The in-plane motion of a Geosynchronous satellite under the gravitational attraction of the sun,the moon and the oblate earth

The in-plane motion of a Geosynchronous satellite under the gravitational effects of the sun, the moon and the oblate earth has been studied. The radial deviation (Δr) and the tangential deviation (r _cΔθ) have been determined. Herer _c represents the synchronous altitude. It has been seen that the sum of the oscillatory terms in Δr for different inclinations is a small finite quantity whereas the sum of the oscillatory terms inr _cΔθ for different inclinations is quite large due to the presence of the low-frequency terms in the denominator     

On the accretion of the earth and moon

The bodies which produced the premare impact craters on the moon contained a much higher proportion of smaller bodies in the earliest observable times than subsequently. This suggests that the earth and moon accreted from small objects with only an occasional large planetoid.If the earliest observable lunar craters are 4.3 × 10⁹ yr old, the half-life of the primitive planetesimals which produced the giant lunar craters larger than 161 km in diameter, was 143 × 10⁶ yr, while the half-life of the primitive planetesimals which produced lunar craters larger than 1 km in diameter was only 88 × 10⁶ yr. The half-life of the bodies which produced 1 km craters was still shorter, about 75 × 10⁶ yr.     

On the apparent secular accelerations of the Moon and the Sun

The discussion of tidal friction in the Earth-Moon system given in successive editions ofThe Earth by Jeffreys is shown to contain a serious dynamical error. When the treatment is corrected, it shows that the moment of inertia of the Earth must be changing. The apparent secular accelerations of the Moon and Sun require a diminishing moment of inertia, and the rate is in agreement with the phase-change hypothesis for the nature of the core.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.     

Calculation of meteoroid impacts on moon and earth

Concise derivations are given for the expected flux of meteoroids to the surfaces of the earth and the moon. Contrary to other published results, we find an accretion rate which is lower for the near side of the moon than for the far side and which is lower for the moon than for the earth, for all earth-moon distances.     

Brightness temperatures of the quiet sun and new moon at the 6 mm wavelength

Absolute brightness temperatures and brightness temperature ratios of a quiet region near the center of the solar disk and the central region of the new moon were measured simultaneously at the 6 mm wavelength. The measured quiet sun/new moon brightness temperature ratios and reported central brightness temperatures of the new moon confirm the measured brightness temperature of the quiet sun at the 6 mm wavelength.Reported central brightness temperatures of the new moon are tabulated and graphed as a function of frequency and wavelength. The equation of a linear regression line for the reported measurements is given for estimating the brightness temperature of the new moon at any millimeter wavelength. Estimated brightness temperatures of the new moon and measured quiet sun/new moon ratios are used to estimate solar brightness temperatures at several millimeter wavelengths. The solar brightness temperatures, the regression line, and the Van de Hulst theoretical model are presented graphically as a function of frequency and wavelength. The regression line equation is given for estimating solar brightness temperatures at any wavelength in the 6 to 1 mm wavelength interval and is solved for the wavelength of the measured ratios.Reported solar brightness temperatures in the millimeter wavelength region are tabulated. The measured temperatures in the 6 to 1 mm wavelength interval and a linear regression line are presented graphically as a function of frequency and wavelength. The regression line equation is given and solved for the solar brightness temperatures at the 6 mm wavelength.This work supported by the U.S. Air Force under Contract No. F04701-69-C-0066.     

A comparison of the magnetic field anomalies for the moon and earth

A comparative analysis of the anomalous magnetic field of the Moon, information about which was obtained by the Apollo 15 subsatellite, and the anomalous magnetic field of the Earth, involving data provided from surveys at various altitudes (up to 500 km) is given. As a result of spectral analysis of these fields it is shown that the main difference of the spectra is in the lower intensity of long period lunar anomalies and the increased rate of their damping with height, which is probably connected with the absence of any kind of magnetization by induction.     

Relation between the apparent magnitude and the parallax for Hyades stars

In this paper, relation was established for Hyades stars between their apparent magnitudes and parallaxes. The precision criteria of this relation are very satisfactory. The importance of this relation was illustrated through its usages as: (1) A criterion for membership of the cluster, (2) a generating function for evaluating some parameters of the cluster.     

Stress differences in the moon as an evidence for a cold moon

Assuming that the lateral variations of density in the lunar crust, the crustal density anomalies, are responsible for the lateral undulations of the lunar gravitational potential, we compute these anomalies for four different lunar models, which include an entirely solid Moon and three different solid lunar models with partially molten layers located within 600 km depth. The stress differences created by the density anomalies are determined for these models. It is found that, since the formation of the mascons, the entirely solid lunar model should have supported stress differences of the order of 70 bars while in the case of the other models, the solid layer overlying the partially molten one should have supported stress differences of more than 100 bars. The high stress differences associated with the partially molten models lead us to conclude that these models are not proper ones, and thus the Moon has always been solid since the formation of the mascons. Lunar Science Institute Contribution No. 97. The research in this paper was done while the author was a Visiting Scientist at the Lunar Science Institute, which is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Variations of the magnetic fields of the sun and the earth in 7–50 day periods

The time variations of solar and terrestrial magnetic fields (background magnetic field, power of the active regions, AE and aa-indices) have been studied. The analysis of these data shows that multiplets of 27, 13.5, 9 and 7 day periods exist in the solar data as in the terrestrial data. The solar multiplets 13.5 and 9 days appear predominantly close to the equatorial zone of the Sun and can plausibly be explained by the presence of active longitudes. The similarity of the variations in period in solar and geophysical data provides evidence that the magnetosphere of the Earth is actually a continuation of the heliosphere. The variations of the terrestrial magnetic field are mainly determined by the solar background magnetic fields in middle heliographic latitudes.     

Analysis of resonant curves and phase portrait in the earth–moon system by using its unperturbed solution and earth’s equatorial ellipticity

In this research article, we have investigated resonant curves due to the rate of change of earth’s equatorial ellipticity parameter $\left(\dot{\gamma }\right)$, steady-state value of the angular velocity of the moon $\left({\dot{\theta }}_{mo}\right)$, and angular velocity of barycenter $\left(\dot{{\alpha }_0}\right)$ in the Earth-Moon system. Equations of motion of the moon are determined in a spherical coordinate system with the help of the gravitational potential of the earth. By using the unperturbed solution, equations of motion of the moon reduced into the second-order differential equation. From the solution it is observed that resonance occurs due to the frequencies $\dot{\gamma }$, ${\dot{\theta }}_{m0}$, and $\dot{{\alpha }_0}$ at the resonant points ${\dot{\theta }}_{m0}=2\dot{\gamma }$, $3{\dot{\theta }}_{m0}=2\dot{\gamma }$, ${\dot{\theta }}_{m0}=\dot{\gamma }$, ${\dot{\theta }}_{m0}={\dot{\alpha }}_0$. Finally, we have analyzed the phase portrait and phase space by method of Poincaré section when the system is free from forces.     

Possibility of a layered moon

Recent lunar data can be interpreted as indicating the Moon has a hard “crust” a few km thick, an “asthenosphere” about a hundred km thick, and a high viscosity “lower mantle.”     

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.     

Farside explorer: unique science from a mission to the farside of the moon

Farside Explorer is a proposed Cosmic Vision medium-size mission to the farside of the Moon consisting of two landers and an instrumented relay satellite. The farside of the Moon is a unique scientific platform in that it is shielded from terrestrial radio-frequency interference, it recorded the primary differentiation and evolution of the Moon, it can be continuously monitored from the Earth–Moon L2 Lagrange point, and there is a complete lack of reflected solar illumination from the Earth. Farside Explorer will exploit these properties and make the first radio-astronomy measurements from the most radio-quiet region of near-Earth space, determine the internal structure and thermal evolution of the Moon, from crust to core, and quantify impact hazards in near-Earth space by the measurement of flashes generated by impact events. The Farside Explorer flight system includes two identical solar-powered landers and a science/telecommunications relay satellite to be placed in a halo orbit about the Earth–Moon L2 Lagrange point. One lander would explore the largest and oldest recognized impact basin in the Solar System— the South Pole–Aitken basin—and the other would investigate the primordial highlands crust. Radio astronomy, geophysical, and geochemical instruments would be deployed on the surface, and the relay satellite would continuously monitor the surface for impact events.     

Magnetism of the moon

The Malkus theory of a precessionally driven magnetoturbulence in a liquid core is applied to the Moon. It is shown that a lunar magnetic field requires the presence of a non-metallic core at at least 2500K or of an iron core at at least 2000K. Within the limits of our present knowledge these requirements may have been satisfied in the past. A new mechanism is proposed which is based on tidal effects in the outer solid and liquid shells whose existence is suggested by measurements of lunar radioactivity. This mechanism could account for the generation of local rather than poloidal fields at low latitudes in agreement with observation.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Viscosity of the moon

Using data from the present gravitational potential and surface topography of the Moon, it is possible to determine a lower limit of about 5 b.y. for the relaxation time of the mascons. Assuming that the Moon has behaved as a Maxwellian viscoelastic body since the formation of the mascons, this relaxation time indicates a value of about 10²⁷ poise for the viscosity of the lunar interior. Such a high viscosity implies that there has been no convection current inside the upper 800 km of the Moon since the formation of the mascons. Lunar Science Institute Contribution No. 99. The research in this paper was done while the author was a Visiting Scientist at the Lunar Science Institute, which is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Some consequences of a steady thermal moon

The Moon is represented as an inhomogeneous spherical body in a steady thermal state. Radioactive heat sources are supposed distributed in a manner which is consistent both with the total measured heat flux near the surface and with the broad seismic evidence. Surface concentrations of uranium and thorium are those suggested by the study of Apollo 11 samples. The resultant internal temperature profile allows the details of Sonett's electrical conductivity profile to be understood if it is accepted that the Moon was not cold 4.5 × 10⁹ yr ago. It would appear further that at least one of the maria was formed by the impact of planetesimals.