Possible new properties of gravity

If static gravity or spacetime curvature information is carried by classical propagating particles or waves, a modern Laplace experiment places a lower limit on their speed of 10¹⁰ c. The so-called Lorentzian modification of special relativity permits such speeds without need of tachyons. But there are other consequences. If ordinary gravity is carried by particles with finite collision cross-section, such collisions would progressively diminish its inverse square character, converting to inverse linear behavior on the largest scales. At scales greater than several kiloparsecs gravity can apparently be modeled, without need for dark matter, by an inverse linear law. The orbital motions of Mercury and Earth may also show traces of this effect. If gravity were carried by particles, a mass between two bodies could partially shield each of them from the gravity of the other. Anomalies are seen in the motions of certain artificial Earth satellites during eclipse seasons that behave like shielding of the Sun's gravity. Certain types of radiation pressure might cause a similar behavior but require many free parameters. Particle-gravity models would change our understanding of gravitation and our views of the nature of time in relativity theory.     

Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

The thermodynamic and electrical properties of mercury vapor at pressures below atmospheric and high temperatures

The thermodynamic properties and electrical conductivity of mercury vapor have been calculated for temperatures between 1000°K and 15,000°K and pressures between atmospheric and 10⁻⁴ atm. The thermodynamic properties were determined by the methods of statistical mechanics. Account has been taken of the lowering of the ionization potential due to local electric fields and the number of terms employed in the electronic partition function has been limited in accordance with the theory of Ecker and Weizel. The electrical conductivity was computed on the basis of “free path” kinetic theory. It is shown that in the presence of a magnetic field the conductivity has directional properties. For a field of 10,000 G the change in conductivity is illustrated for a particular case.     

Lambda-universe in scalar-tensor gravity

We present a lambda-Universe, in scalar-tensor gravity, reviewing Berman and Trevisan’s inflationary case (Berman and Trevisan in Int. J. Theor. Phys., 2009) and then we find a solution for an accelerating power-law scale-factor. The negativity of cosmic pressure implies acceleration of the expansion, even with Λ<0. The cosmological term, and the coupling “constant”, are in fact, time-varying.      

Putative ice flows on Europa: Geometric patterns and relation to topography collectively constrain material properties and effusion rates

Europa's surface exhibits numerous small dome-like and lobate features, some of which have been attributed to fluid emplacement of ice or slush on the surface. We perform numerical simulations of non-Newtonian flows to assess the physical conditions required for these features to result from viscous flows. Our simulations indicate that the morphology of an ice flow on Europa will be, at least partially, influenced by pre-existing topography unless the thickness of the flow exceeds that of the underlying topography by at least an order of magnitude. Three classes of features can be identified on Europa. First, some (possibly most) putative flow-like features exhibit no influence from the pre-existing topography such as ridges, although their thicknesses are generally on the same order as those of ridges. Therefore, flow processes probably cannot explain the formation of these features. Second, some observed features show modest influence from the underlying topography. These might be explained by ice flows with wide ranges of parameters (ice temperatures >230 K, effusion rates >10⁷ m³ year⁻¹, and a wide range of grain sizes), although surface uplift (e.g., by diapirism) and in situ disaggregation provide an equally compelling explanation. Third, several observed features are completely confined by pre-existing topographic structures on at least one side; these are the best known candidates for flow features on Europa. If these features resulted from solid-ice flows, then temperatures >260 K and grain sizes <2 μm are required. Such small grain sizes seem unlikely; low-viscosity flows such as ice slurries or brines provide a better explanation for these features. Our results provide theoretical support for the view that many of Europa's lobate features have not resulted from solid-ice flows.     

Modified gravity in a viscous and non-isotropic background

We study the dynamical evolution of an f(R) model of gravity in a viscous and anisotropic background which is given by a Bianchi type-I model of the Universe. We find viable forms of f(R) gravity in which one is exactly the Einsteinian model of gravity with a cosmological constant and other two are power law f(R) models. We show that these two power law models are stable with a suitable choice of parameters. We also examine three potentials which exhibit the potential effect of f(R) models in the context of scalar tensor theory. By solving different aspects of the model and finding the physical quantities in the Jordan frame, we show that the equation of state parameter satisfy the dominant energy condition. At last we show that the two power law f(R) models behave like quintessence model at late times and also the shear coefficient viscosity tends to zero at late times.     

Visible continuum emission and gravity waves

Observed oscillations in the visible continuum emission (5000 Å) are studied considering the usual visible emission mechanism, NO + O (both two-body and three-body paths). Characteristic parameters of internal gravity waves are obtained using Hines' linear theory. Values of the kinetic energy density ?, and temperature variations Δθ, due to gravity waves are calculated. The results (? ~ 10⁶cm²s^?2, Δθ = 4–9K) are in agreement with those obtained by means of different techniques reported in the literature. A similar analysis of the simultaneous green-line emission data is made and a comparison is drawn between the results obtained for both emissions. An expression relating relative brightness of continuum emission and relative perturbations of atmospheric density is proposed.     

Mars geodesy, rotation and gravity

This review provides explanations of how geodesy, rotation and gravity can be addressed using radioscience data of an orbiter around a planet or of the lander on its surface.The planet Mars is the center of the discussion.The information one can get from orbitography and radioscience in general concerns the global static gravitational field, the time variation of the gravitational field induced by mass exchange between the atmosphere and the ice caps, the time variation of the gravitational field induced by...     

Mars geodesy,rotation and gravity

This review provides explanations of how geodesy, rotation and gravity can be addressed using radioscience data of an orbiter around a planet or of the lander on its surface.The planet Mars is the center of the discussion.The information one can get from orbitography and radioscience in general concerns the global static gravitational field, the time variation of the gravitational field induced by mass exchange between the atmosphere and the ice caps, the time variation of the gravitational field induced by the tides, the secular changes in the spacecraft's orbit induced by the little moons of Mars named Phobos and Deimos, the gravity induced by particular targets, the Martian ephemerides, and Mars' rotation and orientation.The paper addresses as well the determination of the geophysical parameters of Mars and, in particular, the state of Mars' core and its size, which is important for understanding the planet's evolution.Indeed, the state and dimension of the core determined from the moment of inertia and nutation depend in turn on the percentage of light elements in the core as well as on the core temperature, which is related to heat transport in the mantle.For example, the radius of the core has implications for possible mantle convection scenarios and, in particular, for the presence of a perovskite phase transition at the bottom of the mantle.This is also important for our understanding of the large volcanic province Tharsis on the surface of Mars.     

Tests and comparisons of gravity models

Optical observations of the GEOS satellites were used to obtain orbital solutions with different sets of geopotential coefficients. The solutions were compared before and after modification to high order terms (necessary because of resonance) and then analyzed by comparing subsequent observations with predicted trajectories. The most important source of error in orbit determination and prediction for the GEOS satellites is the effect of resonance found in most published sets of geopotential coefficients. Modifications to the sets yield greatly improved orbits in most cases.The sets of coefficients analyzed are APL 3.5, NWL5E-6, Köhnlein (1967), Rapp (1967), Kaula (1967), Smithsonian Astrophysical Observatory (SAO)M-1 (1966), SAO AGU (1969), SAO COSPAR (1969) and SAO 1969 Standard Earth. The SAO 1969 models generally give better orbital fits and prediction results than the other models above. However these models can be improved by corrections to resonant coefficients.The results of these comparisons suggest that with the best optical tracking systems and gravity models, satellite position error due to gravity model uncertainty can reach 50–100 m during a heavily observed 5–6 day orbital arc. If resonant coefficients are estimated, the uncertainty is reduced considerably.     

The bending of light and lensing in modified gravity

Our modified gravity theory (MOG) was used successfully in the past to explain a range of astronomical and cosmological observations, including galaxy rotation curves, the cosmic microwave background acoustic peaks, and the galaxy mass power spectrum. MOG was also used successfully to explain the unusual features of the Bullet Cluster  1E0657−558  without exotic dark matter. In the present work, we derive the relativistic equations of motion in the spherically symmetric field of a point source in MOG and, in particular, we derive equations for light bending and lensing. Our results also have broader applications in the case of extended distributions of matter, and they can be used to validate the Bullet Cluster results and provide a possible explanation for the merging clusters in Abell 520.     

Uniformly rotating homogeneous and polytropic rings in Newtonian gravity

An analytical method is presented for treating the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity. The method is based on an expansion about the thin ring limit, where the cross-section of the ring tends to a circle. The iterative scheme developed here is applied to homogeneous rings up to the 20th order and to polytropes with the index   n = 1  up to the third order. For other polytropic indices no analytic solutions are obtainable, but one can apply the method numerically. However, it is possible to derive a simple formula relating mass to the integrated pressure to leading order without specifying the equation of state. Our results are compared with those generated by highly accurate numerical methods to test their accuracy.     

Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters

With 2 years of tracking data collection from the MRO spacecraft, there is noticeable improvement in the high frequency portion of the spherical harmonic Mars gravity field. The new JPL Mars gravity fields, MRO110B and MRO110B2, show resolution near degree 90. Additional years of MGS and Mars Odyssey tracking data result in improvement for the seasonal gravity changes which compares well to global circulation models and Odyssey neutron data and Mars rotation and precession (). Once atmospheric dust is accounted for in the spacecraft solar pressure model, solutions for Mars solar tide are consistent between data sets and show slightly larger values (k₂ = 0.164 ± 0.009, after correction for atmospheric tide) compared to previous results, further constraining core models. An additional 4 years of Mars range data improves the Mars ephemeris, determines 21 asteroid masses and bounds solar mass loss (dGM_Sun/dt < 1.6 × 10⁻¹³ GM_Sun year⁻¹).