Tests of random density models of terrestrial planets

Random density models are analyzed to determine the low degree harmonics of the gravity field of a planet, and therefrom two properties: an axiality P_l , the percent of the degree variance in the zonal term referred to an axis through the maximum for degree l; and an angularity E_(ln) , the angle between the maxima for two degrees l, n. The random density distributions give solutions reasonably consistent with the axialities and angularities for the low degrees, l < 5, of Earth, Venus, and Moon, but not for Mars, which has improbably large axialities and small angularities. Hence the random density model is an unreliable predictor for the non‐hydrostatic second‐degree gravity of Mars, and thus for the moment‐of‐inertia, which is more plausibly close to 0.365MR^2

Studies of oceanic tectonics based on GEOS-3 satellite altimetry

Using statistical analysis, geoidal admittance (the relationship between the ocean geoid and seafloor topography) obtained from GEOS-3 altimetry was compared to various model admittances. Analysis of several altimetry tracks in the Pacific Ocean demonstrated a low coherence between altimetry and seafloor topography except where the track crosses active or recent tectonic features. However, global statistical studies using the much larger data base of all available gravimetry showed a positive correlation of oceanic gravity with topography. The oceanic lithosphere was modeled by simultaneously inverting surface wave dispersion, topography, and gravity data. Efforts to incorporate geoid data into the inversion showed that the base of the subchannel can be better resolved with geoid rather than gravity data. Thermomechanical models of seafloor spreading taking into account differing plate velocities, heat source distributions, and rock rheologies were discussed

Extrasolar planetary dynamics with a generalized planar Laplace-Lagrange secular theory

The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the traditional Laplace-Lagrange (LL) secular theory in analyses of the motion. We analytically generalize this theory to fourth-order in the eccentricities, compare the result with the second-order theory and octupole-level theory, and apply these theories to the likely secularly-dominated HD 12661, HD 168443, HD 38529 and Ups And multi-planet systems. The fourth-order scheme yields a multiply-branched criterion for maintaining apsidal libration, and implies that the apsidal rate of a small body is a function of its initial eccentricity, dependencies which are absent from the traditional theory. Numerical results indicate that the primary difference the second and fourth-order theories reveal is an alteration in secular periodicities, and to a smaller extent amplitudes of the planetary eccentricity variation. Comparison with numerical integrations indicates that the improvement afforded by the fourth-order theory over the second-order theory sometimes dwarfs the improvement needed to reproduce the actual dynamical evolution. We conclude that LL secular theory, to any order, generally represents a poor barometer for predicting secular dynamics in extrasolar planetary systems, but does embody a useful tool for extracting an accurate long-term dynamical description of systems with small bodies and/or near-circular orbits.Comment: 14 pages, 12 figures, 1 table, accepted for publication in Ap

A critical approach to the concept of a polar, low-altitude LARES satellite

According to very recent developments of the LARES mission, which would be devoted to the measurement of the general relativistic Lense--Thirring effect in the gravitational field of the Earth with Satellite Laser Ranging, it seems that the LARES satellite might be finally launched in a polar, low--altitude orbit by means of a relatively low--cost rocket. The observable would be the node only. In this letter we critically analyze this scenario.Comment: LaTex2e, 11 pages, 4 figures, 1 table. Accepted for publication in Classical and Quantum Gravit

Perspectives in measuring the PPN parameters beta and gamma in the Earth's gravitational fields with the CHAMP/GRACE models

The current bounds on the PPN parameters gamma and beta are of the order of 10^-4-10^-5. Various missions aimed at improving such limits by several orders of magnitude have more or less recently been proposed like LATOR, ASTROD, BepiColombo and GAIA. They involve the use of various spacecraft, to be launched along interplanetary trajectories, for measuring the effects of the solar gravity on the propagation of electromagnetic waves. In this paper we investigate what is needed to measure the combination nu=(2+2gamma-beta)/3 of the post-Newtonian gravitoelectric Einstein perigee precession of a test particle to an accuracy of about 10^-5 with a pair of drag-free spacecraft in the Earth's gravitational field. It turns out that the latest gravity models from the dedicated CHAMP and GRACE missions would allow to reduce the systematic error of gravitational origin just to this demanding level of accuracy. In regard to the non-gravitational errors, the spectral noise density of the drag-free sensors required to reach such level of accuracy would amounts to 10^-8-10^-9 cm s^-2 Hz^-1/2 over very low frequencies. Although not yet obtainable with the present technologies, such level of compensation is much less demanding than those required for, e.g., LISA. As a by-product, an independent measurement of the post-Newtonian gravitomagnetic Lense-Thirring effect with a 0.9% accuracy would be possible as well. The forthcoming Earth gravity models from CHAMP and GRACE will further reduce the systematic gravitational errors in both of such tests.Comment: LaTex2e, 14 pages, 3 tables, no figures, 75 references. To appear in Int. J. Mod. Phys.

Microscopic dynamics underlying the anomalous diffusion

The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200

Interior Models of Uranus and Neptune

'Empirical' models (pressure vs. density) of Uranus and Neptune interiors constrained by the gravitational coefficients J_2, J_4, the planetary radii and masses, and Voyager solid-body rotation periods are presented. The empirical pressure-density profiles are then interpreted in terms of physical equations of state of hydrogen, helium, ice (H_2O), and rock (SiO_2) to test the physical plausibility of the models. The compositions of Uranus and Neptune are found to be similar with somewhat different distributions of the high-Z material. The big difference between the two planets is that Neptune requires a non-solar envelope while Uranus is best matched with a solar composition envelope. Our analysis suggests that the heavier elements in both Uranus' and Neptune's interior might increase gradually towards the planetary centers. Indeed it is possible to fit the gravitational moments without sharp compositional transitions.Comment: 16 pages, accepted for publication in Ap

On a new observable for measuring the Lense-Thirring effect with Satellite Laser Ranging

In this paper we present a rather extensive error budget for the difference of the perigees of a pair of supplementary SLR satellites aimed to the detection of the Lense-Thirring effect.Comment: LaTex2e, 14 pages, 1 table, no figures. Some changes and additions to the abstract, Introduction and Conclusions. References updated, typos corrected. Equation corrected. To appear in General Relativity and Gravitatio

Report of the panel on geopotential fields: Gravity field, section 8

The objective of the Geopotential Panel was to develop a program of data acquisition and model development for the Earth's gravity and magnetic fields that meet the basic science requirements of the solid Earth and ocean studies. Presented here are the requirements for gravity information and models through the end of the century, the present status of our knowledge, data acquisition techniques, and an outline of a program to meet the requirements

Uranus and Neptune: Shape and Rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several hundred meters per second. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets' radio signals and of fits to the planets' magnetic fields; 17.24h and 16.11h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet's deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ~16.58h for Uranus and ~17.46h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.Comment: Accepted for publication in Icarus, 20 pages, 4 tables, 9 figure