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.     

Model Estimates of Non-Hydrostatic Stresses in the Martian Crust and Mantle: 1—Two-Level Model

Regions of maximum shear and tension–compression stresses in the Martian interior have been revealed using two types of models: the elastic model and the model with an elastic lithosphere of varied thickness (150–500 km) positioned on a weak layer that has partially lost its elastic properties. The weakening is simulated by a ten-fold lower value of the shear modulus down to the core boundary. The numerical simulation applies Green’s functions (load number method) with the step of 1 × 1 grade along latitude and longitude down to a depth of 1000 km. The boundary condition is the expansion of the latest data on Martian topography and the gravitational field (model MRO120D) in spherical harmonics up to the degree and order of 90 in relation to the reference surface that is assumed an equilibrium spheroid. The considered two-level compensation model assumes nonequilibrium relief and density anomalies at the crust–mantle boundary to be the sources of the anomalous gravitational field. Calculations are performed for two test models of Martian internal structure with the crust mean thicknesses of 50 to 100 km and mean density of 2900 kg/m³. Considerable tangential and simultaneously compressive stresses occur under the Tharsis region. The main regions of high shear and simultaneously extentional stresses are located in the Hellas region crust and in the lithosphere of the following regions: Argyre Planitia, Mare Acidalium, Arcadia Planitia and Valles Marineris. The zone of high maximum shear and extentional stresses has been found at the base of the lithosphere under the Olympus volcano and that under the Elysium rise.     

Model Estimates of Non-Hydrostatic Stresses in the Martian Crust and Mantle: 2−Three-Level Model

Regions of maximum shear and tension-compression stresses in the Martian interior have been revealed using the three-level compensation model. Nonequilibrium relief, density anomalies at the crust?mantle boundary, and density anomalies at the base of the lithosphere are the sources of the anomalous gravitational field. The thickness of elastic lithosphere positioned on a weak layer that has partially lost its elastic properties varies from 150 to 500 km. The weakening of the layer under the lithosphere is simulated by a tenfold lower value of the shear modulus down to the core boundary. In general, the stresses for the threelevel compensation model differ from the values obtained for the two-level model (nonequilibrium relief and density anomalies at the crust?mantle boundary are the sources of the anomalous gravitational field) by 5?10%. Considerable differences between the models of two-level and three-level compensation are revealed beneath Hellas and Argyre regions.     

Thermal history and evolution of Mars

A theoretical thermal evolution model of Mars is constructed, utilizing as constraints the available geophysical and geological data, including those provided by the Viking missions. The calculation includes conduction and subsolidus mantle convection. Calculated models indicate that Martian evolution can be roughly characterized by four different stages. (1) Core formation and crust differentiation: this stage starts from the planet formation to about 1 by thereafter. During this period, Martian core is separated and the initial crust is differentiated. (2) Heating, expansion, and mantle differentiation: this stage begins after the core separation and extends to about 3 by. First, mantle temperatures rise and reach partial melting. Between 2 and 3 by, extensive melting, differentiation, and outgassing occur. Planetary radius increases and extensional features observed at the surface are most likely generated at this stage. (3) Mature phase: after 3 by, the planet reaches maturity. Between 3 and 4 by slow and sustained evolution continues. Lithosphere thickens and partial melt zone deepens. (4) Cooling period: this stage represents the last phase of Martian history. The planet is cooling slowly. The partial melting zone shrinks and volcanic activity tapers off. At present, Martian lithosphere is about 200 km thick and the mantle is convecting slowly. The models suggest that the core is molten, and the calculated surface heat flux is 35 erg cm^?2 sec^?1.     

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.     

Internal structures of the Galilean satellites

New models for the interiors of Io, Ganymede, and Callisto are proposed. The model of Io consists of a thin, high-rigidity outer layer separated from a solid interior by a thin, molten or partially molten shell. The modulus of rigidity of the outer layer must be at least 100 times larger than that of the underlying partially molten shell. These layers have thicknesses of order 100 km or less. The near-surface partially molten layer was most likely produced early in Io's history as a consequence of accretional heating; enhanced tidal heating in the outer rigid layer has kept the underlying region partially molten to the present day. The model of Ganymede consists of an ice outer layer, a shell of undifferentiated, primordial ice-silicate mixture, and a rock core. Accretional heating is responsible for melting the ice in the outer layers of Ganymede's initially homogeneous ice-silicate interior. Most of the rock in this outer layer accumulates in a shell on top of Ganymede's early cold and rigid central region; the water in the outer layer quickly refreezes. Heating of the undifferentiated region by the decay of radioactive elements in the silicate fraction would gradually warm it and reduce its viscosity. The rock layer would become gravitationally unstable and sink through the undifferentiated materials to form a rock core. Callisto's heavily cratered surface strongly suggests that relatively little, if any, ice-rock differentiation has occured in its interior.     

Tidally forced viscous heating in a partially molten Io

We investigate tidal dissipative heating in two different models of Io. The partially molten asthenosphere model consists of a rigid inner core and a thin (less than 40 km thick) partially molten “decoupling” layer (asthenosphere) surrounded by an elastic lithosphere. In the partially molten interior model the interior beneath the lithosphere is partially molten throughout. The partially molten region in each model assumed to possess negligible shear strength and to be characterized by a Newtonian viscosity. Tidal deformation and dissipation in the core of the thin asthenosphere model are assumed negligible. Fluid in the viscous layers is forced to circulate by the tidal distortion of the outer shell, modeled here as a sinusoidal variation with time of the distortion amplitude. As a result, heat is generated in the fluid by viscous dissipation. There are two heating mechanisms in our models: “elastic” dissipation in the lithosphere ∞ 1/Q and viscous dissipation in the partially molten region. Numerical calculatons are carried out for a 90-km-thick lithosphere with Q = 100. This thickness maximizes dissipation in a decoupled lithosphere; other reasonable values of lithosphere thickness do not alter our conclusions. Under the constraint that total dissipation equals the observed radiated heat loss we derived the iscosity of the partially molten region in each model. We a posteriori evaluate the assumption that the lithosphere is decoupled from the interior by calculating the distortion of an elastic shell due to the viscous stresses on the lower surface of the outr shell. If the interior viscosity is such that the total dissipation is equal to the observed heat flux from Io, viscous stresses produce negligible distortion of a 90-km-thick shell. This validates the assumption of a decoupled shell. The derived viscosity for both models is characteristic of a partially molten rock. In the thin asthenosphere model the derived viscosity is so low that a very high degree of partial melt is necessary, about 40% crystal fraction in a 400-km-thick asthenosphere and about 0% in a 1-km-thick asthenosphere. In the partially molten interior model the derived viscosity corresponds to a magma with about 60% crystals. Consideration of convective efficiencies demonstrates the plausibility of a stable thermal steady state for both models. A significant portion (75% for Q = 100) of Io's tidal heating can be the result of viscous dissipation in a partially molten region that decouples the outer shell from the interior. The partially molten layer can be considered a “global magma ocean”.     

Possible fossil H2O liquid-ice interfaces in the Martian crust

Throughout the northern equatorial region of Mars, extensive areas have been uniformly stripped, roughly to a constant depth. These terrains vary widely in their relative ages. A model is described here to explain this phenomenon as reflecting the vertical distribution of H₂O liquid and ice in the crust. Under present conditions the Martian equatorial regions are stratified in terms of the stability of water ice and liquid water. This arises because the temperature of the upper 1 or 2 km is below the melting point of ice and liquid is stable only at greater depth. It is suggested here that during planetary outgassing earlier in Martian history H₂O was injected into the upper few kilometers of the crust by subsurface and surface volcanic eruption and lateral migration of the liquid and vapor. As a result, a discontinuity in the physical state of materials developed in the Martian crust coincident with the depth of H₂O liquid-ice phase boundary. Material above the boundary remained pristine; material below underwent diagenetic alteration and cementation. Subsequently, sections of the ice-laden zone were erosionally stripped by processes including eolian deflation, gravitational slump and collapse, and fluvial transport due to geothermal heating and melting of the ice. The youngest plains which display this uniform stripping may provide a minimum stratigraphic age for the major period of outgassing of the planet. Viking results suggest that the total amount of H₂O outgassed is less than half that required to fill the ice layer, hence any residual liquid eventually found itself in the upper permafrost zone or stored in the polar regions. Erosion stopped at the old liquid-ice interface due to increased resistance of subjacent material and/or because melting of ice was required to mobilize the debris. Water ice may remain in uneroded regions, the overburden of debris preventing its escape to the atmosphere. Numerous morphological examples shown in Viking and Mariner 9 images suggest interaction of impact, volcanic, and gravitational processes with the ice-laden layer. Finally, volcanic eruptions into ice produces a highly oxidized friable amorphous rock, palagonite. Based on spectral reflectance properties, these materials may provide the best analog to Martian surface materials. They are easily eroded, providing vast amounts of eolian debris, and have been suggested (Toulmin et al., 1977) as possible source rocks for the materials observed at the Viking landing sites.     

Preliminary mariner 9 report on the geology of Mars

Mariner 9 pictures indicate that the surface of Mars has been shaped by impact, volcanic, tectonic, erosional and depositional activity. The moonlike cratered terrain, identified as the dominant surface unit from the Mariner 6 and 7 flyby data, has proven to be less typical of Mars than previously believed, although extensive in the mid- and high-latitude regions of the southern hemisphere. Martian craters are highly modified but their size-frequency distribution and morphology suggest that most were formed by impact. Circular basins encompassed by rugged terrain and filled with smooth plains material are recognized. These structures, like the craters, are more modified than corresponding features on the Moon and they exercise a less dominant influence on the regional geology. Smooth plains with few visible craters fill the large basins and the floors of larger craters; they also occupy large parts of the northern hemisphere where the plains lap against higher landforms. The middle northern latitudes of Mars from 90 to 150† longitude contain at least four large shield volcanoes each of which is about twice as massive as the largest on Earth. Steep-sided domes with summit craters and large, fresh-appearing volcanic craters with smooth rims are also present in this region. Multiple flow structures, ridges with lobate flanks, chain craters, and sinuous rilles occur in all regions, suggesting widespread volcanism. Evidence for tectonic activity postdating formation of the cratered terrain and some of the plains units is abundant in the equatorial area from 0 to 120° longitude.Some regions exhibit a complex semiradial array of graben that suggest doming and stretching of the surface. Others contain intensity faulted terrain with broader, deeper graben separated by a complex mosaic of flat-topped blocks. An east-west-trending canyon system about 100–200 km wide and about 2500 km long extends through the Coprates-Eos region. The canyons have gullied walls indicative of extensive headward erosion since their initial formation. Regionally depressed areas called chaotic terrain consist of intricately broken and jumbled blocks and appear to result from breaking up and slumping of older geologic units. Compressional features have not been identified in any of the pictures analyzed to data. Plumose light and dark surface markings can be explained by eolian transport. Mariner 9 has thus revealed that Mars is a complex planet with its own distinctive geologic history and that it is less primitive than the Moon.     

Thermal evolutions of the terrestrial planets

The thermal evolution of the Moon, Mercury, Mars, Venus and hypothetical minor planets is calculated theoretically, taking into account conduction, solid-state convection, and differentiation. An assortment of geological, geochemical, and geophysical data is used to constrain both the present day temperatures and thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. Initial temperatures and core formation play the most important roles in the early differentiation. The size of the planet is the primary factor in determining its present day thermal state. A planetary body with radius less than 1000 km is unlikely to reach melting given heat source concentrations similar to terrestrial values and in the absence of intensive early heating such as short half-life radioactive heating and inductive heating.Studies of individual planets are constrained by varying amounts of data. Most data exist for the Earth and Moon. The Moon is a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. It is presently cooling rapidly and is relatively inactive tectonically.Mercury most likely has a large core. Thermal calculations indicate it may have a 500 km thick solid lithosphere, and the core may be partially molten if it contains some heat sources. If this is not the case, the planet's interior temperatures are everywhere below the melting curve for iron. The thermal evolution is dominated by core separation and the high conductivity of iron which makes up the bulk of Mercury.Mars, intermediate in size among the terrestrial planets, is assumed to have differentiated an Fe–FeS core. Differentiation and formation of an early crust is evident from Mariner and Viking observations. Theoretical models suggest that melting and differentiation of the mantle silicates has occurred at least up until 1 billion years ago. Present day temperature profiles indicate a relatively thick (250 km) lithosphere with a possible asthenosphere below. The core is molten.Venus is characterized as a planet similar to the Earth in many respects. Core formation probably occurred during the first billion years after the formation. Present day temperatures indicate a partially molten upper mantle overlain by a 100 km thick lithosphere and a molten Fe–Ni core. If temperature models are good indicators, we can expect that today, Venus has tectonic processes similar to the Earth's.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

Tidally induced surface displacements, external potential variations, and gravity variations on Mars

We have used and extended Roosbeek’s tidal potential for Mars to calculate tidal displacements, gravity variations, and external gravitational potential variations. The tides on Mars are caused by the Sun, and to a lesser degree by the natural satellites Phobos (8%, relative to the Sun) and Deimos (0.08%, relative to the Sun). To determine the reaction of Mars to the tidal forcing, the Love numbers h, l, and k and the gravimetric factor δ were calculated for interior models of Mars with different state, density, and radius of the core and for models which include mantle anelasticity. The latitude dependence and frequency dependence of the Love numbers have been taken explicitly into account. The Love numbers are about three times smaller than those for the Earth and are very sensitive to core changes; e.g., a difference of about 30% is found between a model with a liquid core and an otherwise similar model with a solid core. Tidal displacements on Mars are much smaller than on Earth due to the smaller tidal potential, but also due to the smaller reaction of Mars (smaller Love numbers). For both the tidal diplacement and the tidal external potential perturbations, the tidal signal is at the limit of detection and is too small to permit properties of Mars’s interior to be inferred. On the other hand, the Phobos tidally induced gravity changes, which are subdiurnal with typical periods shorter than 12 h, can be measured very precisely by the very broad band seismometer with thermal control of the seismological experiment SEIS of the upcoming NetLander mission. It is shown that the Phobos-induced gravity tides could be used to study the Martian core.     

Phase equilibrium investigations of the Adirondack class basalts from the Gusev plains,Gusev crater,Mars

Abstract— Phase equilibrium experiments have been performed on a synthetic analog of the Gusev plains basalt composition from the Spirit landing site on Mars. Near‐liquidus phase relations were determined over the pressure range of 0.1 to 1.5 GPa and at temperatures from 1125 to 1390 °C in a piston cylinder apparatus and 1 atm gas mixing furnace. The composition is multiply saturated with olivine, orthopyroxene, and spinel near its liquidus at 1320 °C and 1.0 GPa, or 85 km depth on Mars, placing an upper limit constraint on the thickness of the Martian lithosphere at the time of eruption. Our experimental work suggests that the Gusev basalts are anhydrous batch melts of a primitive Martian mantle similar to the composition estimated by Dreibus and Wänke (1984). The temperature of multiple saturation indicates the persistence of high mantle potential temperatures on Mars, similar to those on the modern Earth, until at least the very latest Noachian (3.7 Ga). These high mantle temperatures would be responsible for persistent basaltic volcanism throughout the southern highlands during the first billion years of Mars's history. The source for Gusev basalts differs strongly from the source for shergottite meteorites, reinforcing the idea of the absence of global mantle convection and mixing on Mars. The existence of a relatively primitive mantle reservoir requires that at least part of the mantle underwent little modification during early planetary differentiation.     

Radius and limb topography of Mercury obtained from images acquired during the MESSENGER flybys

Analysis of images obtained by the MESSENGER spacecraft during its three flybys of Mercury yields a new estimate for the planet's mean radius of 2439.25±0.69 km, in agreement with results from Mariner 10 and Earth-based observations, as well as with MESSENGER altimeter and occultation data. The mean equatorial radius and polar radius are identical to within error, suggesting that rotational oblateness is negligible when compared with other sources of topography. This result is consistent with the small gravitational oblateness of the planet. Minor differences in radius obtained at different locations reflect regional variations in topography. Residual topography along three limb profiles has a dynamic range of 7.4 km and a root-mean-square roughness of 0.8 km over hemispherical scales. Following MESSENGER's entry into orbit about Mercury in March 2011, we expect considerable additional improvements to our knowledge of Mercury's size and shape.     

Destruction of basaltic bodies by high-velocity impact

As a simulation of collisional processes among solid bodies of various sizes in the solar system, polycarbonate projectiles of mass 0.37 g were impacted against cubic basaltic rocks of about 2 to 10 cm and larger with a velocity of 2.6 km/sec. The corresponding energy imparted per unit mass of target ranges from about 10⁶ to 10⁹ ergs/g. The phenomena are classified into four categories with increasing target size: (1) complete destruction, (2) remaining core, (3) transition region, and (4) crater formation. Empirical formulas for the cumulative mass of the fragments and the mass of the maximum fragment are given. The similarity of these formulas is briefly discussed. The experimental results are applied to the examination of the hypothesis that a single Martian satellite was once ruptured by impact, leaving the present two satellites. It is suggested that the radius of the parent satellite was larger than about 30 km.     

Thermal history of the Jovian satellite Io

The discovery of large volcanic eruptions on Io suggests that Io is one of the most geologically active planetary bodies. The energy source of this geologic activity is believed to be tidal heating induced by Jupiter. A number of thermal history calculations were done to investigate the effect of tidal heating on the thermal history of Io taking into account solid state convection and advective heat transfer. These simulations show that the total tidal heating energy in Io is almost equal to the advectively transferred heat, indicating that the observed heat flow from Io is nearly equal to the total tidal heating energy. Since total tidal heating energy is dependent on the radius of the liquid mantle and the internal dissipation factor (Q), the radius of the liquid mantle can be estimated for a given value of Q. Some reasonable thermal history models of Io were obtained using a model with Q ≈ 25–50 in which the magma source of Ionian volcanism is at a depth of 100–300 km. The models satisfy the heat flow data and the existence of a thick lithosphere. Using a model with Q = 25 and L = 300 km (thickness of the advective region) as the standard model (model II), we then studied the effect of convective heat transfer and the initial temperature distribution on the Ionian thermal history. In these calculations, the other parameters are the same as in the standard model (model II). These calculations show that although the temperature distribution in the central region reflects the difference in the efficiency of convective heat transfer and initial temperature distribution, the temperature distribution in the outer region does not changes appreciably.     

On the original igneous source of Martian fines

The composition of the silicate portion of Martian regolith fines indicates derivation of the fines from mafic to ultramafic igneous rocks, probably rich in pyroxene. Rock types similar in chemical and mineralogical composition include terrestrial Archean basalts and certain achondrite meteorites. If these igneous rocks weathered nearly isochemically, the nontronitic clays proposed earlier as an analog to Martian fines could be formed. Flood basalts of pyroxenitic lavas may be widespread and characteristic of early volcanism on Mars, analogous to maria flood basalts on the Moon and early Precambrian basaltic komatiites on Earth. Compositional differences between lunar, terrestrial, and Martian flood basalts may be related to differences in planetary sizes and mantle compositions of the respective planetary objects.     

Geology of Mars after the first 40 years of exploration

The knowledge of Martian geology has increased enormously in the last 40 yr. Several missions orbiting or roving Mars have revolutionized our understanding of its evolution and geological features, which in several ways are similar to Earth, but are extremely different in many respects. The impressive dichotomy between the two Martian hemispheres is most likely linked to its impact cratering history, rather than internal dynamics such as on Earth. Mars' volcanism has been extensive, very long-lived and rather constant in its setting. Water was available in large quantities in the distant past of Mars, when a magnetic field and more vigorous tectonics were active.Exogenic forces have been shaping Martian landscapes and have led to a plethora of landscapes shaped by wind, water and ice. Mars' dynamical behavior continues, with its climatic variation affecting climate and geology until very recent times. This paper tries to summarize major highlights in Mars' Geology, and points to deeper and more extensive sources of important scientific contributions and future exploration.     

Upper limits for the Martian exospheric number density during the Planet B/Nozomi mission

Dissociative recombination (DR) of ionospheric O₂⁺ ions is an important source of suprathermal atomic oxygen in the exosphere as previous studies about the Martian upper atmosphere have shown. Because of the weaker gravitational attraction a hot oxygen corona on Mars should be denser than that observed on Venus. Since the most important mechanism for the production of the hot oxygen atoms in the Martian exosphere is DR, we investigated the variability of this production mechanism depending of solar activity. The Japanese Nozomi spacecraft will have the possibility to detect with the neutral mass spectrometer (NMS) for the first time in-situ the theoretically predicted hot oxygen corona on Mars, if the corona number density above the cold background atmosphere is of the order of 10,000 cm⁻³. Due to a problem in the propulsion system Nozomi failed its planned arrival rendevouzs with Mars in October 1999 and will, therefore, arrive at the red planet not before January 2004. Solar activity will reach its maximum in 2001, so the related production rate of hot oxygen atoms will be in the medium range during the new arrival date of Nozomi. We used the ionospheric profiles from the Viking mission for low solar activity conditions (F_10.7≈70) and the Mariner 9 mission with a solar activity of about 120 for medium solar wind activity. The latter is comparable to the level we expect for the Mars arrival of Nozomi. The resulting influence of the hot oxygen corona number density distribution was calculated with a Monte Carlo technique. This technique is used to compute a hot particle density distribution function. We studied the atomic diffusion process in the Martian atmosphere by simulating the collision probability, particle direction and energy loss after collisions by generating random numbers. Compared to previous studies we have improved the Monte Carlo model by using more and smaller altitude steps and more detailed treatment of particles with a temporary downward motion. This has resulted in an increased amount of collisions and a shift to lower energies in the energy spectrum. Our results show that the hot oxygen component should begin to dominate above the cold background atmosphere at an altitude of about 500 km above the Martian surface. The NMS instrument on board of Nozomi should detect the hot oxygen component after its arrival at Mars in January 2004, at an altitude of about 600 km above the Martian surface. Since the solar activity will decrease during the mission the measurements during the first orbits will be the most significant ones. The first in-situ measurements of the hot oxygen number density would be very important for adjusting atmospheric escape models by separating ballistic, satellite and escape trajectories of the hot oxygen atoms, which are significant for studies of the evolution and solar wind interaction of the Martian atmosphere.     

The strength of the lunar lithosphere

A self-gravitating, elastic, spherical thick shell model is used to derive the present state of the lateral variations of density and stress differences within the lunar lithosphere. The model is allowed to deform under the load of an initial surface topography and internal density distribution, such that the resulting deformed body gives rise to the observed surface topography and gravity specified by the spherical harmonics of degree up to 70. Two main models are considered, Model A and Model B, with elastic lithospheres of thickness 300 and 210 km, respectively. Model A displays density perturbations of generally less than ±200 kg/m³ within the crustal layers, reducing rapidly to less than ±20 kg/m³ at the base of the lithosphere. The density perturbations in Model B are similar in the crust and marginally higher at the base of the lithosphere. The major stress differences in the mantle are associated with the mascon basins and are found to reach maximums of 8-10 MPa within the lower lithosphere (150-270 km) of Model A and maximums of 12-16 MPa at 150 to 180 km depth for Model B. A moderate correlation exists between the modeled stress distributions and shallow moonquake epicenters. However, the overall results of this study imply that other remnant stresses, due to processes other than density perturbations, exist and play a critical role in the large shallow moonquakes.