. The strong sensitivity of the stresses character to the parameters of the model of external layers of Venus together with geological data allow us to begin a preliminary investigation of the tectonical structure and geodynamics of the planet.'Geology and Tectonics of Venus', special issue edited by Alexander T. Basilevsky (USSR Acad. of Sci. Moscow), James W. Head (Brown University, Providence), Gordon H. Pettengill (MIT, Cambridge, Massachusetts) and R. S. Saunders (J.P.L., Pasadena).     

Lunar physical librations and laser ranging

The analysis of lunar laser ranging data requires very accurate calculations of the lunar physical librations. Libration terms are given which arise from the additive and planetary terms in the lunar theory. The large size of the recently discovered terms due to third degree gravitational harmonics will allow some of these harmonics to be measured, in addition to and, by laser ranging to the Moon. Combining the laser ranging determinations of = 630.6 ± 0.5 × 10^–6 and = 226.4 ± 3.0 × 10^–6 with lunar orbiter measurements ofC ₂₀ andC ₂₂ givesC/MR ²=0.395 _-0.010 ^+0.006 . Numerical integration promises to be an effective method of calculating librations. Comparison of numerical integrations with analytic series indicates that the calculation of the series due to third and fourth degree harmonics is not yet as accurate as the more extensively developed second degree terms.Communication presented at the Conference on Lunar Dynamics and Observational Coordinate Systems, held January 15–17, 1973, at the Lunar Science Institute, Houston, Tex., U.S.A.     

The Nature of Volatiles in the Lunar Regolith

Layer-by-layer analysis of the fine fraction of Luna-16 sample L1635 by X-ray photoelectron spectroscopy (XPS) revealed a zonal structure of its constituent particles. The outer zone, to a depth of 1200 Å, is enriched with Si and Fe and depleted in refractory elements Mg, Ca, and Al as compared to the bulk composition of the sample. The second zone, in the depth range from 1200 to 4500 Å, is of very unusual composition: it is enriched with carbon (up to 60 at. %) and zinc (up to 4 at. %) and contains some other volatiles. The lower zone, at depths from 4500 to 7000 Å, is composed of a silicate material; however, the concentrations of refractory elements are noticeably higher than those in the near-surface layer. There is a difference in structural and chemical characteristics of most of the elements between different zones. These findings point to the exogenous origin of the enrichment of the studied sample with volatiles and are related to the fall of a volatile-rich body (comet or carbonaceous chondrite) on the Moon. The hypothesis of the cometary (carbonaceous-chondrite) impact explains the main patterns of the volatile distribution in the lunar regolith, including the formation of green and orange glasses from Apollo 15 and 17 collections.     

Inhomogeneities in the internal structure of Mars and the Moon from data on their gravity fields

The interpretation of planetary anomalies in the gravity fields of Mars and the Moon in relationship to their inhomogeneous internal structure is considered. The Martian and lunar gravity field models up to order and degree 20, three-layer (crust, mantle, core) model parameters, and planetary parameters have been used as input data. Models of the three-dimensional density distribution have been constructed for Mars and the Moon. The maps of horizontal density inhomogeneities at depths of 50, 100, and 1700 km for Mars and 60, 100, and 1400 km for the Moon are interpreted.     

Lunar gravity: apollo 15 doppler radio tracking

New detailed gravity measurements were obtained over a 10- to 70-km surface strip from ? 70° to + 70° long. during low-altitude orbits (≈ 12 km at periapsis). The trajectory path (Figure 1) went over the centers of both Maria Serenitatis and Crisium, providing a complete center gravity profile of two large mascons. Consistent with the previous results for Mare Nectaris and Mare Humorum, both Serenitatis and Crisium mascons are approximately disk-shaped near-surface mass anomalies of net uncompensated loading, 800 kg cm^?2. This strengthens Booker's contention that all mascons are approximately the same thickness. Also revealed for the first time are significant positive gravity measurements over mountain ranges - Apennines (near Hadley Mountain) and the Marius Hills. The data suggests that the Apennines have undergone some isostatic compensation, whereas the Marius Hills have not. The crater anomalies detected are all consistently negative as observed before, implying loss of mass from the impact event which formed them.     

Crustal properties of Mercury by morphometric analysis of multi‐ring basins on the Moon and Mars

Abstract— We use satellite altitude free‐air and terrain gravity correlations to differentiate regional variations in crustal viscosity and transient cavity diameters of impact basins on the Moon and Mars that we combine with surface roughness for a rheological assessment of the crust of Mercury. For the Moon and Mars, we separate the free‐air anomalies into terrain‐correlated and terrain‐decorrelated components using the spectral properties of the free‐air and computed terrain gravity effects. Adjusting the terrain effects for the terrain‐correlated anomalies yields compensated terrain effects that we evaluate for crustal thickness variations of the impact basins. We interpret the terrain‐correlated anomalies for uncompensated elements of the crustal thickness variations that we find are strongly correlated with the distribution of basin rings from photogeologic analyses. Hence, we estimate the transient cavity diameter from the innermost diameter of the gravity‐inferred rings. Comparing these diameters with the related crustal thickness estimates clearly differentiates regional variations in the crustal rheologies. For the Moon, the analysis points to a farside crust that was significantly more rigid than the nearside crust during bombardment time. For Mars, the growth in transient cavity diameters with apparent crustal age also reflects increased viscosity due to crustal cooling. These results are also consistent with local estimates of surface roughness developed from the root‐mean‐squared topography over 64 times 64° patches centered on the basins. Hence for Mercury where gravity observations are lacking, rheological inferences on its crust may result from comparing photometric estimates of transient cavity diameter and local surface roughness with the lunar and martian estimates. These results for the Beethoven Basin, a typical multi‐ring impact feature of Mercury, suggest that the viscosity of the mercurian crust was relatively great during bombardment time. This enhanced rigidity, despite crustal temperatures that were probably much hotter than those of the Moon and Mars, may reflect an extremely dry crust for Mercury in its early development.     

The residual permanent magnetic dipole moment of the moon

The residual dipole moment of the outer spherical shell of the Moon, magnetized in the field of an internal dipole is calculated for the case when the permeability of the shell differs from unity. It is shown that, using an average value of surface magnetization from returned lunar crystalline rock samples and a global figure for the lunar permeability of 1.012, that a residual moment of the order of 10¹⁵ to 10¹⁶ Am² is expected. This value is some two or three orders of magnitude lower than the moment for a shell magnetized in an external uniform field and is of the same order as the upper limit of the residual moment detected by Russellet al. (1974). At present the magnetic data and the thermal state of the Moon are not known with sufficient accuracy to distinguish between a crust magnetized in an internal dipole field of constant polarity and a crust magnetized in the dipole field of a self-reversing core dynamo. Refined measurements of the relevant parameters together with the theory presented in this paper could enable these two possibilities to be distinguished.     

Lunar Water: A Brief Review

One of the most exciting recent developments in the field of lunar science has been the unambiguous detection of water (either as OH or H₂O) or water ice on the Moon through instruments flown on a number of orbiting spacecraft missions. At the same time, continued laboratory-based investigations of returned lunar samples by Apollo missions using high-precision, low-detection, analytical instruments have for the first time, provided the absolute abundance of water (present mostly as structurally bound OH⁻ in mineral phases) in lunar samples. These new results suggest that the Moon is not an anhydrous body, questioning conventional wisdom, and indicating the possibility of a wet lunar interior and the presence of distinct reservoirs of water on the lunar surface. However, not all recent results point to a wet Moon and it appears that the distribution of water on the Moon may be highly heterogeneous. Additionally, a number of sources are likely to have contributed to the water inventory of the Moon ranging from primordial water to meteorite-derived water ice through to the water formed during the reaction of solar-wind hydrogen with the lunar soil. Water on the Moon has implications for future astrobiological investigations as well as for generating resources in situ during future exploration of the Moon and other airless bodies in the Solar System.     

The vector approach to the problem of physical libration of the Moon: the linearized problem

A flexible and informative vector approach to the problem of physical libration of the rigid Moon has been developed in which three Euler differential equations are supplemented by 12 kinematic ones. A linearized system of equations can be split into an even and odd systems with respect to the reflection in the plane of the lunar equator, and rotational oscillations of the Moon are presented by superposition of librations in longitude and latitude. The former is described by three equations and consists of unrestricted oscillations with a period of T ₁ = 2.878 Julian years (amplitude of 1.855″) and forced oscillations with periods of T ₂ = 27.201 days (15.304″), one stellar year (0.008″), half a year (0.115″), and the third of a year (0.0003″) (five harmonics altogether). A zero frequency solution has also been obtained. The effect of the Sun on these oscillations is two orders of magnitude less than that of the Earth. The libration in latitude is presented by five equations and, at pertrubations from the Earth, is described by two harmonics of unrestricted oscillations (T ₅ ≈ 74.180 Julian years, T ₆ ≈ 27.347 days) and one harmonic of forced oscillations (T ₃ = 27.212 days). The motion of the true pole is presented by the same harmonics, with the maximum deviation from the Cassini pole being 45.3″. The fifth (zero) frequency yields a stationary solution with a conic precession of the rotation axis (previously unknown). The third Cassini law has been proved. The amplitudes of unrestricted oscillations have been determined from comparison with observations. For the ratio $ \frac{{\sin I}} {{\sin \left( {I + i} \right)}} \approx 0.2311 $ \frac{{\sin I}} {{\sin \left( {I + i} \right)}} \approx 0.2311 , the theory gives 0.2319, which confirms the adequacy of the approach. Some statements of the previous theory are revised. Poinsot’s method is shown to be irrelevant in describing librations of the Moon. The Moon does not have free (Euler) oscillations; it has oscillations with a period of T ₅ ≈ 74.180 Julian years rather than T ≈ 148.167 Julian years.     

Topographic mapping of the Moon

Contour maps of the Mooon have been compiled by photogrammetric methods that use stereoscopic combinations of all available metric photographs from the Apollo 15, 16, and 17 missions. The maps utilize the same format as the existing NASA shaded-relief Lunar Planning Charts (LOC-1, -2, -3, and -4), which have a scale of 1:2 750 000. The map contour interval is 500m. A control net derived from Apollo photographs by Doyle and others was used for the compilation. Contour lines and elevations are referred to the new topographic datum of the Moon, which is defined in terms of spherical harmonics from the lunar gravity field. Compilation of all four LOC charts was completed on analytical plotters from 566 stereo models of Apollo metric photographs that cover approximately 20% of the Moon. This is the first step toward compiling a global topographic map of the Moon at a scale of 1:5 000 000.     

A Large Basin on the Near Side of the Moon

The differences between the surface structure of the near side and the far side of the Moon have been topics of interest ever since photographs of the far side have been available. One recurrent hypothesis is that a large impact on the near side has deposited ejecta on the far side, resulting in thicker crust there. Specific proposals were made by P.H. Cadogan for the Gargantuan Basin and by E.A. Whitaker for the Procellarum Basin. Despite considerable effort, no consensus has been reached on the existence of these basins. The problem of searching for such a basin is one of finding its signature in a somewhat chaotic field of basin and crater impacts. The search requires a model of the topographic shape of an impact basin and its ejecta field. Such a model is described, based on elevation data of lunar basins collected by the Lidar instrument of the Clementine mission and crustal thickness data derived from tracking Clementine and other spacecraft. The parameters of the model are scaled according to the principles of dimensional analysis and isostatic compensation in the early Moon. The orbital dynamics of the ejecta and the curvature of the Moon are also taken into account. Using such a scaled model, a search for the best fit for a large basin led to identification of a basin whose cavity covers more than half the Moon, including the area of all of the impact basins visible on the near side. The center of this basin is at 22 degrees east longitude and 8.5 degrees north latitude and its average radius is approximately 3,160 km. It is a megabasin, a basin that contains other basins (the far side South Pole-Aitken Basin also qualifies for that designation). It has been called the Near Side Megabasin. Much of the material ejected from the basin escaped the Moon, but the remainder formed an ejecta blanket that covered all of the far side beyond the basin rim to a depth of from 6 to 30 km. Isostatic compensation reduced the depth relative to the mean surface to a range of 1–5 km, but the crustal thickness data reveals the full extent of the original ejecta. The elevation profile of the ejecta deposited on the far side, together with modification for subsequent impacts by known basins (especially the far side South Pole-Aitken Basin) matches the available topographic data to a high degree. The standard deviation of the residual elevations (after subtracting the model from the measured elevations) is about one-half of the standard deviation of the measured elevations. A section on implications discusses the relations of this giant basin to known variations in the composition, mineralogy, and elevations of different lunar terranes.     

The Earth-figure perturbations in the Lunar theory

We compute the perturbations on the motion of the Moon due to the shape of the Earth. The zonal terms inJ ₂,J ₃, andJ ₄ are considered. The accuracy is estimated at 3×10^–5 and the results compared with previous theories.     

Consequences of a geosynchronous phase for the moon

Fission from the Earth's mantle explains why the density of the Moon is similar to that of the Earth's mantle.If following the fission origin of the Moon, the Earth-Moon distance increases progressively, the Moon can recollect chemicals evaporated by the Earth but not volatile enough to be lost as gases.In this way, the surface of the Moon can be enriched in refractory elements as most of the authors have proposed.At 3 Earth radii the long geosynchronous phase allows the formation of a solid crust which will record the Earth's magnetic field and the equilibrium hydrostatic from at that distance.When geosynchronism is broken the Moon will recede; its shape will no longer fit the hydrostatic form. The crust will either break or will exercise pressure on the lower layers. Meteor craters will allow lava to come to the surface. Such flows will be very large where the shape of the crust does not fit at all the geosynchronous form. Large lava flows will appear this way on the near side where the shape has changed the most. The new lava flows no longer record the magnetic field of the Earth because with the end of the synchronous position the field is alternative for the Moon; only the remanent field can influence the new lava.Three out of five samples dated at 3.6 b.y. suggest nevertheless that the field decreased slowly without becoming alternative. This means that the geosynchronous phase may have lasted longer and put the Moon on a more distant orbit, as Alfvén and Arrhenius suggested.The interpretation of lunar magnetism as influenced by the Earth cannot discard any interpretation or suggestion of its own lunar magnetic process. It is quite possible that both mechanisms have worked as some samples show.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademic Nazionale del Lincei in Rome, Italy.