Selenodetic control network

Identification details of the 66 first-order selenodetic control points - i.e., points consisting of craters having diameters larger than 8 km - are given. The distribution of all 211 reference points of the network on the Blagg-Müller maps is also presented. In the Appendix the corresponding Blagg-Müller and LPL Catalogue number for each crater as well as the frame numbers of Lunar Orbiter IV photographs in which the craters have been studied are included.On leave from the Astronomy Department, University of Athens, Greece.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration. This paper is Lunar Science Institute Contribution No. 237.     

Viscosity of the moon

Using data from the present gravitational potential and surface topography of the Moon, it is possible to determine a lower limit of about 5 b.y. for the relaxation time of the mascons. Assuming that the Moon has behaved as a Maxwellian viscoelastic body since the formation of the mascons, this relaxation time indicates a value of about 10²⁷ poise for the viscosity of the lunar interior. Such a high viscosity implies that there has been no convection current inside the upper 800 km of the Moon since the formation of the mascons. Lunar Science Institute Contribution No. 99. The research in this paper was done while the author was a Visiting Scientist at the Lunar Science Institute, which is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Stress differences in the moon as an evidence for a cold moon

Assuming that the lateral variations of density in the lunar crust, the crustal density anomalies, are responsible for the lateral undulations of the lunar gravitational potential, we compute these anomalies for four different lunar models, which include an entirely solid Moon and three different solid lunar models with partially molten layers located within 600 km depth. The stress differences created by the density anomalies are determined for these models. It is found that, since the formation of the mascons, the entirely solid lunar model should have supported stress differences of the order of 70 bars while in the case of the other models, the solid layer overlying the partially molten one should have supported stress differences of more than 100 bars. The high stress differences associated with the partially molten models lead us to conclude that these models are not proper ones, and thus the Moon has always been solid since the formation of the mascons. Lunar Science Institute Contribution No. 97. The research in this paper was done while the author was a Visiting Scientist at the Lunar Science Institute, which is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Density and stress distribution in the moon

A model is presented for the lateral variations of density within the Moon. The model gives rise to a gravitational potential which is equal to the observed potential at the lunar surface, moreover, it minimizes the total shear-strain energy of the Moon. The model exhibits lateral variations of about ±0.25 g cc^–1 within 50 km depth. The variations, however, reduce to ±0.06 and ±0.008 g cc^–1 within layers at 50–135 and 135–235 km respectively, and they become negligible below this region. The associated stress differences are found to be about 50 bar within 600 km depth, having their maximum values of about 90 bars at a depth of about 250 km. On the basis of these stress differences a strength of about 100 bar is concluded for the upper 400 km of the lunar interior for the last 3.3 b.y.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration. This paper is Lunar Science Institute Contribution No. 117.     

Mare serenitatis: a preliminary definition of surface units by remote observations

There are many surface units in Mare Serenitatis and in the adjacent Montes Haemus that can be defined by remote, Earth-based observations at visual, infrared, and radar wavelengths. These highland and mare surface units are obvious in color-difference photographs and in radar images, while the infrared images have little or no differences. These characteristics are consistent with units having definite chemical differences. However, a better definition of these surfaces requires the synthesis of many more data sets.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.This paper presents 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.     

Infrared atlas charts of the eclipsed moon

The objective of this atlas is to present the thermal response of the lunar surface observed during an eclipse of the Moon with accurate position data. The observations were made at a wavelength of 11 µm with an angular resolution of 10, equivalent to 17 km at the disk center. Over a thousand thermally anomalous regions (hot spots) were detected. They cool more slowly than their environs and remain warmer than their environs during the umbral phase. In addition to these very localized hot spots some of the maria show thermal enhancements during the eclipse.Fourty four charts make up this atlas which are identical in coverage and projection to the Lunar Atlas Charts (LAC) series. The charts are in the form of digital images of a normalized temperature difference which is particularly useful for studying regions of small thermal enhancements. Each increase of intensity corresponds to 4 K temperature increase. Grid lines are drawn every two degrees with tic marks each one-half degree. A brief outline of the observations and data reduction methods is given. The map construction techniques are described along with a discussion on how the atlas could be used.The appendix is a list of the published infrared atlantes. These include isothermal contour maps and images of the day-time, eclipsed and night-time Moon, and catalogues of thermal anomalies of the eclipsed and night-time Moon.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973. A portion of the research reported in this paper was done while the author was a Visiting Scientist at The Lunar Science Institute, which is operated by the Universities Space Research Association under Contract NSR-09-051-001 with the National Aeronautics and Space Administration. This paper is Lunar Science Institute Contribution No. 111.     

Igneous vs impact processes for the origin of the mare lavas

In spite of chemical and petrological data furnished by the early Apollo missions, disagreement has persisted as to the ultimate origin of the mare lavas - were they true igneous magmas or impact melts? Examination of Lunar Orbiter and Apollo photographs of Tsiolkovsky, Mare Orientale and Humboldt crater, as examples of mare-filled impact structures, has suggested the answer. It has been found that the mare lavas possibly stem from internal melting because a considerable time interval has elapsed between the time of basin excavation and basaltic extrusions. This was most effectively shown by crater counts on the ejecta blanket and mare filling of Mare Orientale. The central mare filling is distinctly younger than the ejecta cover, as shown by the lower crater densities on the mare surface as compared with the ejecta. Furthermore, many craters on the ejecta blanket of Orientale were flooded by lava long after the impact had occurred. Mare-type lavas are not only confined to large circular impact basins, but also fill irregular depressions, like Mare Australe, where evidence for different flooding episodes has been observed.     

On the thermal history of the moon

A giant impact causes the lateral variations of the temperature distribution inside the Moon and it provides a thick lithosphere beneath the basin strong enough to support the mascon to be created in this region, and a thin lithosphere beneath the surrounding highland which supplies the lava filling of the basin.The Lunar Science Institute Contribution No. 132.     

The relationship between lunar hot spots and the geomorphic index

The previously developed geomorphic index of lunar surfaces is applied to the surface distribution of the lunar hot spots. It was found that the hot spot number density is the highest in areas of intermediate geomorphic index, corresponding to mature maria. Young and old maria and the terrae have fewer hot spots per unit area. An hypothesis is presented relating the probability of formation of a hot spot by impact with the evolutionary stage of the regolith of the target surface. The older is the surface, the deeper is the regolith and also the smaller is the average boulder size. For these reasons hot spots will be less probable. The paucity of hot spots in young maria could also be related with the evolution of the regolith, but fundamental changes in the petro-physics of the mare effusions cannot be ruled out.This paper constitutes contribution no. 04 of the Lunar Science Institute and was performed under NASA Contract No. NSR 09-051-001.     

Lunar cartography with the Apollo 17 Alse radar imagery

Lunar position differences between thirteen lunar craters in Mare Serenitatis were computed from VHF radar-imagery obtained by the Lunar Sounder instrument flown on the Apollo 17 Command Module. The radar-derived position differences agree with those obtained by conventional photogrammetric reductions of Apollo metric photography. This demonstrates the feasibility of using the Apollo Lunar Sounder data to determine the positions of lunar features along the Apollo 17 orbital tracks. This will be particularly useful for western limb and farside areas, where no Apollo metric camera pictures are available.This paper presents 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.     

Tidal evolution in close binary systems,II

The aim of the present investigation will be to determine the explicit forms of differential equations which govern secular perturbations of the orbital elements of close binary systems in the plane of the orbit (i.e., of the semi-major axisA, eccentricitye, and longitude of the periastron ), arising from the lag of dynamical tides due to viscosity of stellar material. The results obtained are exact for any value of orbital eccentricity comprised between 0e<1; and include the effects produced by the second, third and fourth-harmonic dynamical tides, as well as by axial rotation with arbitrary inclination of the equator to the orbital plane.In Section 2 following brief introductory remarks the variational equations of the problem of plane motion will be set up in terms of the rectangular componentsR, S, W of disturbing accelerations with respect to a revolving system of coordinates. The explicit form of these coefficients will be established in Section 3 to the degree of accuracy to which squares and higher powers of quantities of the order of superficial distortion can be ignored. Section 4 will be devoted to a derivation of the explicit form of the variational equations for the case of a perturbing function arising from axial rotation; and in Section 5 we shall derive variational equations which govern the perturbation of orbital elements caused by lagging dynamical tides.Numerical integrations of these equations, which govern the tidal evolution of close binary systems prompted by viscous friction at constant mass, are being postponed for subsequent investigations.Prepared at the Lunar Science Institute, Houston, Texas, under the joint support of the Universities Space Research Association, Charlottesville, Virginia, and the National Aeronautics and Space Administration Manned Spacecraft Center, Houston, Texas, under Contract No. NSR 09-051-001. This paper constitutes Lunar Science Institute Contribution no. 100.Normally at the Department of Astronomy, University of Manchester, England.     

Tidal evolution in close binary systems

The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 10⁷ yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

The effects of viscous friction on the precession and nutation of celestial bodies

The aim of the present study has been to set the system of differential equations which govern the precession and nutation of self-gravitating globes of compressible viscous fluid, due to the attraction exerted on the rotating configuration by its companion; and to construct their approximate solution which are correct to terms of the second order in small dependent variables of the problem. Section 2 contains an explicit formulation of the effects of viscosity arising in this connection, given exactly as far as the viscosity remains a function of radial distancer only; but irrespective of its magnitude. In Section 3 the equations of motion will be linearized for the case of near-circular orbits and small inclinations andi of the equator of the rotating configuration, and of its orbital plane, to the invariable plane of the system; while in Section 4 further simplifications will be introduced which are legitimate for studies of secular (or long-periodic) motions of the nodes and inclinations. The actual solutions of so simplified a system of equations are constructed in Section 5; and these represent a generalization of the results obtained in our previous investigation (Kopal, 1969) of the inviscid case.The physical significance of the new results will be discussed in the concluding Section 6. It is demonstrated that the axes of rotation of deformable components in close binary systems are initially inclined to the orbital plane, viscous dissipation produced by dynamical tides will tend secularly to rectify their positions until perpendicularity to the orbital plane has been established, and the equators as well as orbit made to coincide with the invariable plane of the system-in a similar manner as other effects of tidal friction are bound eventually to synchronize the velocity of axial rotation with that of orbital revolution in the course of time.An application of the results of the present study to the dynamics of the Earth-Moon system discloses that the observed inclination of 1°.5 of the lunar equator to the ecliptic cannot be regarded as being secularly constant, but representing the present deviations from perpendicularity of oscillatory motion of very long period.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR-09-051-001 with the National Aeronautics and Space Administration. This paper constitutes the Lunar Science Institute Contribution No. 85.     

The spatial and temporal distribution of lunar mare basalts as deduced from analysis of data for lunar meteorites

In this work we analyze data for lunar meteorites with emphasis on the spatial and temporal distribution of lunar mare basalts. The data are mostly from the Lunar Meteorite Compendium (http://www-curator.jsc.nasa.gov/antmet/lmc/contents.cfm cited hereafter as Compendium) compiled by Kevin Righter, NASA Johnson Space Center, and from the associated literature. Analysis of the data showed that (i) a significant part of the lunar meteorite source craters are not larger than hundreds of meters in diameter; (ii) cryptomaria seem to be rather abundant in lunar highlands; (iii) the ratios of lunar meteorites belonging to three broad petrologic groups (mare basalt/gabbro, feldspatic highland breccias, and mingled breccias which are a mixture of mare and highland components) seem to be roughly proportional to the areal distribution of these rocks on the lunar surface; and (iv) the meteorite mare basalt ages show a range from ～2.5 to 4.3 Ga and fill the gaps in the Apollo/Luna basalt age distribution. The ages of mare basalt clasts from mingled breccias seem to be systematically higher than those of “normal” mare basalts, which supports the suggestion that mingled breccias originated mostly from cryptomaria.     

Spectrophotometry of Comet Austin (1982g) during post-perihelion period

Lunar crustal shortening does not seem to be restricted to the lava-filled basins alone; but there are some young scarp-like terra ridges in places around mare areas where they often continue other tectonic structures. This crustal shortening has not reached the same intensity as in the case of the lobate scarp overthrusts on Mercury. Young lunar terra ridges indicate that crustal shortening with an areal extent also took place slightly around mare basins. Thus they link tensional rille tectonics with compressional mare ridge tectonics and indicate that areal heating/bending/extension — cooling/ shortening/compression may describe an important explaining factor in lunar mare- and near-mare tectonics in addition to the volcanic extrusions.     

Lunar surface mass distribution from dynamical point-mass solution

Combined efforts of the Jet Propulsion Laboratory and Aerospace Corporation have provided a front side lunar gravity field using the Doppler tracking data from the United States Lunar Orbiters IV and V. Data reduction was accomplished with a model which included all dynamical motion due to gravitational perturbations, as well as all tracking geometries. The field is represented as a grid of 580 surface mass points which are contoured and show correlations with various lunar surface features.This paper presents 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.     

Some aspects of condensation in clouds

Several general features of nucleation characteristics of low density cosmic clouds are discussed. These are: (1) tendency for metastable condensates to form, (2) non-occurrence of nominal refractory molecule in the gas, (3) a strong temperature dependence of condensation at relatively low temperatures, and (4) significant vibrational disequilibrium in cosmic clouds. These support previous analyses by the author which indicate that equilibrium calculations have restricted applicability. A kinetic treatment of condensation is required for cosmic grains and the possibility of formulating such an analysis is pointed out.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium, held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.     

Comparison of the analytical results from the surveyor,Apollo, and Luna missions

The principal chemical element composition and inferred mineralogy of the powdered lunar surface material at seven mare and one terra sites on the Moon are compared. The mare compositions are all similar to one another and comparable to those of terrestrial ocean ridge basalts except in having higher titanium and much lower sodium contents than the latter. These analyses suggest that most, if not all, lunar maria have this chemical composition and are derived from rocks with an average density of 3.19 g cm^–3. Mare Tranquillitatis differs from the other maria in having twice the titanium content of the others.The chemical composition of the single highland site studied (Surveyor 7) is distinctly different from that of any of the maria in having much lower amounts of titanium and iron and larger amounts of aluminium and calcium. Confirmation of these general characteristics of lunar highland material has come from recent observations by the Apollo 15 Orbiter. The inferred mineralogy is 45 mole percent high anorthite plagioclase and the parent rocks have an estimated density of 2.94 g cm^–3. The Surveyor 7 chemical composition is the principal contributor to present estimates of the overall chemical composition of the lunar surface.Presented at the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September 14–25, 1971. This paper is an expanded and updated version of a paper presented at the Apollo 12 Lunar Science Conference, Houston, Texas, January 11–14, 1971, and published in the Proceedings of this Conference (Turkevich, 1971).     

Tectonic pattern of the crater Grimaldi region of the Moon

The tectonics of the Grimaldi area are described and analyzed in detail from high-resolution Lunar Orbiter photographs.Rille grabens are long and narrow fault zone structures of lunar terra. The polygonal rille graben pattern indicates the importance of lunar internal activity with an adjoining thin lithosphere in the areal tectonics at the time of rille grabening. The graben subsidence developed during tensional bending of this thin terra lithosphere. The en échelon graben offsets indicate the existence of strikeslip movements along the main fault under tensional lithosphere conditions.In some places mare ridge ranges continue in the direction of the rille graben indicating the connection of these structures to each other as part of the lunar tectonic evolution. The very thin mare lithosphere was affected more easily and over a longer period of time by lunar internal forces. The effect of older structural units is thus less conspicuous within mare areas. Proposed Riedel-shear-like structures indicate a slight shortening and compression of the mare basin lithosphere during movements along lava-covered zones of weakness.     

Analysis of crater distributions in mare units on the lunar far side

Mare material is asymmetrically distributed on the Moon. The Earth-facing hemisphere, where the crust is believed to be 26 km thinner than on the farside, contains substantially more basaltic mare material. Using Lunar Topographic Orthophoto Maps, we calculated the thickness of the mare material in three farside craters, Aitken (0.59 km), Isaev (1.0 km), and Tsiolkovskiy (1.75 km). We also studied crater frequency distribution in five farside mare units (Aitken, Isaev, Lacus Solitudinis, Langemak, and Tsiolkovskiy) and one light plains unit (in Mendeleev). Nearly 10 000 farside craters were counted. Analysis of the crater frequency on the light plains unit gives an age of 4.3 billion yr. Crater frequency distributions on the mare units indicate ages of 3.7 and 3.8 billion yr, suggesting that the units are distributed over a narrow time period of approximately 100 million yr. Returned lunar samples from nearside maria give dates as young as 3.1 billion yr. The results of this study suggest that mare basalt emplacement on the far side ceased before it did on the near side.