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.     

A recalibration of the quiet Sun millimeter spectrum based on the Moon as an absolute radiometric standard

The solar millimeter continuum between 1 and 20 mm is recalibrated using observations of the average lunar brightness temperature at the center of lunar disk and new Moon brightness temperatures. The solar data are placed on a common scale according to the average lunar brightness temperature distribution proposed by Linsky. A least-squares parabolic regression curve is proposed for the solar millimeter continuum. A small departure from this regression curve near 8 mm may indicate the existence of an absorption feature.Staff member, Laboratory Astrophysics Division, National Bureau of Standards.     

The results of an accurate analysis of EAO charts of the Moon marginal zone constructed on the basis of lunar occultations

A computer‐readable version of the Moon's charts which refer to the center of its mass and the principal axes of the inertia were constructed on the basis of large‐scale star calibrated lunar photographies. The accuracy of six charts have been examined by reduction of observations of lunar occultations on the basis of the theory LE200.     

The great-circle pattern of large circular maria: product of an earth-moon encounter

The circular maria - Orientale, Imbrium, Serenitatis, Crisium, Smythii, and Tsiolkovsky -lie nearly on a lunar great circle. This pattern can be considered the result of a very close, non-capture encounter between Moon and Earth early in solar-system history. Of critical importance in analyzing the effects of such an encounter is the position of the weightlessness limit of the Earth-Moon System which is located at about 1.63R _e, measured from the center of Earth to center of Moon. Within this weightlessness limit, material can be pulled from the lunar surface and interior by Earth's gravity and either escape from the Moon or be redistributed onto the lunar surface. In the case of an encounter with a non-spinning Moon, backfalling materials would be distributed along a lunar great circle. However, if the Moon is rotating during the encounter, the backfall pattern will deviate from the great circle, the amount depending on the rate and direction of spin. Such a close encounter model may be related to the pattern of circular maria if materials departing from the source region are visualized as spheroids of molten lunar upper mantle basalt. These spheroids, then, would impact onto the lunar surface to form a pattern of lava lakes. Radiometric dates from mare rocks are consistent with this model of mare formation if the older mare rock dates are considered to date the encounter and younger dates are considered to date subsequent volcanic eruptions on a structurally weakened Moon.     

Lunar global figure from mare surface elevations

Laser altimetry data from the Apollo 15, 16, and 17 missions show that the ringed maria surfaces lie on one particular reference surface and that the center of gravity is definitely displaced from the optical center. If these extensive surfaces are assumed to be near hydrostratic surfaces, then there must have existed a time in lunar history when lunar tides and/or internal processes were much different than they are today.This paper presents one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Location definition of selenographic control points based on lunar craters

It is suggested that selenographic positions of circular lunar craters used as reference points should be defined by the position of the center as determined from a best fit to the crater's rim.     

Selenography and selenodesy with Apollo whole-disk lunar photographs I. Selenography

The Apollo whole-disk lunar photographs, with spacecraft lunar nadirs about 70° from the center of mean face, have considerable selenodetic potential provided that the requirements of resolution and precision can be met. Uncertainties in the internal camera geometry degrade the precision and make selenodetic applications doubtful, but selenographic work based on the assumption of a rigorously spherical moon makes lesser demands on the data and is still possible with useful accuracy. The selenographic method is fully developed here and applied to photographs 2505 and 2506 of Apollo 8 to produce a catalog of 635 positions. Of these 206 are farside and extend to 130° East Longitude. A new type of 5-character position word, appropriate for the entire lunar sphere, is used to define sequence in the catalog.     

The evolution of the moon

The thermal evolution of the Moon as it can be defined by the available data and theoretical calculations is discussed. A wide assortment of geological, geochemical and geophysical data constrain both the present-day temperatures and the thermal history of the lunar interior. On the basis of these data, the Moon is characterized as a differentiated body with a crust, a 1000-km-thick solid mantle (lithosphere) and an interior region (core) which may be partially molten. The presence of a crust indicates extensive melting and differentiation early in the lunar history. The ages of lunar samples define the chronology of igneous activity on the lunar surface. This covers a time span of about 1.5 billion yr, from the origin to about 3.16 billion yr ago. Most theoretical models require extensive melting early in the lunar history, and the outward differentiation of radioactive heat sources.Thermal history calculations, whether based on conductive or convective computation codes define relatively narrow bounds for the present day temperatures in the lunar mantle. In the inner region of the 700 km radius, the temperature limits are wider and are between about 100 and 1600°C at the center of the Moon. This central region could have a partially or totally molten core.The lunar heat flow values (about 30 ergs/cm²s) restrict the present day average uranium abundance to 60 ± 15 ppb (averaged for the whole Moon) with typical ratios of K/U = 2000 and Th/U = 3.5. This is consistent with an achondritic bulk composition for the Moon.The Moon, because of its smaller size, evolved rapidly as compared to the Earth and Mars. The lunar interior is cooling everywhere at the present and the Moon is tectonically inactive while Mars could be and the Earth is definitely active.     

Fundamental physics and absolute positioning metrology with the MAGIA lunar orbiter

MAGIA is a mission approved by the Italian Space Agency (ASI) for Phase A study. Using a single large-diameter laser retroreflector, a large laser retroreflector array and an atomic clock onboard MAGIA we propose to perform several fundamental physics and absolute positioning metrology experiments: VESPUCCI, an improved test of the gravitational redshift in the Earth?CMoon system predicted by General Relativity; MoonLIGHT-P, a precursor test of a second generation Lunar Laser Ranging (LLR) payload for precision gravity and lunar science measurements under development for NASA, ASI and robotic missions of the proposed International Lunar Network (ILN); Selenocenter (the center of mass of the Moon), the determination of the position of the Moon center of mass with respect to the International Terrestrial Reference Frame/System (ITRF/ITRS); this will be compared to the one from Apollo and Lunokhod retroreflectors on the surface; MapRef, the absolute referencing of MAGIA??s lunar altimetry, gravity and geochemical maps with respect to the ITRF/ITRS. The absolute positioning of MAGIA will be achieved thanks to: (1) the laboratory characterization of the retroreflector performance at INFN-LNF; (2) the precision tracking by the International Laser Ranging Service (ILRS), which gives two fundamental contributions to the ITRF/ITRS, i.e. the metrological definition of the geocenter (the Earth center of mass) and of the scale of length; (3) the radio science and accelerometer payloads; (4) support by the ASI Space Geodesy Center in Matera, Italy. Future ILN geodetic nodes equipped with MoonLIGHT and the Apollo/Lunokhod retroreflectors will become the first realization of the International Moon Reference Frame (IMRF), the lunar analog of the ITRF.     

Comments on the figure of the moon from apollo landmark tracking

Optical observations were made from the orbiting spacecraft to craters on the lunar surface during Apollo missions 8, 10, 11, 12, 14, and 15. Very accurate selenographic locations for 31 craters have been obtained from these data. The estimated radius values, with respect to the center of mass of the Moon, for the near side maria were smaller than the nominally accepted value of 1738 km. Gross figure of the Moon estimates were obtained for both a sphere and a constrained ellipsoid. These data appear to provide some proof that there is a displacement between the center of figure and the center of mass of the Moon.     

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.     

A preliminary experience in the use of Chang’E-1 IIM data

The Interference Imaging Spectrometer (IIM) onboard the first lunar satellite of China, Chang’E-1, has acquired 84% of the area between south and north latitude 70°. To contribute to its usability, this paper presents our preliminary experience in the use of IIM data. Firstly, we provide one practicable method for the on-orbit correction of the inhomogeneity of sensor response. Secondly, aiming at the problem that the spectral range of IIM does not cover the absorption peak of the mafic mineral completely, we explore a method to approximate the absorption band center for IIM data. A strong correlation between the absorption band center and the wavelength at which the first derivative equals to 0 (i.e., stagnation point) was revealed. Based on the corrected data and the correlation, the absorption band center of several large craters was mapped. The distribution of rocks and minerals shown in the map of absorption band center for Aristarchus and Copernicus is in agreement with previous studies but with much finer structure. Horizontal and vertical lithologic diversity was detected in Zucchius crater. This paper demonstrates the potential of IIM data for the identification of lunar rocks due to its high spatial and spectral resolution. In a future study we will produce a global map of the absorption band center with greater accuracy and it is expected that this global map will provide complementary information for other hyperspectral data such as SP on KAGUYA or M³ on Chandrayaan-1.     

Broadband submillimeter measurements of the full Moon center brightness temperature and application to a lunar eclipse

We report on observations of the full Moon brightness temperature covering the frequency range of 300-950 GHz, and also on observations of the lunar eclipse of July 16, 2000, though only covering the frequency range of 165-365 GHz due to poor atmospheric transmission at higher frequencies. All observations were performed from the summit of Mauna Kea (HI) using a Fourier Transform Spectrometer mounted on the Caltech Submillimeter Observatory and supplemented by measurements of the atmospheric opacity using a 183 GHz Water Vapor Monitor. The telescope was pointed to the center of the lunar disk (with a footprint of ∼45-15 km on the Moon at 300 through 900 GHz). In order to obtain the correct values of the Moon brightness temperatures at all frequencies we carefully corrected for the atmospheric absorption, which varies across the submillimeter domain. This correction is fully described. The measured pre-eclipse brightness temperature is around 337 K in the 165-365 GHz range. This temperature slightly increases with frequency to reach ∼353 K at 950 GHz, according to previous broader band data. The magnitude of the temperature drop observed during the eclipse at 265 GHz (central frequency of the band covered) was about ∼70 K, in very good agreement with previous millimeter-wave measurements of other lunar eclipses. We detected, in addition, a clear frequency trend in the temperature drop that has been compared to a thermal and microwave emission model of the lunar regolith, with the result of a good match of the relative flux drop at different frequencies between model and measurements.     

Lunar baselines and libration from differential Vlbi observations of alseps

Differential very-long-baseline interferometric observations of signals from Apollo Lunar Surface Experiment Package telemetry transmitters will yield the relative projected positions of the transmitters with uncertainty of only 1-3 m, set mainly by uncertainty of the lunar ephemeris. Noise and systematic instrumental errors which in the past affected similar observations have been reduced to the equivalent of a few centimeters on the lunar surface by the development of a new type of differential receiver. Continued observations should yield a determination of the motion of the Moon about its center of mass with uncertainty less than 1 s of selenocentric arc. Improvements (by other means) in our knowledge of the Moon's orbital motion would allow a further order-of-magnitude refinement in the libration and relative position results obtainable by differential VLBI.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.     

Lunar Occultation of Saturn II. The normal reflectances of Rhea,Titan, and Iapetus

An inversion procedure to obtain the reflectance of the central region of a satellite's disk from lunar occultation data is presented. The scheme assumes that the limb darkening of the satellite depends only on the radial distance from the center of the disk. Given this assumption, normal reflectances can be derived that are essentially independent of the limb darkening and the diameter of the satellite. The procedure has been applied to our observations of the March 1974 lunar occultation of Tethys, Dione, Rhea, Titan, and Iapetus. In the V passband we derive the following normal reflectances: Rhea (0.97±0.20), Titan (0.24±0.03), Iapetus, bright face (0.60±0.14). For Tethys and Dione the values derived have large uncertainties, but are consistent with our result for Rhea.     

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.     

Petrography,mineralogy, and trace element geochemistry of lunar meteorite Dhofar 1180

Abstract— Here we report the petrography, mineralogy, and trace element geochemistry of the Dhofar 1180 lunar meteorite. Dhofar 1180 is predominantly composed of fine‐grained matrix with abundant mineral fragments and a few lithic and glassy clasts. Lithic clasts show a variety of textures including cataclastic, gabbroic, granulitic, ophitic/subophitic, and microporphyritic. Both feldspathic and mafic lithic clasts are present. Most feldspathic lithic clasts have a strong affinity to ferroan anorthositic suite rocks and one to magnesian suite rocks. Mafic lithic clasts are moderately to extremely Fe‐rich. The Ti/[Ti+Cr]‐Fe/[Fe+Mg] compositional trend of pyroxenes in mafic lithic clasts is consistent with that of low‐Ti mare basalts. Glasses display a wide chemical variation from mafic to feldspathic. Some glasses are very similar to those from Apollo 16 soils. KREEP components are essentially absent in Dhofar 1180. One glassy clast is rich in K, REE and P, but its Mg/[Mg+Fe] is very low (0.25). It is probably a last‐stage differentiation product of mare basalt. Molar Fe/Mn ratios of both olivine and pyroxene are essentially consistent with a lunar origin. Dhofar 1180 has a LREE‐enriched (La 18 × CI, Sm 14 × CI) pattern with a small positive Eu anomaly (Eu 15 × CI). Th concentration is 0.7 ppm in Dhofar 1180. Petrography, mineralogy, and trace element geochemistry of Dhofar 1180 are different from those of other lunar meteorites, indicating that Dhofar 1180 represents a unique mingled lunar breccia derived from an area on the lunar nearside but far away from the center of the Imbrium Basin.     

对月日潮汐摩擦耗散的估计

月日潮汐摩擦和地球惯量矩变化是日长长期变化的主要原因．在本文中，利用最新的地球物理和古生物钟数据，对过去15亿年以来的月日潮汐摩擦、地球惯量矩变化和日长长期变化等作了数值对比研究．由此得到二个重要结论：一是仅利用地球的自转形变不能解释J2的变化，这说明地球的重力分异现象至今仍存在着；其二是在几亿年前的潮汐摩擦比现在大得多，若取潮汐耗散与距离的立方成反比时，理论结果与由古生物钟得到的回归年日数和朔望月日数数据较为符合。     

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.     

Uranium-lead ages for lunar zircons: Evidence for a prolonged period of granophyre formation from 4.32 to 3.88 Ga

Abstract The ages of a number of small fragments of lunar granophyre have been determined by the in situ U-Th-Pb isotopic analysis of zircon using a sensitive high mass-resolution ion microprobe (SHRIMP I). The zircon from lunar granophyre is characterized by consistently high U and Th contents (most 200–500 ppm and 100–300 ppm, respectively) compared to zircon from mafic lunar rocks. Some fragments of lunar granophyre are found to be as old as 4.32 Ga, supporting other evidence that the original lunar magma ocean crystallized completely within ～200 Ma of the formation of the Moon itself. Other fragments are as young as 3.88 Ga, which is much later than the time of formation of most of the lunar crust. The older lunar granophyres have rare-earth-element (REE) patterns that are similar to lunar KREEP, whilst the younger granophyres have bow-shaped REE patterns that feature a greater relative enrichment in the heavy REE. The wide range of ages of numerous lunar zircons, lunar granophyres and other rocks indicates that zircon-forming magmatism in the lunar highlands was most active prior to 4.3 Ga but continuous until at least 3.88 Ga. The U-Pb isotopic composition of much lunar zircon is near concordant, but the effects of isotopic disturbance as late as ～1.0 Ga are observed in some zircon, both within granophyre fragments recrystallized by reheating and within fragments in which the original delicate silica-K-feldspar granophyric intergrowth is well preserved. It is therefore essential to make multiple analyses of individual zircon grains, and preferably analyses of suites of zircons from lunar igneous rocks if they are to be dated reliably by the U-Pb method. It is possible that some of the younger lunar granophyres are the product of large-scale silicate-liquid immiscibility within late-stage differentiates, but this remains unproven until remnants of demonstrably cogenetic, Fe-rich, immiscible liquid are positively identified.