Search

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

The second Mercury encounter has resulted in the acquisition of about 360 pictures of the south polar regions which provide a reliable cartographic and geologic tie between the two sides of the planet photographed on the first encounter. Stereoscopic coverage of large areas of the southern hemisphere was obtained by combining Mercury 1 and 2 pictures taken at different viewing angles. The south polar regions consist of heavily cratered terrain and intercrater plains interspersed with patches of smooth plains. No large areas of smooth plains similar to those surrounding Caloris occur in the south polar regions. No new types of terrain have been recognized, but lobate scarps are common. The second largest basin seen by Mariner 10 has been confirmed on the new photography. At high solar elevations the surface displays an abundance of rays and rayed craters.

A geologic terrain map of Mercury has been constructed by use of the photogeologic methods employed for the moon and Mars. The oldest and most widespread unit, intercrater plains, forms nearly level to rolling surfaces on which are superposed numerous secondary impact craters. This unit may represent a very old surface that predates the last heavy bombardment of the inner planets. The effects of this bombardment are recorded in a second widespread unit, heavily cratered terrain, consisting of closely spaced craters and basins from 30 km to several hundred kilometers in diameter. Units formed by excavation of the 1300-km-diameter Caloris basin are widespread on one hemisphere of the planet. The development of the Caloris basin was followed relatively quickly by emplacement of widespread plains materials, most of which are probably volcanic.

A plausible surface history of Mercury is presented which is suggested by Mariner 10 television pictures. Five periods are postulated which are delineated by successive variations in the modification of the surface by external and internal processes: accretion and differentiation, terminal heavy bombardment, formation of the Caloris basin, flooding of that basin and other areas, and light cratering accumulated on the smooth plains. Each period is described in detail; the overall history is compared with the surface histories of Venus, Mars, and the moon; and the implications of this history for earth are discussed. It is tentatively concluded that: Mercury is a differentiated planet most likely composed of a large iron core enclosed by a relatively thin silicate layer; heavy surface bombardment occurred about four billion years ago, which probably affected all the inner planets, and was followed by a period of volcanic activity; no surface modifications caused by tectonic, volcanic, or atmospheric processes took place after the volcanic period.

The surface morphology and optical properties of Mercury resemble those of the moon in remarkable detail and record a very similar sequence of events. Chemical and mineralogical similarity of the outer layers of Mercury and the moon is implied; Mercury is probably a differentiated planet with a large iron-rich core. Differentiation is inferred to have occurred very early. No evidence of atmospheric modification of landforms has been found. Large-scale scarps and ridges unlike lunar or Martian features may reflect a unique period of planetary compression near the end of heavy bombardment by small planetesimals.

Mercury has a heavily cratered surface containing basins up to at least 1300 kilometers diameter flooded with mare-like material. Many features are closely similar to those on the moon, but significant structural differences exist. Major chemical differentiation before termination of accretion is implied.

The Mariner 10 television cameras imaged the planet Venus in the visible and near ultraviolet for a period of 8 days at resolutions ranging from 100 meters to 130 kilometers. The general pattern of the atmospheric circulation in the upper tropospheric/lower stratospheric region is displayed in the pictures. Atmospheric flow is symmetrical between north and south hemispheres. The equatorial motions are zonal (east-west) at approximately 100 meters per second, consistent with the previously inferred 4-day retrograde rotation. Angular velocity increases with latitude. The subsolar region, and the region downwind from it, show evidence of large-scale convection that persists in spite of the main zonal motion. Dynamical interaction between the zonal motion and the relatively stationary region of convection is evidenced by bowlike waves.

The morphology and optical properties of the surface of Mercury resemble that of the moon in remarkable detail, recording a very similar sequence of events; chemical and mineralogical similarity of the outer layers is implied. Mercury is probably a differentiated planet with an iron-rich core. Differentiation is inferred to have occurred very early. No evidence of atmospheric modification of any landform is found. Large-scale scarps and ridges unlike lunar or Martian features may reflect a unique period of planetary compression near the end of heavy bombardment, perhaps related to contraction of the core.

It is shown that Mercury's surface has only 70% as many large craters (of at least 200 km in diameter) as the moon. The density of Mercurian impact craters having diameters over 400 km is 30% of that of the moon, and for craters with diameters between 400 and 700 km, Mercurian density is 21% of that of the moon. The size-frequency distribution curve of Mercury is the same as the lunar cumulative -2 slope. The Mercurian curve, however, lies well below the 10% surface saturation level of the lunar curve. This may indicate that the old, heavily-cratered Mercurian terrain is not presently in a state of cratering equilibrium. The differences in crater and basin densities observed between Mercury and the moon may be functions of crater-production rates or of different crustal histories. The total isostatic compensation of impact craters having diameters of about 800 km suggests that the average viscosity of the Mercurian crust during approximately the past 4 eons was the same as that of the moon.

The morphology and optical properties of the surface of Mercury resemble those of the Moon in remarkable detail, recording a very similar sequence of events; chemical and mineralogical similarity of the outer layers is implied. Mercury is probably a differentiated planet with an iron-rich core. Differentiation is inferred to have occurred very early. No evidence of atmospheric modification of any landform is found. Large-scale scarps and ridges unlike lunar or Martian features may reflect a unique period of planetary compression near the end of heavy bombardment, perhaps related to contraction of the core.

Evidence concerned with (1) the character and distribution of terrain surrounding fresh basins; (2) albedo, color, and temporal differences between a basin rim and smooth plains on its floor; and (3) the stratigraphic relations and local distribution of smooth plains in the hilly and lineated terrain are cited as additional evidence for an internal origin of much of the Mercurian smooth plains. Although the question of Mercurian volcanism should be kept open, this evidence together with that presented in an earlier paper suggests that volcanism occurred on Mercury early in its history.

Recent exploration of the planets has been highlighted by the development of visual imaging systems carried on board the spacecraft. This paper describes the evolution of planetary camera systems from the earliest reconnaissance flight to Mars in 1965 (Mariner 4) through the planned mission to Jupiter and Saturn in 1977. Advances in telecommunication performance, mission planning and operations, and digital processing of images are also discussed. Science objectives and changes in the imaging systems required to meet these objectives are discussed for the Mariner Mars 1971 (Mariner 9), Mariner Venus-Mercury (Mariner 10), Viking 1975 (Mars Orbiter), and Mariner Jupiter-Saturn 1977 missions. The last section of the paper describes future plans for imaging experiments based on cameras using solid-state sensors, particularly charge-coupled devices.

Study of materials of possible volcanic origin in the lunar highlands, including highland plains materials, materials forming closely spaced hills in which summit furrows and chains of craters are common, and materials forming closely spaced hills (some of which parallel the lunar grid) on which summit furrows and chain craters are rare. The highland plains materials probably are basaltic lavas with less Fe and Ti than the mare plains materials. The two hilly units appear to consist of materials that, if volcanic, were more viscous in the molten state than any of the lunar plains units; thus these materials may be significantly enriched in felsic components. Most of the highland materials of possible volcanic origin formed after the Imbrium multiring basin but before mare material completed flooding parts of the moon; they therefore postdate accretion of the moon and may represent several episodes of pre-mare volcanism.

Vidicon photographs returned to earth by Rangers 7, 8, and 9 in 1964 and 1965 were used to study the details of lunar geologic units previously recognized from earth-based telescopic photographs and to make geologic maps at a variety of scales. The photographs from each mission changed continuously in scale as the spacecraft approached impact. The final frames had resolutions some 1,000 times better than the best earthbased photographs. Lunar stratigraphic units mapped at a scale of 1:1,000,000 displayed, at these larger scales, differences in properties and, possibly, in ages, but a clear-cut stratigraphic succession of subunits was not apparent. The plains-forming materials in both terra and mare were divisible into units mainly on the basis of the differences in the total number of superposed craters and in the relative number of craters of various morphologic types.

Study of an imaging experiment planned for the 1973 Mariner Venus/Mercury flyby mission. Scientific objectives are presented together with mission constraints, analysis of alternative systems, and the rationale for the final choice. The final selection was a vidicon camera quite similar to that used for Mariner Mars 1971, but with the capability of real time transmission during the Venus and Mercury flybys. Systematic high resolution UV photography of Venus is planned after encounter in an attempt to understand the nature of the mysterious UV markings and their apparent 4- to 5-day rotation period.

Apollo 14 lunar module landing site geology, studying samples from regolith and block ejecta deposit around young crater

The Lunar Crater volcanic field in east-central Nevada includes cinder cones, maars, and basalt flows of probably Quaternary age that individually and as a group resemble some features on the moon. Three episodes of volcanism are separated by intervals of relative dormancy and erosion. Changes in morphology of cinder cones, degree of weathering, and superposition of associated basalt flows provide a basis for determining the relative ages of the cones. A method has been devised whereby cone heights, base radii, and angles of slope are used to determine semiquantitatively the age relationships of some cinder cones. Structural studies show that cone and crater chains and their associated lava flows developed along fissures and normal faults produced by tensional stress. The petrography of the basalts and pyroclastics suggests magmatic differentiation at depth which produced interbedded subalkaline basalts, alkali-olivine basalts, and basanitoids. The youngest flows in the field are basanitoids.

Lunar geology based on Apollo 14 photographs and soil and rock samples

Lunar surface fine structure and geological analysis from ranger 7, 8 and 9 photographs

Geological maps of potential Apollo landing sites on lunar surface

Morphology of lunar craters from Ranger photographs, noting distribution and possible competing processes of crater formation and destruction

Tabulated maximum polarization values of lunar geologic units mapped on basis of observations from earth

Geology of Copernicus quadrangle of moon

Stratigraphy and structure of Pitatus region of moon

Size-frequency and spatial distributions of small craters on moon from Ranger Block III PHOTOGRAPHS

Lunar geologic mapping of Mare Tranquillitatis and stratigraphy from Ranger VIII photographs