Tidal effects in the earth–moon system and the earth's rotation

Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived. Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial logarithmic decrement ν of the Chandler wobble are evaluated:  mas, . In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Icy craters on the Galilean satellites?

A model which possibly accounts for the unusual radar scattering behavior observed for Europa, Ganymede, and Callisto postulates a thick surface layer of ice saturated with nearly hemispherical craters. In the development of this model it is noted that a single reflection at normal incidence reverses the rotational sense of circularly polarized incident radiation, in conflict with the radar observations which show an echo predominantly not reversed. Furthermore, an ensemble of backscattering events, each the result of a large number of successive dielectric reflections, tends to produce a weak and unpolarized echo. However, two coupled reflections can produce the observed backscattering behavior, provided the angles of incidence lie between the Brewster angle and its complement. The effect is maximum when the angles equal 45°, and, for water ice, yields a ratio of 1.9 for components of the echo received in rotational senses the same as, and opposite to, the sense transmitted. Randomly oriented reflecting facets, either of ice on the surface or of rocks in the interior, cannot yield the observed behavior since too few of the total possible backscattering configurations meet the above requirement. Hemispherical surface craters, on the other hand, favor 45° dual reflection. A model consisting of such craters in ice is investigated and found capable of explaining the observed results, not only in respect to polarization, but in respect to albedo and angular scattering law as well.     

Secondary craters and ejecta across the solar system: Populations and effects on impact-crater–based chronologies

We review the secondary-crater research over the past decade, and provide new analyses and simulations that are the first to model an accumulation of a combined primary-plus-secondary crater population as discrete cratering events. We develop the secondary populations by using scaling laws to generate ejecta fragments, integrating the trajectories of individual ejecta fragments, noting the location and velocity at impact, and using scaling laws to estimate secondary-crater diameters given the impact conditions. We also explore the relationship between the impactor size–frequency distribution (SFD) and the resulting secondary-crater SFD. Our results from these analyses indicate that the “secondary effect” varies from surface to surface and that no single conclusion applies across the solar system nor at any given moment in time—rather, there is a spectrum of outcomes both spatially and temporally, dependent upon target parameters and the impacting population. Surface gravity and escape speed define the spatial distribution of secondaries. A shallow-sloped impactor SFD will cause proportionally more secondaries than a steeper-sloped SFD. Accounting for the driving factors that define the magnitude and spatial distribution of secondaries is essential to determine the relative population of secondary craters, and their effect on derived surface ages.     

Possible Effect of the Earth’s Inertial Induction on the Orbital Decay of LAGEOS

The theory of velocity dependent inertial induction, based upon extended Mach’s principle, has been able to generate many interesting results related to celestial mechanics and cosmological problems. Because of the extremely minute magnitude of the effect its presence can be detected through the motion of accurately observed bodies like Earth satellites. LAGEOS I and II are medium altitude satellites with nearly circular orbits. The motions of these satellites are accurately recorded and the past data of a few decades help to test many theories including the general theory of relativity. Therefore, it is hoped that the effect of the Earth’s inertial induction can have any detectable effect on the motion of these satellites. It is established that the semi-major axis of LAGEOS I is decreasing at the rate of 1.3 mm/d. As the atmospheric drag is negligible at that altitude, a proper explanation of the secular change has been wanting, and, therefore, this paper examines the effect of the Earth’s inertial induction effect on LAGEOS I. Past researches have established that Yarkovsky thermal drag, charged and neutral particle drag might be the possible mechanisms for this orbital decay. Inertial induction is found to generate a perturbing force that results in 0.33 mm/d decay of the semi major axis. Some other changes are also predicted and the phenomenon also helps to explain the observed changes in the orbits of a few other satellites. The results indicate the feasibility of the theory of inertial induction i.e. the dynamic gravitation phenomenon of the Earth on its satellites as a possible partial cause for orbital decay.     

When and where were the satellites of uranus formed?

Uranus exhibits an unusually large obliquity compared to other planets of the solar system; its equator is inclined by 98° to the plane of its orbit. However its five satellites are remarkably regular, with eccentricities and inclinations very nearly zero, but of course with orbit planes that are tilted by ～98° to the plane of the ecliptic. This circumstance is used here to relate the formation of satellites to planet formation. Six different cases are discussed, of which two can be ruled out and two others are highly improbable. In the analysis, use is made of the fact that satellites in near-equatorial orbits could not follow a rapid (“non-adiabatic”) change of the planet's obliquity. We assume, also, that the observed obliquity is the result of the last stages of planet accumulation. We can therefore exclude contemporaneous formation of planet and satellites, and conclude instead that the satellites were formed or acquired after the planet's axis had been tilted. A plausible scenario involves the tidal capture of a body having 5% to 10% of the planet's mass—sufficient to account for the tilt—followed by its accretion. However, tidal forces break up the body into chunks, slow the accretion, and allow ～1% of the chunks to form the satellites through interaction with a temporary dense atmosphere. The same reasoning may apply also for Saturn and Jupiter. It should be noted that the synchronous orbit it well within the Roche limit for all three planets.     

Poynting–Robertson (P–R) drag and oblateness effects on motion around the triangular equilibrium points in the photogravitational R3BP

This paper investigates the motion of a test particle around the triangular equilibrium points under the effects of radiation pressure of the second primary and its Poynting–Robertson (P–R) effect when the first primary is an oblate spheroid. It is seen that triangular points are influenced by the presence of these parameters: radiation pressure from the secondary and the incidental P–R effect and the oblateness of the first primary. The linear stability of the problem is studied and applied to the binary system RXJ 0450.1-5856, the triangular points are unstable due to positive roots in the Lyapunov sense when P–R effect is considered as against their conditional stability in the absence of P–R drag effect.     

On the thermal history of Saturn’s satellites Titan and Enceladus

The thermal histories of two geologically active satellites of Saturn—Titan and Enceladus—are discussed. During the Cassini mission, it was found that there are both nitrogen-containing compounds—NH₃ and N₂-and CO₂ and CH₄ in the water plumes of Enceladus; at that, ammonia is the prevailing form. This may testify that during evolution, the material of the satellite was warmed up to T ∼ 500–600 K, when NH₃ (the form of nitrogen capable of being accreted) could only be partly converted into N₂. Contrary to Enceladus, the temperature inside Titan probably reached values higher than 800 K or even higher than 1000 K, since the process of the chemical dissociation of ammonia was completely finished on this satellite and its atmosphere contains only molecular nitrogen. While the internal heating of Titan up to high temperatures can be explained by its large mass, the heating source for Enceladus’ interior is far from evident. Such traditional heating sources as the energy of gravitational differentiation and the radiogenic heating due to shortliving ²⁶Al and ⁶⁰Fe could not be effective. The first one is because of the small size of Enceladus (RE ≈ 250 km), and the inefficiency of the second one is caused by the fact that the satellite was formed not earlier than 8–10 Myr after the formation of calcium and aluminum-enriched inclusions in carbonaceous chondrites (CAI), i.e., after ²⁶Al had completely decayed. In the present paper, we propose other heating mechanisms-the heat of long-living radioactive elements and tidal heat, which could provide the observed chemical composition of the water plumes of Enceladus rather than only the differentiation of its protomatter into the ironstone core and the ice mantle.     

Finite size effects on the Poynting–Robertson effect: A fully general relativistic treatment

Even since the first discovery of Poynting and Robertson, the radiation source has been treated as merely a point. Even in a very few studies where the size of the source has been taken into account, the treatment of the problem remained largely non-relativistic. In the present work, we address the issue of the finite size effects on the Poynting–Robertson effect in a fully relativistic manner for the first time. As a result, the emergence and the characteristic of the critical point/suspension orbit can be studied in a systematic and detailed manner.     

Dynamics of two satellites in the 2/1 Mean–Motion resonance: application to the case of Enceladus and Dione

The dynamics of a pair of satellites similar to Enceladus–Dione is investigated with a two-degrees-of-freedom model written in the domain of the planar general three-body problem. Using surfaces of section and spectral analysis methods, we study the phase space of the system in terms of several parameters, including the most recent data. A detailed study of the main possible regimes of motion is presented, and in particular we show that, besides the two separated resonances, the phase space is replete of secondary resonances.     

GETEMME—a mission to explore the Martian satellites and the fundamentals of solar system physics

GETEMME (Gravity, Einstein??s Theory, and Exploration of the Martian Moons?? Environment), a mission which is being proposed in ESA??s Cosmic Vision program, shall be launched for Mars on a Soyuz Fregat in 2020. The spacecraft will initially rendezvous with Phobos and Deimos in order to carry out a comprehensive mapping and characterization of the two satellites and to deploy passive Laser retro-reflectors on their surfaces. In the second stage of the mission, the spacecraft will be transferred into a lower 1500-km Mars orbit, to carry out routine Laser range measurements to the reflectors on Phobos and Deimos. Also, asynchronous two-way Laser ranging measurements between the spacecraft and stations of the ILRS (International Laser Ranging Service) on Earth are foreseen. An onboard accelerometer will ensure a high accuracy for the spacecraft orbit determination. The inversion of all range and accelerometer data will allow us to determine or improve dramatically on a host of dynamic parameters of the Martian satellite system. From the complex motion and rotation of Phobos and Deimos we will obtain clues on internal structures and the origins of the satellites. Also, crucial data on the time-varying gravity field of Mars related to climate variation and internal structure will be obtained. Ranging measurements will also be essential to improve on several parameters in fundamental physics, such as the Post-Newtonian parameter ?? as well as time-rate changes of the gravitational constant and the Lense-Thirring effect. Measurements by GETEMME will firmly embed Mars and its satellites into the Solar System reference frame.     

Combined effects of perturbations, radiation and oblateness on the periodic orbits in the restricted three-body problem

This paper investigates the periodic orbits around the triangular equilibrium points for 0<μ<μ _c , where μ _c is the critical mass value, under the combined influence of small perturbations in the Coriolis and the centrifugal forces respectively, together with the effects of oblateness and radiation pressures of the primaries. It is found that the perturbing forces affect the period, orientation and the eccentricities of the long and short periodic orbits.     

Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system

In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration.     

The Q Values of the Galilean Satellites and their Tidal Contributions to the Deceleration of Jupiter''''s Rotation

The relationship between the k2/Q of the Galilean satellites and the k2J/QJ of Jupiter is derived from energy and momentum considerations. Calculations suggest that the Galilean satellites can be divided into two classes according to their Q values: Io and Ganymede have values between 10 and 50, while Europa and Callisto have values ranging from 200 to 700. The tidal contributions of the Galilean satellites to Jupiter's rotation are estimated. The main deceleration of Jupiter, which is about 99.04% of the total, comes from Io.     

Finite-β effects on the radiative thermal instability in magnetized plasmas

The radiative thermal instability is investigated taking into account finite-, or electromagnetic, effects. The two-fluid model for magnetized plasmas together with the Maxwell equations are used to derive a general dispersion relation valid for compressional perturbations with frequency below the electron-cyclotron frequency. The growth rates of the radiative thermal instabilities involving fast magnetosonic flute-like and low-frequency hydromagnetic perturbations are presented.     

The Non-Gravitational Perturbations impact on the BepiColombo Radio Science Experiment and the key rôle of the ISA accelerometer: direct solar radiation and albedo effects

The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key rôle of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10^?6 m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about $10^{-9}\,m/s^{2}/\sqrt{Hz}The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key r?le of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10⁻⁶ m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about in the frequency band of 3·10⁻⁵–10⁻¹ Hz, guarantees a very significant reduction of the non-gravitational accelerations impact on the space mission accuracy, especially of the dominant direct solar radiation pressure.     

Long-term predictive assessments of solar and geomagnetic activities made on the basis of the close similarity between the solar inertial motions in the intervals 1840–1905 and 1980–2045

The solar inertial motions (orbits) (SIMs) in the years 1840–1905 and 1980–2045 are of a disordered type and they are nearly identical. This fact was used for assessing predictive capabilities for the sizes of three future sunspot cycles and for the time variation of the geomagnetic aa-index up to 2045. The author found that the variations in sunspot numbers in the interval 1840–1867 and in the interval 1980–2007 are similar, especially after 1850 (1990). The differences may be ascribed to the lower quality of the sunspot data before 1850. A similarity between the variations in geomagnetic aa-index in the intervals 1844–1867 and 1984–2007 is also found. Moreover, the aa-index in these intervals have the same best fit lines (the polynomials of the fourth order) with close positions of the extrema. The extrema of the best fit line for the aa-index in the interval 1906–1928 which corresponds to the first half of the ordered, trefoil interval of the SIM have the opposite positions to them. The correlation coefficient between the aa-indices in the interval 1844–1866 and in the interval 1984–2006 is 0.61. In contrast, the correlation coefficient between the aa-indices in the interval 1844–1866 and in the interval 1906–1928 is ?0.43. Cautious predictions have been made: the author believes that the cycles 24–26 will be a repeat of cycles 11–13, i.e. they could have heights around 140 (100), 65 and 85, they will have lengths of 11.7, 10.7 and 12.1 years. The maxima of the cycles should occur in 2010, 2023 and 2033, the minima in 2007, 2018, 2029 and 2041. Up to 2045, the aa-index could repeat its values for the interval 1868–1905. The results indicate that solar and geomagnetic activities are non random processes. If these predictions may come true, then further evidence of the primary role of the SIM in solar variability is established.