A magnetic dynamo in the moon?

The existence of fossil lunar magnetism has caused speculation that the Moon had, at one time, an internally produced dynamo magnetic field. Quantitative analysis of this idea, constrained by the largest iron lunar core compatible with observations, implies that the Moon would have had to rotate faster than its breakup angular velocity in order to support a dynamo magnetic field.A paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

The physical librations of the moon,including higher harmonic effects

The equations of the physical libration of the Moon are developed using a representation of the Earth-Moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. TheImproved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10 six-yearly (argument), 1.2 three-yearly, 0.5 annual, and 0.1 monthly; on pole direction they are on the order of 0.5 six-yearly and 1.0 monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.Paper dedicated to Prof. Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

Photoelectrons and solar wind/lunar limb interaction

It is suggested that boundary conditions for solar wind/lunar limb interactions are active. The whole-Moon limb does not evoke a shock cone because warm (13 eV/electron) solar wind electrons are replaced by cool (2 eV/electron) photoelectrons that are ejected from the generally smooth areas of the lunar terminator illuminated at glazing angles by the Sun. A localized volume of low thermal pressure is created in the solar wind by these cool photoelectrons. The solar wind expands into this turbulence-suppressive volume without shock production. Conversely, directly illuminated highland areas exchange hot photoelectrons (> 20 eV/electron) for warm solar wind electrons. The hot electrons generate a localized pressure increase (p) in the adjacent solar wind flow which evokes a shock streamer in the solar wind. Shock streamers are identifiable by a coincident increase in the magnitude (B p) of the solar wind magnetic field immediately external to the lunar wake. Shock occurrence is controlled by lunar topography, solar activity in the hard ultraviolet (> 20 eV), solar wind electron density and thermal velocity, and the intensity of the solar wind magnetic field.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.     

Problems associated with estimating the relative impact rates on mars and the moon

The lunar cratering rate is known reasonably well from comparison of observed crater frequencies with radiometric ages. Attempts to obtain a cratering rate for Mars have usually been based on calculation of the relative flux of asteroidal and cometary bodies on Mars and the Moon.The asteroidal flux on Mars cannot be obtained in a simple way from the observed number of Mars-crossing asteroids, i.e. those asteroids with perihelia within the orbit of Mars. Calculations of the secular perturbations of these asteroids by several authors, particularly williams, has shown that most of these bodies rarely come near even to Mars' aphelion when they are in the vicinity of the ecliptic plane, and their contribution to the Martian meteoroid flux is much smaller than has been commonly stated. Ring asteroids in the vicinity of the secular resonances discovered by Williams, high velocity fragments of asteroids on the inner edge of the asteroid belt, and possibly objects obtained from the 2:1 Kirkwood gap by a process described by Zimmerman and Wetherill are probably of greater importance in the 10³-10⁶ g meteoroid size range but are much less important in the production of large craters. Calculations of the Martian asteroidal and cometary impact rate are made, but the present unavoidable uncertainties in the results of these calculations result in their being of little value in establishing a Martian chronology. Suggestions for improving this situation are discussed.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

United States lunar mapping — a basis for and result of project apollo

This paper includes 3 related presentations on United State lunar mapping made to the International symposium A Hundred Years of Lunar Mapping at Athens, Greece in May 1978. It reviews Project Apollo's role as both stimulas to and beneficiary of lunar mapping. Lunar cartographic technology and products employed and produced by the U.S. Defense Mapping Agency and its predecessor organizations, are discussed.Presented at the IAU-COSPAR Julius Schmidt Symposium on 100 Years of Lunar Mapping held at Lagonissi, Greece, 25–27 May, 1978.     

Periodic orbits of stars in axisymmetrical stellar systems

Periodic orbits of stars in axisymmetrical nearly spherical stellar systems have been investigated. Generating orbits have been found among periodic ones relating to the spherically-symmetrical field. The linear approximation appears to be insufficient for constructing periodic trajectories. Possible variants of the generating periodic solutions have been found, which give rise to disturbed periodic orbits in the second approximation.

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Пульсар в краБе: замагниченные трещины в коре как ключ к механизмам истечения вещества, радио- и высокочастотного излучений

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Horizontal-branch star models

Evolutionary tracks of 0.9M , 0.7M and 0.6M models for Population II stars have been computed in the post-red giant phase. The stars are initially composed of a helium core containing a mass fraction equal to 0.9 and of a hydrogen-rich envelope. They represent hypothetical remnants of stars after substantial mass loss in previous evolutionary phases or/and at the helium flash.u 0,9M , 0,7M 0,6M . , 90% , . , .Riassunto È stata calcolata per modelli di stelle di 0,9M , 0,7M e 0,6M di Popolazione II l'evoluzione successiva allo stadio di gigante rossa. Inizialmente i modelli constano di un nucleo di elio contenente il 90% della massa totale e di un inviluppo idrogenico. Essi possono interpretarsi come i resti di stelle che abbiano perso una frazione di massa considerevole in fasi evolutive precedenti, o all'innesco violento dell'elio al centro.     

Electrical conductivity of lunar surface rocks and chondritic meteorites

The electrical conductivities of several samples from returned Apollo 11 and 12 lunar rocks and from chondritic meteorites were measured from 300 to 1100K. Collectively the lunar samples represent all three of the major NASA classifications of lunar surface rocks. Of general interest is the observation that the conductivities of the lunar samples are much larger than the values which have previously been used in theoretical discussions of lunar phenomena. It is also found that the conductivity at 300K, (300), is extremely sensitive to the thermal history of the sample for both lunar and meteoritic material. Magnetic measurements are presented to help characterize the changes which occur upon heating.Principal Investigator - Apollo Lunar Science Program, Geophysics Research Laboratory, University of Tokyo, Japan.     

Containment of an adiabatic plasma on magnetic lines of force by a self-generated electrostatic field

One component of a three-fluid adiabatic plasma is under certain conditions contained in a restricted region of space by a large-scale electrostatic field generated within the plasma. The containment is discussed here for plasma consisting of ions and two populations of electrons characterized by different pitch angle distribution functions.The bouncing motion of electrons along open fieldlines between a magnetic mirror and an electrostatic mirror produces a velocity distribution function similar to that generated by bouncing particles on closed fieldlines.     

Some characteristic magnetic properties of lunar materials

One of the typical magnetic characteristics of lunar materials is the composition of their ferromagnetic constituent. Lunar breccias often contain kamacite (less than 7 weight per cent of Ni content) as well as almost pure metallic iron. Metallic ferromagnetics in most igneous rocks are almost pure iron, but the kamacite phase also has been found in some Apollo 15 igneous rocks. It seems likely therefore the metallic ferromagnetics in the lunar crust are more or less similar to those in chondrites.Another typical magnetic characteristic of lunar materials is the presence of a considerable amount of superparamagnetically fine particles of metallic iron. A higher relative content of such fine iron particles results in a higher value of the ratio of magnetic susceptibility (o) to saturation magnetization (I _s), a smaller ratio of the coercive force (H _c) to remanence coercive force (H _RC), and an extremely higher ratio of the viscous component (I _v) to the stable one (I _s) of the remanent magnetization.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Density within the moon and implications for lunar composition

Density models for the Moon, including the effects of temperature and pressure, can satisfy the mass and moment of inertia of the Moon and the presence of a low density crust indicated by the seismic refraction results only if the lunar mantle is chemically or mineralogically inhomogeneous. IfC/MR ² exceeds 0.400, the inferred density of the upper mantle must be greater than that of the lower mantle at similar conditions by at least 0.1 g cm^–3 for any of the temperature profiles proposed for the lunar interior. The average mantle density lies between 3.4 and 3.5 g cm^–3, though the density of the upper mantle may be greater. The suggested density inversion is gravitationally unstable, but the implied deviatoric stresses in the mantle need be no larger than those associated with lunar gravity anomalies. UsingC/MR ³=0.400 and the recent seismic evidence suggesting a thin, high density zone beneath the crust and a partially molten core, successful density models can be found for a range of temperature profiles. Temperature distributions as cool as several inferred from the lunar electrical conductivity profile would be excluded. The density and probable seismic velocity for the bulk of the mantle are consistent with a pyroxenite composition and a 100 MgO/(MgO+FeO) molecular ratio of less than 80.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Conservation laws and Liapounov stability of the free rotation of a rigid body

The paper derives the well known stabilities of free rotation of a rigid body about its principal axes of least and greatest moments of inertia directly from the constancy of the kinetic energy and of the square of the angular momentum. The resulting proof of Liapounov stability yields new quantitative measures of this stability. Involving only simple algebra, it depends on satisfying a weak sufficient condition that insures an unchanging sign of the main component of the angular velocity . The method cannot be used, however, to prove the well known instability of rotation about the intermediate axis.The quantitative results for the radii of the spheres in -space that occur in the Liapounov proof lead to a physical result that may be of interest. If the earth were truly a rigid body, rotating freely, the angular deviation of its instantaneous polar axis from the nearest principal axis could not increase from a given initial value by more than the factor 2.These same quantitative results for the radii of the Liapounov spheres in -space also lead to suflicient conditions for the rotational stability of almost spherical bodies of various shapes, prolate or oblate. They may be pertinent in designing spheres to be used in currently planned experiments to test general relativity by observing the rate of precession of a rotating sphere in orbit about the earth.The above results follow from restricted Liapounov stability alone. The last section contains the proof of general Liapounov stability.This paper was prepared under the sponsorship of the Electronics Research Center of the National Aeronautics and Space Administration through NASA Grant NGR 22-009-262.     

Les raies du triplet de l'helium de la Nova Delphini 1967

The aim of this paper has been to study the neutral helium triplet emission lines identified in the spectrum of the envelope of Nova Delphini. By comparing the observed flux of the neutral helium lines with that calculated theoretically by Robbins, we find that the optical thickness in the center of the line 3889 is of the order of 21.50 for summer 1969. The optical thickness obtained by this method is here denoted _tran(3889).On the other hand, we obtain the number of neutral helium atoms in the 2³S state [N(2³S)] by considering the equilibrium between the mechanisms that populate and depopulate this state. We then find that the depopulation by photoionization due to the radiation of Ly (Hi), transitions to the 2¹S, 2¹p and 2³p states by electron collision, photoionization due to the continuum radiation of the central star, are 82.70%, 13.20%, 2.40%, 0.90% and 0.80% respectively. We find that the mechanism of the photoionization by Ly is the dominant mechanism of depopulation of 2³S state. We calculated ( 3889) of the order of 82.37, fromN(2³S), obtained in the preceding paragraph. The optical thickness obtained by this method is here denoted _bal(3889).The difference between _tran(3889) and _bal(3889) is very large and it cannot be attributed to calculation errors. We have considered all the mechanisms that can depopulate the 2³S state, so we then conclude that the difference between _tran(3889) and _bal(3889) is due to the heterogeneity of the envelope of the Nova, already found by us in our previous study of the profiles of the permitted and forbidden lines. Finally, we find from this study a filling factor of the order of 0.30.     

On quasi-integrable problems. The example of the artificial satellites perturbed by the Earth's zonal harmonics

With the Hamiltonian parameters developed for the two-fixed-centers problem a simple and very accurate expression of the quasi-integral can be given for the motion of artificial satellites perturbed by the Earth's zonal harmonics. This motion can be considered as integrable.A theoretical analysis shows that Hénon's semi-ergodic regions or chaotic regions are extremely small in this problem, and almost all orbits are of the regular or quasi-periodic type. Furthermore, the relative difference between the true motion and the corresponding integrable motion remains forever less than 10^–14 for all regular orbits even in the vicinity of critical inclinations.For chaotic orbits this very small difference remains verified at least for centuries, nevertheless there are some exceptional orbits that finally diverge from the integrable model.     

Some effects of elasticity on lunar rotation

A general Hamiltonian for a rotating Moon in the field of the Earth is expanded in terms of parameters orienting the spin angular momentum relative to the pricipal axes of the Moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love numberk ₂. The principal periodic terms in the longitude of a point on the Moon due to variations of the tide caused by the Earth are shown to have amplitudes between 3.9 × 10^–3 and 1.6 × 10^–2 with a period of an anomalistic month, 3.0 × 10^–4 and 1.2 × 10^–3 with a period of one-half an anomalistic month and 2.4 × 10^–4 and 9.6 × 10^–4 with a period of one-half of a nodical month. The extremes in the amplitudes correspond to rigidities of 8 × 10¹¹ cgs and 2 × 10¹¹ cgs, respectively, the former rigidity being comparable to that of the Earth. Only the largest amplitude given above is comparable to that detectable by the projected precision of the laser ranging to the lunar retrorereflectors, and this amplitude corresponds to an improbably low rigidity for the Moon. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given, where it is shown that elasticity can alter the period of the free wobble of 75.3 yr by only 3 × 10^–4 to 10^–3 of this period. Also, the effect of elasticity on the period of free libration is completely negligible by many orders of magnitude. If the Moon's rigidity is close to that of the Earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the Moon can be determined from variations in the rotation.Currently on leave from the Dept. of Physics, University of California, Santa, Barbara, California.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

A lunar signature in the geomagnetic ap-index

A study has been performed in an effort to detect a lunar signature in geomagnetic data. Ap-indices available for the period 1932–1972 have been used for this purpose. The data have been divided into some 500 lunar months which were superimposed in synchronism with the phase of the Moon. At or shortly after full Moon a peak appears which exceeds the average value by about 3 standard deviations. Possible explanations for the generation of geomagnetic disturbances by the Moon are given.Paper presented at the Conference on Interactions of the Interplanetary Plasma with the Modern and Ancient Moon, sponsored by the Lunar Science Institute, Houston, Texas and held at the Lake Geneva Campus of George Williams College, Wisconsin, between September 30 and October 4, 1974.     

The solar O i λ 7773 triplet

The reduction of observations of the O i 7773 triplet obtained at high spatial resolution (0.5) at two disk positions is described. Two sets of triplet profile data are presented at each disk position. One set represents data taken from 0.5 regions centered on the brightest granules, while the other set represents data taken from 0.5 regions centered on the cooler infalling intergranular material.     

Evolution and nature of north-south asymmetry in the heliospheric current sheet

The nature and evolution of north-south asymmetry in the heliospheric current sheet (HCS) has been investigated using solar and interplanetary magnetic field (IMF) observations for the past few solar cycles. The mean heliographic latitude of the HCS (averaged over the solar longitude) a ₀ is found to be non-zero during many solar rotations indicating that the large-scale solar magnetic field is more ordered in a system where the origin is shifted away from the centre of the Sun. We have shown that the asymmetry in HCS manifests in different forms depending on the transition heliographic latitude of the reversal of dominant polarity of the IMF ( _T) and the difference in the maximum latitudinal extension of the HCS in the two solar hemispheres (). The classification of the observed asymmetry during 1971–1985 and its effect on IMF observations near Earth has been studied. We have also inferred the sign of _T during 1947–1971 using inferred IMF polarity data. The observed sign reversals of _T suggest the importance of periodicities less than the solar cycle period to be associated with the evolution of asymmetry in HCS. Asymmetry in sunspot activity about the solar equator does not seem to relate consistently well with the asymmetry in HCS about the heliographic equator.