Satellite measurements of the moon's magnetic field: A preliminary report

A preliminary analysis of the data from the UCLA magnetometer on board the Apollo 15 subsatellite indicates that remnant magnetization is a characteristic property of the Moon, that its distribution is such as to produce a rather complex pattern or fine structure, and that a detailed mapping of its distribution is feasible with the present experiment. The analysis also shows that lunar induction fields produced by transients in the interplanetary magnetic field are detectable at the satellite orbit so that in principle the magnetometer data can be used to determine the latitudinal and longitudinal as well as radial dependences of the distribution of electrical conductivity within the Moon. Finally, the analysis indicates that the plasma void or diamagnetic cavity which forms behind the Moon when the Moon is in the solar wind, is detectable at the satellite's orbit and that the flow of the solar wind near the limbs is usually rather strongly disturbed.Publication No. 981. Institute of Geophysics and Planetary Physics.     

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.     

Origin and early evolution of the planetary system

It is shown by linear stability analysis that a preplanetary (presatellite) disk of dust and gas with Keplerian velocity field can become unstable due to the collective self-gravity of the disk. The radial distribution of rings, which may result from this instability, is derived. These rings later on can be the formation sites for planets around the Sun and for satellites around the planets. The derived orbits are shown to be in good agreement with that of the planets and the satellites (of Jupiter, Saturn, and Uranus). Predictions and conclusions seem to be possible for the existence of three yet unknown Uranian satellites, the origin of the early Moon and the possible radial extension of the planetary system.     

Optimisation of seismic network design: Application to a geophysical international lunar network

Fundamental scientific questions concerning the internal structure and dynamics of the Moon, and their implications on the Earth-Moon System, are driving the deployment of a new broadband seismological network on the surface of the Moon. Informations about lunar seismicity and seismic subsurface models from the Apollo missions are used as a priori information in this study to optimise the geometry of future lunar seismic networks in order to best resolve the seismic interior structure of the Moon. Deep moonquake events and simulated meteoroid impacts are the assumed seismic sources. Synthetic P and S wave arrivals computed in a radial seismic model of the Moon are the assumed seismic data. The linearised estimates of resolution and covariance of radial seismic velocity perturbations can be computed for a particular seismic network geometry. The non-linear inverse problem relating the seismic station positions to the linearised estimates of covariance and resolution of radial seismic velocity perturbations is written and solved by the Neighbourhood Algorithm. This optimisation study favours near side seismic station positions at southern latitudes in order to constrain the deep mantle structure from deep moonquake data at large epicentral distances. The addition of a far side station allows to divide by two the size of the error bar on the seismic velocity model. The monitoring of lunar impact flashes from the Earth allows to improve the radial seismic model in the top of the mantle by adding much more meteor impact data at short epicentral distances due to the high accuracy of the space/time location of these seismic sources. Such meteor impact detections may be necessary to investigate the 3D structure of the lunar crust.     

Unipolar induction in the moon and a lunar limb shock mechanism

The unipolar induction mechanism is employed to calculate electric field profiles in the interior of a chemically homogeneous Moon possessing a steep radial thermal gradient characteristic of long-term radioactive heating. The thermal models used are those of Fricker, Reynolds, and Summers. From the magnetic field, the magnetic back pressure upon the solar wind is found. The electric field profile is shown to depend only upon the activation energy,E _o, of the geological material and the radial gradient of the reciprocal temperature. The current is additionally dependent upon the coefficient of the electrical conductivity function but only by a scale factor. Since the Moon is experimentally known to correspond to the case of weak interaction with the solar wind, the magnetic back pressure is calculated without the need for an iterative procedure. The results indicate that a hot Moon can yield sufficient current flow so that the magnetic back pressure is observable as a vestigial limb shock wave using an activation energy of about 2/3 eV together with a conductivity coefficient of about 10³ mhos/m. Such matter is approximated by diabase-like composition, although the result that both the activation energy and coefficient enter into the current determination does not rule out the possibility of a match with other similar substances. The calculations are entirely consistent with earlier results which indicated a model where the unipolar current density is dominated by a high impedance surface layer and a strong shock wave is inhibited. In addition to the magnetic back pressure, the integration of the current continuity equation permits current densities and joule heating rates to be calculated, though the magnitude of the latter for present solar wind conditions is not thermally important.On leave from NASA Ames Research Center     

Fission and geosynchronous release of the Moon

The problem of the origin of the Moon has led to various hypotheses: simultaneous accretion, fission, capture, etc. These theories were based primarily on global mechanical considerations. New geological data (Turcotteet al., 1974; Kahn and Pompea, 1978) have led to fresh approaches and new versions of these theories.As suggested by Wise (1969) and O'Keefe (1972), the initial Earth may have taken unstable forms when radial segregation sped up the rotation. The Moon may have been created as the small part of the pyroid of Poincaré.Fission theory was mainly discarded, in the past, on the basis of energy considerations. We are now arriving at the conclusion that these considerations are void if the fission was followed by a very long period of geostationary rotation of the Moon at a distance of about 3 Earth radius (i.e., out of the Roche limit). Indeed the large amount of energy of the initial system could have been released slowly and therefore evacuated by losses of material and radiation.The accretion of the Earth and the radial segregation of heavy chemicals toward the center has led to a differential rotation of the different layers with a faster rotation at the center. During the geostationary period the Moon was synchronous with respect to the surface layer. That Earth-Moon system has both a correct angular momentum and a large stability provided that the viscosity of intermediate layers was small enough, which is in concordance with its high temperature.Even with a very hot system, a superficial cold layer appears because of its low conductivity and the radiation equilibrium with outer space. This implies a slow loss of energy: the geosynchronous Moon receded extremely slowly.During the geostationary period lithophile elements were extracted with water by the radial segregation and were deposited in the area facing the Moon. One massive continent was formed, as suggested by Grjebine (1978).As the continent became thicker and sank into the mantle, convection currents appeared and speeded up the cooling of the Earth. The viscosity increased and the synchronization between the Moon and the surface of the Earth became more difficult to maintain. When synchronism was broken important lunar tides transferred energy and momentum from the Earth to the Moon which receded toward its present position and the modification of its equilibrium shape explains the formation of lunar maria in the near side.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

A motivating exploration on lunar craters and low-energy dynamics in the Earth–Moon system

It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L ₂ of the Earth–Moon system within the framework of the Circular Restricted Three-Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four-Body Problem. In the former case, as main outcome, we observe a more relevant bombardment at the apex of the lunar surface, and a percentage of impact which is almost constant and whose value depends on the assumed Earth–Moon distance d_EM. In the latter, it seems that the Earth–Moon and Earth–Moon–Sun relative distances and the initial phase of the Sun θ ₀ play a crucial role on the impact distribution. The leading side focusing becomes more and more evident as d_EM decreases and there seems to exist values of θ ₀ more favorable to produce impacts with the Moon. Moreover, the presence of the Sun makes some trajectories to collide with the Earth. The corresponding quantity floats between 1 and 5 percent. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth–Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering.     

Observations of the 7 March, 1970 total solar eclipse at wavelengths of 3.2 and 8.3 mm

The 7 March, 1970 total solar eclipse was observed at wavelengths of 3.2 and 8.3 mm; the object being to use the knife edge of the Moon as it passed across the Sun to improve angular resolution on the Sun. This in turn would provide a radial brightness distribution of the Sun with an angular resolution of a few seconds of arc.Excellent eclipse curves were obtained at 3 mm; however, some external interference marred the 8 mm record near totality.The 8 mm brightness distribution is subject to some uncertainty, but tends to show limb brightening. The 3 mm brightness distribution shows a well defined complex limb brightening within about 1 arc min of the optical limb. The maximum brightening is approximately 30% above the average disc temperature.     

Nonuniform cratering of the terrestrial planets

We estimate the impact flux and cratering rate as a function of latitude on the terrestrial planets using a model distribution of planet crossing asteroids and comets [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433]. After determining the planetary impact probabilities as a function of the relative encounter velocity and encounter inclination, the impact positions are calculated analytically, assuming the projectiles follow hyperbolic paths during the encounter phase. As the source of projectiles is not isotropic, latitudinal variations of the impact flux are predicted: the calculated ratio between the pole and equator is 1.05 for Mercury, 1.00 for Venus, 0.96 for the Earth, 0.90 for the Moon, and 1.14 for Mars over its long-term obliquity variation history. By taking into account the latitudinal dependence of the impact velocity and impact angle, and by using a crater scaling law that depends on the vertical component of the impact velocity, the latitudinal variations of the cratering rate (the number of craters with a given size formed per unit time and unit area) is in general enhanced. With respect to the equator, the polar cratering rate is about 30% larger on Mars and 10% on Mercury, whereas it is 10% less on the Earth and 20% less on the Moon. The cratering rate is found to be uniform on Venus. The relative global impact fluxes on Mercury, Venus, the Earth and Mars are calculated with respect to the Moon, and we find values of 1.9, 1.8, 1.6, and 2.8, respectively. Our results show that the relative shape of the crater size-frequency distribution does not noticeably depend upon latitude for any of the terrestrial bodies in this study. Nevertheless, by neglecting the expected latitudinal variations of the cratering rate, systematic errors of 20-30% in the age of planetary surfaces could exist between equatorial and polar regions when using the crater chronology method.     

Lunar Water: A Brief Review

One of the most exciting recent developments in the field of lunar science has been the unambiguous detection of water (either as OH or H₂O) or water ice on the Moon through instruments flown on a number of orbiting spacecraft missions. At the same time, continued laboratory-based investigations of returned lunar samples by Apollo missions using high-precision, low-detection, analytical instruments have for the first time, provided the absolute abundance of water (present mostly as structurally bound OH⁻ in mineral phases) in lunar samples. These new results suggest that the Moon is not an anhydrous body, questioning conventional wisdom, and indicating the possibility of a wet lunar interior and the presence of distinct reservoirs of water on the lunar surface. However, not all recent results point to a wet Moon and it appears that the distribution of water on the Moon may be highly heterogeneous. Additionally, a number of sources are likely to have contributed to the water inventory of the Moon ranging from primordial water to meteorite-derived water ice through to the water formed during the reaction of solar-wind hydrogen with the lunar soil. Water on the Moon has implications for future astrobiological investigations as well as for generating resources in situ during future exploration of the Moon and other airless bodies in the Solar System.     

Accretion process of the moon

Recent geochemical and geophysical data suggest that the initial temperature of the Moon was strongly peaked toward the lunar surface. To explain such an initial temperature distribution, a simple model of accretion process of the Moon is presented. The model assumes that the Moon was formed from the accumulation of the solid particles or gases in the isolated, closed cloud. Two equations are derived to calculate the accretion rate and surface temperature of the accreting Moon. Numerical calculations are made for a wide range of the parameters particle concentration and particle velocity in the cloud. A limited set of the parameters gives the initial temperature profiles as required by geochemical and geophysical data. These models of the proto-moon cloud indicate that the lunar outershell, about 400 km thick, was partially or completely molten just after the accretion of the Moon and that the Moon should have been formed in a period shorter than 1000 yr. If the Moon formed at a position nearer to the Earth than its present one, the Moon might have been formed in a period of less than one year.On leave from Geophysical Institute, University of Tokyo.Contribution No. 2104, Division of Geological and Planetary Sciences, California Institute of Technology.     

Current bombardment of the Earth-Moon system: Emphasis on cratering asymmetries

We calculate the current spatial distribution of projectile delivery to the Earth and Moon using numerical orbital dynamics simulations of candidate impactors drawn from a debiased Near-Earth Object (NEO) model. We examine the latitude distribution of impactor sites and find that for both the Earth and Moon there is a small deficiency of time-averaged impact rates at the poles. The ratio between deliveries within 30° of the pole to that of a 30° band centered on the equator is small for Earth (<5%) (0.958±0.001) and somewhat greater for the Moon (∼10%) (0.903±0.005). The terrestrial arrival results are examined to determine the degree of AM/PM asymmetry to compare with the PM excess shown in meteorite fall times. We find that the average lunar impact velocity is 20 km/s, which has ramifications in converting observed crater densities to impactor size distributions. We determine that current crater production on the leading hemisphere of the Moon is 1.28±0.01 that of the trailing when considering the ratio of craters within 30° of the apex to those within 30° of the antapex and that there is virtually no nearside-farside asymmetry, in agreement with observations of rayed craters. As expected, the degree of leading-trailing asymmetry increases when the Moon's orbital distance is decreased.     

Disturbance compensating control of orbit radially aligned two-craft Coulomb formation

This paper investigates the orbit radial stabilization of a two-craft virtual Coulomb structure about circular orbits and at Earth–Moon libration points. A generic Lyapunov feedback controller is designed for asymptotically stabilizing an orbit radial configuration about circular orbits and collinear libration points. The new feedback controller at the libration points is provided as a generic control law in which circular Earth orbit control form a special case. This control law can withstand differential solar perturbation effects on the two-craft formation. Electrostatic Coulomb forces acting in the longitudinal direction control the relative distance between the two satellites and inertial electric propulsion thrusting acting in the transverse directions control the in-plane and out-of-plane attitude motions. The electrostatic virtual tether between the two craft is capable of both tensile and compressive forces. Using the Lyapunov’s second method the feedback control law guarantees closed loop stability. Numerical simulations using the non-linear control law are presented for circular orbits and at an Earth–Moon collinear libration point.     

A Kinetic Model of Coronal Heating and Acceleration by Ion-Cyclotron Waves: Preliminary Results

We present a kinetic model of the heating and acceleration of coronal protons by outward-propagating ion-cyclotron waves on open, radial magnetic flux tubes. In contrast to fluid models which typically insist on bi-Maxwellian distributions and which spread the wave energy and momentum over the entire proton population, this model follows the kinetic evolution of the collisionless proton distribution function in response to the combination of the resonant wave-particle interaction and external forces. The approximation is made that pitch-angle scattering by the waves is faster than all other processes, resulting in proton distributions which are uniform over the resonant surfaces in velocity space. We further assume, in this preliminary version, that the waves are dispersionless so these resonant surfaces are portions of spheres centered on the radial sum of the Alfvén speed and the proton bulk speed. We incorporate the fact that only those protons with radial speeds less than the bulk speed will be resonant with outward-propagating waves, so this rapid interaction acts only on the sunward half of the distribution. Despite this limitation, we find that the strong perpendicular heating of the resonant particles, coupled with the mirror force, results in substantial outward acceleration of the entire distribution. The proton distribution evolves towards an incomplete shell in velocity space, and appears vastly different from the distributions assumed in fluid models. Evidence of these distinctive distributions should be observable by instruments on Solar Probe.     

Volatile retention from cometary impacts on the Moon

Impacts of comets and asteroids play an important role in volatile delivery on the Moon. We use a novel method for tracking vapor masses that reach escape velocity in hydrocode simulations of cometary impacts to explore the effects of volatile retention. We model impacts on the Moon to find the mass of vapor plume gravitationally trapped on the Moon as a function of impact velocity. We apply this result to the impactor velocity distribution and find that the total impactor mass retained on the Moon is approximately 6.5% of the impactor mass flux. Making reasonable assumptions about water content of comets and the comet size-frequency distribution, we derive a water flux for the Moon. After accounting for migration and stability of water ice at the poles, we estimate a total 1.3×10⁸-4.3×10⁹ metric tons of water is delivered to the Moon and remains stable at the poles over 1 Ga. A factor of 30 uncertainty in the estimated cometary impact flux is primarily responsible for this large range of values. The calculated mass of water is sufficient to account for the neutron fluxes poleward of 75° observed by Lunar Prospector. A similar analysis for water delivery to the Moon via asteroid impacts shows that asteroids provide six times more water mass via impacts than comets.     

A 3D hybrid simulation study of the electromagnetic field distributions in the lunar wake

A three-dimensional hybrid code is used to study the electromagnetic disturbances in the solar wind that arise due to the absorption effect of the Moon. Due to the nearly insulating nature of the Moon, interplanetary magnetic fields (IMFs) can move through the interior without hindrance. However, the near-vacuum created in the wake region due to the lunar absorption effect will lead to enhancement of the strength of the magnetic field by a factor of about 1.4 in the middle of the lunar wake and lead to depletions at two sides. The situations arising from different orientations of the interplanetary magnetic fields relative to the radial direction are compared. Asymmetries of the inward diffusions both along and perpendicular to the field lines are also observed. The electric field formed from the plasma convection could reach a magnitude of 0.2–0.8 mV/m at the border of the wake. The role of the electric field on the inward accelerations is important to the geometry of the lunar wake.     

On the fissions of a solid body under influence of tidal force; with application to the problem of twin craters on the moon

The internal strain due to the tidal force in the proximity of a tide-generating body (in the present case, the Moon) is calculated according to the Lord Kelvin theory of Earth tides. The conditions for which uniform elastic sphere possessing a definite tensile strength is crushed near the surface of the Moon is investigated. The state of internal stress is almost independent of the value of elastic constants. Many lunar features, such as twin craters, craterous walled plains of irregular forms, compound craters, may be explained by fission of the meteoritic material before impact.     

A correlation between large-scale asymmetry of the Moon and the foci of moonquakes

Some evidence is produced to show that the Moon is asymmetric on the large scale as regards its figure, structure, composition, the distribution of tidal force, natural remnant magnetism and magnetic anomaly. This asymmetry produces the state of stress in the Moon, causing most foci of moonquakes to be located in the nearside of the Moon.     

The alkali metal atmospheres on the Moon and Mercury: Explaining the stable exospheres by heavy Rydberg Matter clusters

Despite recent progress in the modeling of alkali atmospheres like those around the Moon and Mercury, many problems still exist. It is proposed that Rydberg Matter (RM) clusters containing Na and K atoms are the main part of the alkali atmospheres of the Moon and Mercury, forming large clouds. RM clusters are studied in the laboratory with laser fragmentation and laser spectroscopy methods. Due to the very large collision cross sections of Rydberg atoms and RM clusters, the atmospheres are not collision free, as normally assumed based on the low densities of free alkali atoms. The non-escaping radial density variation for the Na atoms, observed, e.g., on the Moon, and the Maxwellian velocity distributions observed on Mercury are caused by a true atmosphere with collisional equilibration; this process is not possible in an exosphere. Fast alkali atoms are released from the RM clusters already at large heights by solar photons and charged particle impact. The kinetic temperatures derived for the atmospheres agree with the quantized energy release. The cluster model predicts that the rate of loss from the surface is much smaller than for a purely atomic model, since the transient storage is in the RM cluster form in the atmosphere and not at the surface. The conductance of the atmosphere is of the order of 100 S due to the facile collisional ionization of the RM clusters. The apparent depletion of K in the atmosphere of Mercury is explained.