Fission origin of the Moon: Cause and timing

A new scenario is offered for the origin of the Moon. It is assumed that the Earth formed initially with about the maximum amount of angular momentum consistent with dynamical stability. This state is approximated by the secularly unstable Maclaurin spheroids (highly flattened, hamburger-shaped bodies). It is shown that the Earth cannot depart from this state at a resonable rate as long as its viscosity is in the range of liquid rock. Since core formation supplies about 1600 kJ kg^?1 the Earth will not leave this state until core formation is complete. When cooling produces a rise in viscosity, the Earth will necessarily evolve along a path which is approximated by the Riemann ellipsoids (which have rapid internal motion). The evolution is toward a Jacobi ellipsoid, but it is intercepted by the development of a third-harmonic (pearshaped) instability, which is catastrophic and leads to fission. The process of fission itself may be fundamentally analogous to the breaking of a wave in water. We cannot exclude the possibility that some other planets evolved similarly.     

Neutral sodium atoms release from the surface of the Moon induced by meteoroid impacts

In this work, we calculate the vapour and neutral Na production rates on the Moon, as due to the impacts of meteoroids in the radius range of 10⁻⁸–0.15 m. We limit our calculations to this size range, since meteoroids with radius larger than 0.15 m have not been found to be important for the production of the exosphere in a time interval comparable with that of the observations.
We have considered a new dynamical model of the flux of meteoroids at the heliocentric distance of the Moon, regarding objects in the radius range of 10⁻²–0.15 m. Instead, the flux of smaller meteoroids (radius range 10⁻⁸–10⁻² m) has been calculated using the two distributions adopted by Cintala and Love & Brownlee.
The results of our model are that (i) the neutral Na production rate is  ∼3–4.9 × 10⁴ atoms cm⁻² s⁻¹  , slightly larger than the previous estimates  (∼2–3 × 10⁴ atoms cm⁻² s⁻¹)  , and (ii) only about 6 per cent of neutral Na is produced by the impacts of meteoroids in the size range 10⁻³–0.15 m, whereas about 94 per cent of the Na comes from the  10⁻⁵–10⁻³ m  size range.     

Neutral sodium atoms release from the surfaces of the Moon and Mercury induced by meteoroid impacts

In this work, we calculate the neutral Na production rates on the Moon and Mercury, as due to the impacts of meteoroids having an impact probability on the surface that can influence the daily observations of the exosphere: the meteoroids radius range considered for the Moon and Mercury are 10⁻⁸–0.15 and 10⁻⁸–0.10 m, respectively. We also estimate the mass of meteoroids that has impacted the surfaces of the Moon and Mercury in the last 3.8 Gy (after the end of the Late Heavy Bombardment).The results of our model are that (i) the Na production rates are ∼(3–4.9)×10⁴ and ∼(1.8–2.3)×10⁶ atoms cm⁻² s⁻¹, for Moon and Mercury, respectively, and (ii) in the last 3.8 Gy, the mass of meteoroids that has impacted the whole surface of the Moon and Mercury has been 8.86×10¹⁸ and 2.66×10¹⁹ g, respectively.     

An analytical simulation of the geosynchronous plasma environment

A procedure for analytically simulating the parameters necessary to characterize the geosynchronous plasma is developed in terms of the daily A_p index and local time. Although based on a limited set of ATS-5 data, the simulation adequately models the simultaneous variations in the warm plasma (50 eV–50 keV) electron and ion populations during injection events. Developed primarily to estimate the varying potentials expected on a shadowed, electrically isolated surface, the simulation can also be employed in a variety of cases where knowledge of the general characteristics of the geosynchronous plasma is necessary.     

Consequences of a geosynchronous phase for the moon

Fission from the Earth's mantle explains why the density of the Moon is similar to that of the Earth's mantle.If following the fission origin of the Moon, the Earth-Moon distance increases progressively, the Moon can recollect chemicals evaporated by the Earth but not volatile enough to be lost as gases.In this way, the surface of the Moon can be enriched in refractory elements as most of the authors have proposed.At 3 Earth radii the long geosynchronous phase allows the formation of a solid crust which will record the Earth's magnetic field and the equilibrium hydrostatic from at that distance.When geosynchronism is broken the Moon will recede; its shape will no longer fit the hydrostatic form. The crust will either break or will exercise pressure on the lower layers. Meteor craters will allow lava to come to the surface. Such flows will be very large where the shape of the crust does not fit at all the geosynchronous form. Large lava flows will appear this way on the near side where the shape has changed the most. The new lava flows no longer record the magnetic field of the Earth because with the end of the synchronous position the field is alternative for the Moon; only the remanent field can influence the new lava.Three out of five samples dated at 3.6 b.y. suggest nevertheless that the field decreased slowly without becoming alternative. This means that the geosynchronous phase may have lasted longer and put the Moon on a more distant orbit, as Alfvén and Arrhenius suggested.The interpretation of lunar magnetism as influenced by the Earth cannot discard any interpretation or suggestion of its own lunar magnetic process. It is quite possible that both mechanisms have worked as some samples show.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 Accademic Nazionale del Lincei in Rome, Italy.     

Luni-solar effects of geosynchronous orbits at the critical inclination

The luni-solar effects of a geosynchronous artificial satellite orbiting near the critical inclination is investigated. To tackle this four-degrees-of-freedom problem, a preliminary exploration separately analyzing each harmonic formed by a combination of the satellite longitude of the node and the Moon longitude of the node is opportune. This study demonstrates that the dynamics induced by these harmonics does not show resonance phenomena. In a second approach, the number of degrees of freedom is halved by averaging the total Hamiltonian over the two non-resonant angular variables. A semi-numerical method can now be applied as was done when considering solely the inhomogeneity of the geopotential (see Delhaise et Henrard, 1992). Approximate surfaces of section are constructed in the plane of the inclination and argument of perigee. The main effects of the Sun and Moon attractions compared to the terrestrial attraction alone are a strong increase in the amplitude of libration in inclination (from 0.6° to 3.2°) and a decrease of the corresponding libration period (from the order of 200 years to the order of 20 years).Research Assistant for the Belgian National Fund for Scientific Research     

Bessel and librations of the Moon

On the occasion of the twohundredth anniversary of F. W. Bessel's birth, his method of heliometric observations for the determination of the Moon's physical libration constants and of the reduction of these observations is presented.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sterwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846).     

An intrinsic volatility scale relevant to the Earth and Moon and the status of water in the Moon

The notion of a dry Moon has recently been challenged by the discovery of high water contents in lunar apatites and in melt inclusions within olivine crystals from two pyroclastic glasses. The highest and most compelling water contents were found in pyroclastic glasses that are not very common on the lunar surface. To obtain more representative constraints on the volatile content of the lunar interior, we measured the Zn content, a moderately volatile element, of mineral and rock fragments in lunar soils collected during Apollo missions. We here confirm that the Moon is significantly more depleted in Zn than the Earth. Combining Zn with existing K and Rb data on similar rocks allows us to anchor a new volatility scale based on the bond energy of nonsiderophile elements in their condensed phases. Extrapolating the volatility curve to H shows that the bulk of the lunar interior must be dry (≤1 ppm). This contrasts with the water content of the mantle sources of pyroclastic glasses, inferred to contain up to approximately 40 ppm water based on H₂O/Ce ratios. These observations are best reconciled if the pyroclastic glasses derive from localized water‐rich heterogeneities in a dominantly dry lunar interior. We argue that, although late addition of 0.015% of a chondritic veneer to the Moon seems required to explain the abundance of platinum group elements (Day et al. 2007), the volatile content of the added material was clearly heterogeneous.     

Stresses in the Moon

It is argued that a reliable theory of the stress history of the Moon should take into account several factors; and that direct observations of the Moon's surface can throw much light on this subject.     

Topographic mapping of the Moon

Contour maps of the Mooon have been compiled by photogrammetric methods that use stereoscopic combinations of all available metric photographs from the Apollo 15, 16, and 17 missions. The maps utilize the same format as the existing NASA shaded-relief Lunar Planning Charts (LOC-1, -2, -3, and -4), which have a scale of 1:2 750 000. The map contour interval is 500m. A control net derived from Apollo photographs by Doyle and others was used for the compilation. Contour lines and elevations are referred to the new topographic datum of the Moon, which is defined in terms of spherical harmonics from the lunar gravity field. Compilation of all four LOC charts was completed on analytical plotters from 566 stereo models of Apollo metric photographs that cover approximately 20% of the Moon. This is the first step toward compiling a global topographic map of the Moon at a scale of 1:5 000 000.     

Internal structure of the Moon and moonquakes

I discuss the relation between the internal structure of the Moon and the radial distribution of the moonquake foci. I believe that the important factor conditioning the radial distribution is the fact that the rigidity of the lunar material decreases with increasing depth. Using a two-layer model, solutions of the elasticity equations are found for the cases of a uniform surface load and of a uniform radial body force. The results show that when the inner sphere is less rigid than the outer shell, the maximum sheer stress is located near the boundary of the two components, thus explainning why the moonquakes are mostly deep quakes. The results also suggest that a liquid core exists in the Moon.     

Stress history of the Moon

The character of the lunar surface indicates that surface faulting has not been an important mechanism for the build-up of the lunar surface. If the radioactive content of the Moon is of the same order as that of chondritic meteorites, then the absence of major surface faults can be explained in a number of ways. A near-surface concentration of radioactivity will provide an equality of heat production and surface heat flow necessary for the maintenance of a constant lunar radius. Alternatively, the radioactivity could be deeply buried, with the radius still remaining constant over the past 2,000,000,000 years. Heat transported by mechanisms other than radiation and thermal conduction will also tend to keep the radius of the Moon at a constant value.

Even though the radius of the Moon remains constant, there is a major build-up of strain energy throughout the Moon. The rate is such that, on the average, something on the order of 10²⁴–10²⁵ ergs of distortional energy should be released per year throughout the Moon, provided the radioactivity is uniformly distributed. A near-surface concentration of the radioactivity might decrease this rate of energy release but certainly by no more than an order of magnitude. Under all circumstances it would appear that a Moon of chondritic composition would have strong Scismic activity.     

Cometary impact and the magnetization of the Moon

Collisions of comets with planetary bodies are capable of impressing patterns of magnetization onto them that match those observed for the Moon and possibly for Mercury. The ambient solar wind magnetic field is briefly but strongly enhanced as the large partially ionized cometary atmosphere is compressed against the planetary surface. Just at the time of peak field enhancement, the solid part of the comet collides with the surface and the compressed fields are permanently imprinted by shock magnetization.     

Local time asymmetries of the SSC-associated hydromagnetic variations at the geosynchronous altitude

167 SSC events have been studied by using the data observed at the multiple-satellites at the geosynchronous altitude. The strong local time asymmetry of the SSC amplitude which was found by Kokubun (1983) has been confirmed. The pronounced local time asymmetry has also been found with the direction of the initial movement of Psc magnetic pulsations. Those local time effects are interpreted by the intensification of the magnetopause surface current during a SSC event, and by the distance between the geosynchronous satellite and the surface current. It has also been clarified that the SSC signal propagates with a speed of 400–700 km s^?1 across the field lines in the magnetosphere as suggested by Wilken et al. (1982).     

On the capture of the Moon

This paper studies the possibility of lunar capture depending on variations of the solar mass under certain well specified conditions and assumptions regarding the behaviour of the three-body dynamical system formed by the Sun, Earth and Moon. It is found that a large amount of decrease in the solar mass (approximately 37%) would be required to allow capture if the model of the planar restricted problem of three bodies is assumed, if the masses of the Earth and Moon did not change and if the angular momentum of the Sun-Earth system did not change. Such large mass-changes of the Sun can not be associated with radiation mass losses only with catastrophic events, such as stellar close approaches.     

The effect of the radiation pressure on the orbital evolution of geosynchronous objects

The effect of the radiation pressure and Poynting-Robertson effect on the evolution of the orbits of geosynchronous satellites is studied, depending on their area to mass ratio. The qualitative changes of the orbital evolution caused by these disturbances are considered. The reflection coefficient of the satellite’s surface was assumed to be 1.44. In the vicinity of the stable point with the longitude of 75° the exit from the libration resonance mode was registered when the area to mass ratio value changed from 5.9 to 6.0 m²/kg; in the vicinity of the unstable point at 345° with the area to mass ratio of 1.4 it occurred at 1.5 m²/kg. Re-entry to Earth occurs at values of the area to mass ratio above 32.2 m²/kg, and hyperbolic exit from the low-Earth orbit occurs at values of the area to mass ratio over 5267 m²/kg. At high values of the area to mass ratio, slopes of initially equatorial orbits can reach 49°. It is shown that due to the Poynting-Robertson effect the secular decrease in the semimajor axis of orbit in libration resonance region is 3–4 orders of magnitude less than outside of it.