Antipodal effects of lunar basin-forming impacts: Initial 3D simulations and comparisons with observations

3D simulations of basin-scale lunar impacts are carried out to investigate: (a) the origins of strong crustal magnetic fields and unusual terrain observed to occur in regions antipodal to young large basins; and (b) the origin of enhanced magnetic and geochemical anomalies along the northwest periphery of the South Pole-Aitken (SPA) basin. The simulations demonstrate that a basin-forming impact produces a massive, hot, partially ionized cloud of vapor and melt that expands thermally around the Moon, converging near the basin antipode approximately 1 h after the impact for typical impact parameters. In agreement with previous work, analytic calculations of the interaction of this vapor-melt cloud with an initial ambient magnetic field predict a substantial temporary increase in field intensity in the antipodal region. The time of maximum field amplification coincides with a period when impacting ejecta also converge near the antipode. The latter produce antipodal shock stresses within the range of 5-25 GPa where stable shock remanent magnetization (SRM) of lunar soils has been found experimentally to occur. Calculated antipodal ejecta thicknesses are only marginally sufficient to explain the amplitudes of observed magnetic anomalies if mean magnetization intensities are comparable to those produced experimentally. This suggests that pre-existing ejecta materials, which would also contain abundant metallic iron remanence carriers, may be important anomaly sources, a possibility that is consistent with enhanced magnetic anomalies observed peripheral to SPA. The latter anomalies may be produced by amplified secondary ejecta impact shock waves in the thick SPA ejecta mantle occurring near the antipodes of the Imbrium and Serenitatis impacts. Together with converging seismic compressional waves, these antipodal impact shocks may have produced especially deep fracture zones along the northwest edge of SPA near the Imbrium antipode, allowing the ascent of magma with enhanced KREEP concentrations.     

Tektites - volcanic ejecta from the moon?

The problem of the origin of the enigmatic tektites is still unsolved. The two leading hypotheses - viz., ejecta from terrestrial impacts, and ejecta from lunar volcanoes or lunar impacts, each encounters serious difficulties. The former has ballistic and water content difficulties, while the latter has some compositional difficulties, especially in the trace elements, as determined from the returned samples. It is possible that the latter problem may be met through lunar volcanic ejecta from sites suggesting more differentiation than the majority of the Moon. That such features may exist is suggested from the identity of some granitic material in the returned rocks and soil samples implying fairly sizable source regions on the Moon. The rare terrestrial strewn tektite fields require restrictive ballistic trajectories from the Moon. Calculations reveal that ellipses of varying, decreasing sizes which depend on velocity of vertical ejection from which ejecta will intersect the earth at low-entrance angles occur on the nearside of the Moon. Reasonable velocities were chosen (2.55 to 3.0 km s^?1) and these ellipses circumscribe areas with longitudes between 30 and 50° east and latitudes between 7° north and south of the Moon's equator. These areas were searched for evidence of volcanism. As tektites have compositions ranging from acidic (major tektites) to basic (micro-tektites) contents of silica (SiO₂) both acidic and basic volcanic features were sought. Since tektites range in age from about 30 million to 700000 yr old, they imply recent volcanism. Lunar Transient Phenomena (LTP) and data from various Apollo missions indicate that mild internal activity may still be occurring on the Moon. LTP sites are logical sources to investigate, of which four occur within the above delimited regions. These and their surroundings were examined and a number of possible explosive volcanism sites were found. These sites are identified and discussed after a review of the manifestations found from the various kinds of terrestrial volcanism for which lunar counterparts were sought.     

Comments on the moon's magnetism

Various lines of evidence indicate that permanent magnetization of lunar rocks, acquired during the early history of the Moon, is responsible for the weak (tens of gammas) and patchy magnetic field found at the surface of the Moon. It would be necessary to invoke a core dynamo (with all its important implications) in order to account for the inducing fieldB of not less than 10³ in which lunar rocks acquired their stable permanent magnetization if no other source ofB can be found. In this connection we point out that the magnetic effects of high-velocity meteoroid impacts have not yet been ruled out. Indeed, according to rough calculations these effects might not be negligible and detailed studies would be worth carrying out. Shock waves followed by rarefaction waves would spread out into the body of the Moon from the area of impact, first demagnetizing any material shock-heated above the Curie temperature and then, as the material cools rapidly during the passage of the rarefaction wave, re-magnetizing the material to an intensity determined by the background fieldB. The main source ofB would be the pulse of electric current generated by magneto-hydrodynamic interaction between the electrically-conducting ejecta from the explosion and the weak ambient interplanetary magnetic field.This impact dynamo hypothesis also has possible implications concerning the magnetism of meteorites.     

Meteoritic material on the moon

Three types of meteoritic material are found on the Moon: micrometeorites, ancien planetesimal debris from the ‘early intense bombardment’, and debris of recent, crater-forming projectiles. Their amounts and compositions have been determined from trace element studies. The micrometeorite component is uniformly distributed over the entire lunar surface, but is seen most clearly in mare soils. It has a primitive, C1-chondrite-like composition, and comprises 1-1.5% of mature soils. Apparently it represents cometary debris. The mean annual influx rate is 2.4 × 10^?9 g cm^?2 yr^?1. It shows no detectable time variation or dependence on selenographic position. The ancient component is seen in highland breccias and soils more than 3.9 AE old. It has a fractionated composition, with volatiles depleted relative to siderophiles. The abundance pattern does not match that of any known meteorite class. At least two varieties exist (LN and DN, with Ir/Au, Re/Au 0.25-0.5 and > 0.5 the C1 value). Both seem to represent the debris of planetesimals that produced the mare basins and highland craters during the first 700 Myr of the Moon's history. It appears that the LN and DN objects impacted at less then 10 km s^?1, had diameters less than 100 km, contained more than 15% Fe, and were not internally differentiated. Both were depleted in volatiles; the LN objects also in refractories (Ir, Re). This makes it unlikely that the LN bodies served as important building blocks of the Moon. The crater-forming component has remained elusive. Only a possible hint of this component has been seen, in ejecta from Dune Crater and Apollo 12 KREEP glasses of Copernican (?) origin.     

Impact ejecta exceeding lunar escape velocity

Microrater frequencies caused by fast (? 3 km s^?1) ejecta have been determined using secondary targets in impact experiments. A primary projectile (steel sphere, diam 1.58 mm, mass 1.64 × 10^?2 g) was shot in Duran glass with a velocity of 4.1 km s^?1 by means of a light gas gun. The angular distribution of the secondary crater number densities shows a primary maximum around 25°, and a secondary maximum at about 60° from the primary target surface. The fraction of mass ejected at velocities of ? 3 km s^?1 is only a factor of 7.5 × 10^?5 of the primary projectile mass. A conservative calculation shows that the contribution of secondary microcraters (caused by fast ejecta) to primary microcrater densities on lunar rock surfaces (caused by interplanetary particles) is on the statistical average below 1% for any lunar surface orientation. Calculation of the interplanetary dust flux enhancement caused by Moon ejecta turned out to be in good agreement with Lunar Explorer 35in situ measurements.     

Measurement of Impact Ejecta from Regolith Targets in Oblique Impacts

This paper reports the results of experiments on projectile impact into regolith targets at various impact angles. Copper projectiles of 240 mg are accelerated to 197 to 272 m s⁻¹ using an electromagnetic gun. The ejecta are detected by thin Al foil targets as secondary targets, and the resulting holes on the foil are measured to derive the spatial distribution of the ejecta. The ejecta that penetrated the foil are concentrated toward the downrange azimuths of impacting projectiles in oblique impacts. In order to investigate the ejecta velocity distribution, the nondimensional volume of ejecta with velocities higher than a given value is calculated from the spatial distribution. In the case of the vertical impact of the projectile, most ejecta have velocities lower than 24% of the projectile speed (∼50 m s⁻¹), and there are only several ejecta with velocities higher than 72 m s⁻¹. This result confirms the existence of an upper limit to the ejection velocity in the ejecta velocity distribution (Hartmann cutoff velocity) (W. K. Hartmann, 1985, Icarus63, 69-98). On the other hand, it is found that, in the oblique impacts, there are a large number of ejecta with velocities higher than the Hartmann cutoff velocity. The relative quantity of ejecta above the Hartmann cutoff velocity increases as the projectile impact angle decreases. Taking these results with the results of S. Yamamoto and A. M. Nakamura (1997, Icarus128, 160-170) from impact experiments using an impact angle of 30°, it can be concluded that the ejecta from these regolith targets exhibit a bimodal velocity distribution. Below a few tens of m s⁻¹, we see the expected velocity distribution of ejecta, but above this velocity we see a separate group of high-velocity ejecta.     

On the relative and absolute ages of seven lunar front face basins: I. From Viscosity Arguments

The seven basins, Orientale, Imbrium, Crisium, Nectaris, Humorum, and an unnamed basin between Werner and the Altai Ring show rims whose absolute and relative heights are correlated with the sharpness and crispness of the features. On the assumption that the decline in average outer rim height, not scarp height, measures the age of the basin and also that the decline represents a hot creep of rocks of very high viscosity, absolute ages were derived. Basins were found to increase in age in the sequence listed above, with a range from about 3.82 to 4.30 × 10⁹ years. The average or effective viscosity of the surface layers down to whatever level was involved in the creep was calculated as increasing from 9.46 × 10²⁴ poises at about 4.30 × 10⁹ years to 1.86 × 10³⁰ poises at present.It should be clear at the outset what the assumptions and associated observations are and why they are necessary to a solution. They will be listed in this abstract and expanded upon in the text.

• 1.(1)The original rim height of each basin was a function only of basin diameter.
• 2.(2)The original rim height was given by Pike's (1983) relation for fresh craters extrapolated to basin diameters.
• 3.(3)The present rim height is that of the most prominent ring structure.
• 4.(4)The smaller rim height of all seven basins, relative to the height predicted by (2) is due largely to creep in the lunar rocks down to some undetermined level. Other forces may contribute to the sinking of the rims, but these are considered to be of lesser importance and are discussed in the text.
• 5.(5)The relative ages of the seven basins are as given in Table I. This sequence differs slightly from that of Wilhelms (1984), for example, but it is that found in Baldwin, 1974, Baldwin, 1987 and is consistent with the results of this paper.
• 6.(6)The age of formation of the Imbrium basin (3.85 × 10⁹ years) inferred from lunar sample studies (particularly Apollo 15) is correct.
• 7.(7)The age of formation of the Serenitatis basin (3.87 +/− .04) × 10⁹ years, inferred from petrologic and geochemical studies of Apollo 17 boulders is incorrect. This is not an assumption, but is a result of the analysis of this paper.
• 8.(8)The rheology of the Moon may be described, for the purposes of this paper, by an effective viscosity valid throughout the layers involved in the creep.
• 9.(9)This effective viscosity is used as a tool to determine basin ages and is not important in itself. It does appear to vary in the same range as terrestrial rocks, but not the lithosphere.
• 10.(10)Other factors such as isostasy, shaking due to jar from later impacts, modification due to rim relief by ejecta, and erosion from small impacts are all close to exponential in nature, declining toward the present, and hence may be included in the determination of the effective viscosity.
• 11.(11)The rim height of the Imbrium basin subsided by 25 m in the last 2.5 × 10⁹ years. This value was chosen arbitrarily. It could have been 250–300 m and the basin ages would not have been affected except for Orientale and that only minutely.
• 12.(12)The effective viscosity of the Moon was observed to change continuously and monotonically with time.
• 13.(13)Judging by Table III, the probable error of an absolute age is in the range of 10 to 50 × 10⁶ years. It is difficult to determine exactly what this means. It will be constrained by points (14), (15), and (16).
• 14.(14)An error in the age determination should not be large enough to alter the relative ages of the basins, judging by crater counts (Baldwin, 1974, Baldwin, 1987).
• 15.(15)If the viscosity of the Moon declined in the post-Imbrium period of mare formation the only basin to be affected would be Orientale and this by no great amount inasmuch as the basin is older than nearby maria.
• 16.(16)If the effective viscosity were less than about 10²² poises at the time of the oldest basin then presaturation surfaces would not show the numerous craters and portions of craters that are obvious in this time span.
• 17.(17)Considerably prior to the time of saturation the outer layers of the Moon had a low enough viscosity so that they could not retain the record of the then occuring cratering.
• 18.(18)The approximations of this paper were adopted because it does not appear possible to make an unambiguous selection from the more elegant mathematical treatments of creep and isostasy that would lead toward reasonable ages for the giant basins.

     

The rayed crater Zunil and interpretations of small impact craters on Mars

A 10-km diameter crater named Zunil in the Cerberus Plains of Mars created ∼¹⁰⁷ secondary craters 10 to 200 m in diameter. Many of these secondary craters are concentrated in radial streaks that extend up to 1600 km from the primary crater, identical to lunar rays. Most of the larger Zunil secondaries are distinctive in both visible and thermal infrared imaging. MOC images of the secondary craters show sharp rims and bright ejecta and rays, but the craters are shallow and often noncircular, as expected for relatively low-velocity impacts. About 80% of the impact craters superimposed over the youngest surfaces in the Cerberus Plains, such as Athabasca Valles, have the distinctive characteristics of Zunil secondaries. We have not identified any other large (?10 km diameter) impact crater on Mars with such distinctive rays of young secondary craters, so the age of the crater may be less than a few Ma. Zunil formed in the apparently youngest (least cratered) large-scale lava plains on Mars, and may be an excellent example of how spallation of a competent surface layer can produce high-velocity ejecta (Melosh, 1984, Impact ejection, spallation, and the origin of meteorites, Icarus 59, 234-260). It could be the source crater for some of the basaltic shergottites, consistent with their crystallization and ejection ages, composition, and the fact that Zunil produced abundant high-velocity ejecta fragments. A 3D hydrodynamic simulation of the impact event produced 10¹⁰ rock fragments ?10 cm diameter, leading to up to 10⁹ secondary craters ?10 m diameter. Nearly all of the simulated secondary craters larger than 50 m are within 800 km of the impact site but the more abundant smaller (10-50 m) craters extend out to 3500 km. If Zunil is representative of large impact events on Mars, then secondaries should be more abundant than primaries at diameters a factor of ∼1000 smaller than that of the largest primary crater that contributed secondaries. As a result, most small craters on Mars could be secondaries. Depth/diameter ratios of 1300 small craters (10-500 m diameter) in Isidis Planitia and Gusev crater have a mean value of 0.08; the freshest of these craters give a ratio of 0.11, identical to that of fresh secondary craters on the Moon (Pike and Wilhelms, 1978, Secondary-impact craters on the Moon: topographic form and geologic process, Lunar Planet. Sci. IX, 907-909) and significantly less than the value of ∼0.2 or more expected for fresh primary craters of this size range. Several observations suggest that the production functions of Hartmann and Neukum (2001, Cratering chronology and the evolution of Mars, Space Sci. Rev. 96, 165-194) predict too many primary craters smaller than a few hundred meters in diameter. Fewer small, high-velocity impacts may explain why there appears to be little impact regolith over Amazonian terrains. Martian terrains dated by small craters could be older than reported in recent publications.     

Generation and emplacement of fine-grained ejecta in planetary impacts

We report here on a survey of distal fine-grained ejecta deposits on the Moon, Mars, and Venus. On all three planets, fine-grained ejecta form circular haloes that extend beyond the continuous ejecta and other types of distal deposits such as run-out lobes or ramparts. Using Earth-based radar images, we find that lunar fine-grained ejecta haloes represent meters-thick deposits with abrupt margins, and are depleted in rocks ?1 cm in diameter. Martian haloes show low nighttime thermal IR temperatures and thermal inertia, indicating the presence of fine particles estimated to range from ∼10 μm to 10 mm. Using the large sample sizes afforded by global datasets for Venus and Mars, and a complete nearside radar map for the Moon, we establish statistically robust scaling relationships between crater radius R and fine-grained ejecta run-out r^* for all three planets. On the Moon, r^* ∼ R^−0.18 for craters 5-640 km in diameter. For Venus, radar-dark haloes are larger than those on the Moon, but scale as r^* ∼ R^−0.49, consistent with ejecta entrainment in Venus’ dense atmosphere. On Mars, fine-ejecta haloes are larger than lunar haloes for a given crater size, indicating entrainment of ejecta by the atmosphere or vaporized subsurface volatiles, but scale as R^−0.13, similar to the ballistic lunar scaling. Ejecta suspension in vortices generated by passage of the ejecta curtain is predicted to result in ejecta run-out that scales with crater size as R^1/2, and the wind speeds so generated may be insufficient to transport particles at the larger end of the calculated range. The observed scaling and morphology of the low-temperature haloes leads us rather to favor winds generated by early-stage vapor plume expansion as the emplacement mechanism for low-temperature halo materials.     

Energetic lunar nighttime ion events

The Rice University Suprathermal Ion Detector Experiment regularly observes ion events normally ranging from 250 eV q^?1 to 1000 eV q^?1 all through the lunar night. These ion events occur most often 2 to 3 days prior to the sunrise terminator. There is also a secondary activity peak 3 to 4 days after local sunset on the Moon. The events are normally of 4 hr or less in duration and the integral flux is 10⁶ ions cm^?2 s^?1 ster^?1. This article discusses the character of these events and presents the preliminary findings of a detailed study begun on this subject.     

A Large Basin on the Near Side of the Moon

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

On the heat flow of a gravitationally-differentiated moon of fission origin

It is shown that the mean value for the heat flow of a gravitationally-differentiated Moon of fission origin is about 13 erg cm^?2 s^?1 and that the heat flow varies regionally from about 3 erg cm^?2s^?1 to more than 45 erg cm^?2s^?1. These regional variations in the heat flow are caused by a non-uniform distribution of K, U and Th in the KREEP zone at the crust-upper mantle boundary and the redistribution of crustal materials and K, U and Th rich KREEP materials by basin-forming impacts. The scale of these regional variations is hundreds of km. The models presented are in accord with the Apollo 15 and 17 heat flow measurements.     

Lunar electric fields,surface Potential and Associated Plasma Sheaths

This paper reviews the electric field environment of the Moon. Lunar surface electric potentials are reported as follows: Solar Wind - Dayside: ø_o + 10 to + 18 V Solar Wind - Terminator: ø_o ç ? 10 to ? 100 V Electron and ion densities in the plasma sheath adjacent to each surface potential regime are evaluated and the corresponding Debye length estimated. The electric fields are then approximated by the surface potential over the Debye length. The results are: Solar Wind - Dayside: E_o ? 10 V m^?1 outward Solar Wind - Terminator: E_o ç 1 to 10 V m^?1 inward These fields are all at least 3 orders of magnitude higher than the pervasive solar wind electric field; however they are confined to within a few tens of meters of the lunar surface.     

The Alfvén-wave theory of solar flares

Evidence is discussed showing that a representative solar flare event comprises three or more separate but related phenomena requiring separate mechanisms. In particular it is possible to separate the most energetic effect (the interplanetary blast) from the thermal flare and from the rapid acceleration of particles to high energies. The phenomena are related through the magnetic structure characteristic of a composite flare event, being a bipolar surface field with most of its field lines ‘closed’. Of primary importance are helical twists on all scales, starting with the ‘flux rope’ of the spot pair which was fully twisted before it emerged. Subsequent untwisting by the upward propagation of an Alfvén twist wave provides the main flare energy.

1. The interplanetary blast model is based on subsurface, helically twisted flux ropes which erupt to form spots and then transfer their twists and energy by Alfvén-twist waves into the atmospheric magnetic fields. The blast is triggered by the prior-commencing flash phase or by a coronal wave.
2. The thermal flare is explained in terms of Alfvén waves travelling up numerous ‘flux strands’ (Figure 3) which have frayed away from the two flux ropes. The waves originate in interaction (collisions, bending, twisting, rubbing) between subsurface flux strands; the sudden flash is caused by a collision. The classical twin-ribbon flare results from the collision of a flux rope with a tight bunch of S-shaped flux strands.
3. The impulsive acceleration of electrons (hard X-ray, EUV, Hα and radio bursts) is tentatively attributed to magnetic reconnection between fields in two parallel, helically twisted flux strands in the low corona.
4. Flare (Moreton) waves in the corona have the same origin as the interplanetary blast. Sympathetic flares represent only the start of enhanced activity in a flare event already in the slow phase. Filament activation also occurs during the slow phase as twist Alfvén waves store their energy in the atmosphere.
5. Flare ejecta are caused by Alfvén waves moving up flux strands. Surges are attributed to packets of twist Alfvén waves released into bundles of flux strands; the waves become non-linear and drive plasma upwards. Spray-type prominences result from accumulations of Alfvén wave energy in dome-shaped fields; excessive energy density eventually explodes the field.

     

Rummaging through Earth's Attic for Remains of Ancient Life

We explore the likelihood that early remains of Earth, Mars, and Venus have been preserved on the Moon in high enough concentrations to motivate a search mission. During the Late Heavy Bombardment, the inner planets experienced frequent large impacts. Material ejected by these impacts near the escape velocity would have had the potential to land and be preserved on the surface of the Moon. Such ejecta could yield information on the geochemical and biological state of early Earth, Mars, and Venus. To determine whether the Moon has preserved enough ejecta to justify a search mission, we calculate the amount of terran material incident on the Moon over its history by considering the distribution of ejecta launched from the Earth by large impacts. In addition, we make analogous estimates for Mars and Venus. We find, for a well-mixed regolith, that the median surface abundance of terran material is roughly 7 ppm, corresponding to a mass of approximately 20,000 kg of terran material over a 10×10-square-km area. Over the same area, the amount of material transferred from Venus is 1-30 kg and material from Mars as much as 180 kg. Given that the amount of terran material is substantial, we estimate the fraction of this material surviving impact with intact geochemical and biological tracers.     

Tectonics of the Caloris area on Mercury: An alternative view

Both morphologic and geometric studies of the “lineated terrains” around Caloris provide evidence of several types of tectonic motions inside the ejecta blanket of the basin. These motions preferentially occurred along a preexisting pattern. In spite of several similarities to mare-filled multiring basins on the Moon, many geometric and chronologic differences suggest that the ridge pattern inside the Caloris basin may not be produced, as observed on the Moon, exclusively by subsidence of the inner basin under volcanic loading. A model of membrane stresses which yield a decrease of the radius of Caloris and the observed tectonics is proposed.     

Sun–Earth L_{1} and L_{2} to Moon transfers exploiting natural dynamics

This paper examines the design of transfers from the Sun–Earth libration orbits, at the \(L_{1}\) and \(L_{2}\) points, towards the Moon using natural dynamics in order to assess the feasibility of future disposal or lifetime extension operations. With an eye to the probably small quantity of propellant left when its operational life has ended, the spacecraft leaves the libration point orbit on an unstable invariant manifold to bring itself closer to the Earth and Moon. The total trajectory is modeled in the coupled circular restricted three-body problem, and some preliminary study of the use of solar radiation pressure is also provided. The concept of survivability and event maps is introduced to obtain suitable conditions that can be targeted such that the spacecraft impacts, or is weakly captured by, the Moon. Weak capture at the Moon is studied by method of these maps. Some results for planar Lyapunov orbits at \(L_{1}\) and \(L_{2}\) are given, as well as some results for the operational orbit of SOHO.     

Relation of a contracting earth to the apparent accelerations of the sun and moon

The tidal theory of the evolution of the lunar orbit has remained inconsistent with the observational values of the apparent secular accelerations of the Sun and Moon since it was first developed by Jeffreys in 1920. Allowance for a changing moment of inertia of the Earth enables the discrepancy to be completely removed if a decrease is occurring at a rate of just about the amount already required by the phase-change theory of the nature of the terrestrial core. The agreement of the resulting theory with the latest determinations of the lunar acceleration increases confidence in the phase-change hypothesis. On the other hand the theory renders it most unlikely that a changing constant of gravitation will prove necessary to account for the observations. On the present theory of itself the Moon would have been extremely close to the Earth only about 10⁹ yr ago which suggests that some additional process may at times have influenced the lunar orbit.     

On the petrology and structure of a gravitionally differentiated moon of fission origin

In a previous paper, it was shown that the basic properties and the developmental history of a gravitationally differentiated Moon of fission origin match those known for the Moon. In the first part of this report, the models of a differentiated Moon are critically reviewed based on second order considerations of some of the chemical systems used to develope the earlier models and based on new lunar data. As a result, slightly updated models are developed and the results indicate that a Moon of fission origin has a feldspar rich crust (≈70% Or_0.8Ab_5.3An_93.9 with ≈30% pyroxene and olivine) reaching an average depth of ≈65 km. A KREEP rich layer is located at the interface of the crust and the upper mantle. The upper mantle consists of peridotite (≈80% Wo₁₀En₇₀Fs₂₀ and ≈20% Fo_75–80 with ≈3% Al₂O₃ and ≈ 2% TiO₂) and reaches a depth of 300–400 km. Below 300–400 km lies a dunite (≈Fo₉₅) lower mantle. A simple model for the distribution of K, U and Th (and by inference, KREEP) in the differentiated Moon model is developed using a distribution coefficient of 0.1 for the three elements. This coefficient is derived from published data on the distribution of U in Apollo 11 basalts. The simple model successfully accounts for the observed K, U and Th contents of the various mare basalts and upland rocks and yields a heat flow of 21 erg cm^?2s^?1 for the Moon. A model for the fine structure of the peridotite upper mantle of the model Moon is developed based on the TiO₂ and trace element variations observed in the various mare basalts. It is proposed that the upper mantle is rhythmically banded on the scale of 10's of km and that this banding leads to local variations of a factor of ±3 in the K, U and Th content, _-10 ⁺⁵ in the TiO₂ content and _-∞ ⁺² in the olivine content of the peridotite. It is also proposed that this banding leads to large scale horizontal inhomogenuities in the composition of the upper mantle. It is also shown that the formation of the primitive suite of upland rocks is easily explained by the cumulation of plagioclase, which carried varying amounts of pyroxene, olivine and melt with it, during the peritectic crystallization of the last 20% of the differentiating Moon. It is found that the 100 Mg/(Mg+Fe) ratios of the mafics and the An contents of the plagioclases of the rocks are controlled by several factors, the most important of which is the ratio of melt to crystals which together formed the various upland rocks. The inverse relationship between the An contents and the Mg contents of the upland rocks is a direct consequence of the differentiation sequence proposed. The results and models presented in this paper further support the hypothesis that the Moon formed as a result of fission from the proto-Earth.     

Phobos,Deimos, and the Moon: Size and distribution of crater ejecta blocks

The size and radial distributions of ejecta blocks around craters (D = 0.8 to 10 km) on Phobos and Deimos have been compared to those around lunar craters (D = 0.2 to 3.5 km). The radial distribution of blocks was found to be similar on Phobos and the Moon, but more dispersed on Deimos. For the best imaged crater on Deimos (D = 800 m), the size distributions of blocks and the fraction of excavated volume present as blocks are similar to those on the Moon. The wider dispersal of blocks on Deimos is consistent with other findings on the spread of finer ejecta over the satellite.