Figure-Figure Interaction Between Bodies Having Arbitrary Shapes and Mass Distributions: A Power Series Expansion Approach

We derive an expression for the mutual gravitational force and torque of two bodies having arbitrary shapes and mass distributions, as an expansion in power series of their products of inertia and of the relative coordinates of their centres of mass. The absolute convergence of all the power series developed is rigorously demonstrated. The absence of transcendental functions makes this formalism suitable for fast numerical applications. The products of inertia used here are directly related to the spherical harmonics coefficients, and we provide a detailed analysis of this relationship.Comment: 13 pages, accepted by Celestial Mechanics and Dynamical Astronom

Eccentricity Evolution for Planets in Gaseous Disks

We investigate the hypothesis that interactions between a giant planet and the disk from which it forms promote eccentricity growth. These interactions are concentrated at discrete Lindblad and corotation resonances. Interactions at principal Lindblad resonances cause the planet's orbit to migrate and open a gap in the disk if the planet is sufficiently massive. Those at first order Lindblad and corotation resonances change the planet's orbital eccentricity. Eccentricity is excited by interactions at external Lindblad resonances which are located on the opposite side of corotation from the planet, and damped by co-orbital Lindblad resonances which overlap the planet's orbit. If the planet clears a gap in the disk, the rate of eccentricity damping by co-orbital Lindblad resonances is reduced. Density gradients associated with the gap activate eccentricity damping by corotation resonances at a rate which initially marginally exceeds that of eccentricity excitation by external Lindblad resonances. But the corotation torque drives a mass flux which reduces the density gradient near the resonance. Sufficient partial saturation of corotation resonances can tip the balance in favor of eccentricity excitation. A minimal initial eccentricity of a few percent is required to overcome viscous diffusion which acts to unsaturate corotation resonances by reestablishing the large scale density gradient. Thus eccentricity growth is a finite amplitude instability. Formally, interactions at the apsidal resonance, which is a special kind of co-orbital Lindblad resonance, appears to damp eccentricity faster than external Lindblad resonances can excite it. However, apsidal waves have such long wavelengths that they do not propagate in protoplanetary disks. This reduces eccentricity damping by the apsidal resonance to a modest level.Comment: Submitted to Ap

Towards a theory for Neptune's arc rings

It is proposed that the incomplete rings of Neptune consist of a number of short arcs centered on the corotation resonances of a single satellite. The satellite must have a radius of the order of 100 km or more and move on an inclined orbit. Corotation resonances are located at potential maxima. Thus, mechanical energy dissipated by interparticle collisions must be continually replenished to prevent the arcs from spreading. It is shown that each corotation resonance is associated with a nearby Lindblad resonance, which excites the ring particles' orbital eccentricity, thus supplying the energy required to maintain the arc. The ultimate energy reservoir is the satellite's orbital energy. Therefore, interaction with the arcs damps the satellite's orbital inclination. The self-gravity of the arcs limits their contraction and enforces a relation between arc length and mass. The estimated arc masses are so small, of the order of 10^16 g, that the satellite's orbital inclination suffers negligible decay over the age of the solar system. The inferred surface mass densities are comparable to those found in the major rings of Saturn and Uranus

The dynamics of elliptical rings

We investigate the evolution of eccentric rings under the influence of (1) differential precession due to the planetary quadrupole moment; (2) self-gravity; (3) viscous forces due to interparticle collisions; and (4) eccentricity excitation by shepherd satellites. The principal conclusions are that: (a) Uniform precession can be enforced by self-gravity (Goldreich and Tremaine 1979b); the resulting configuration is both dynamically and secularly stable. (b) Due to viscous forces the line of apsides at the inner ring edge is not exactly aligned with the line of apsides at the outer edge; the apse shift may be detectable in the ɑ and β rings of Uranus. (c) The mean eccentricity is determined by a balance between viscous damping and excitation by shepherds. (d) We expect the dimensionless eccentricity gradient ɑΔe/Δɑ to be positive and of order unity in most eccentric rings, as observed

Precession of inclined rings

Differential precession due to the planet's quadrupole moment tends to destroy the alignment of particles in inclined rings. We propose that alignment is maintained by the self-gravity of the ring. This hypothesis predicts that δi/δɑ>0 across the ring. If δi/i0<(1, δe/e_0 <(1, ɑδi/δɑ<(1, and ɑδe/δɑ< 1, a further prediction is that δi/i_0 = δe/e_0. The ɑ and β rings of Uranus may be used to test these predictions

Excitation of inclinations in ring-satellite systems

Resonant gravitational interactions between a ring and a satellite produce secular variations of their orbital inclinations. Interactions at vertical resonances, analogous to Lindblad resonances but involving inclinations instead of eccentricities, excite inclinations. There is no inclination analog of the corotation resonance. An equatorial ring changes the inclination of a nearby satellite in qualitatively the same way that a satellite in an equatorial orbit changes the inclination of a nearby ring. Viscous dissipation in a ring leads to an equilibrium value of its inclination. These results provide a basis for discussing the origins of the inclinations of planetary rings

Mars and frame-dragging: study for a dedicated mission

In this paper we preliminarily explore the possibility of designing a dedicated satellite-based mission to measure the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of Mars. The focus is on the systematic error induced by the multipolar expansion of the areopotential and on possible strategies to reduce it. It turns out that the major sources of bias are the Mars'equatorial radius R and the even zonal harmonics J_L, L = 2,4,6... of the areopotential. An optimal solution, in principle, consists of using two probes at high-altitudes (a\approx 9500-9600 km) and different inclinations, and suitably combining their nodes in order to entirely cancel out the bias due to \delta R. The remaining uncancelled mismodelled terms due to \delta J_L, L = 2,4,6,... would induce a bias \lesssim 1%, according to the present-day MGS95J gravity model, over a wide range of admissible values of the inclinations. The Lense-Thirring out-of-plane shifts of the two probes would amount to about 10 cm yr^-1.Comment: LaTex2e, 16 pages, 5 figures, no tables. To appear in General Relativity and Gravitatio

The shape and dynamics of a heliotropic dusty ringlet in the Cassini Division

The so-called "Charming Ringlet" (R/2006 S3) is a low-optical-depth, dusty ringlet located in the Laplace gap in the Cassini Division. This ringlet is particularly interesting because its radial position varies systematically with longitude relative to the Sun in such a way that the ringlet's geometric center appears to be displaced away from Saturn's center in a direction roughly toward the Sun. In other words, the ringlet is always found at greater distances from the planet's center at longitudes near the sub-solar longitude than it is at longitudes near Saturn's shadow. This "heliotropic" behavior indicates that the dynamics of the particles in this ring are being influenced by solar radiation pressure. In order to investigate this phenomenon, which has been predicted theoretically but has never been observed this clearly, we analyze multiple image sequences of this ringlet obtained by Cassini in order to constrain its shape and orientation. These data can be fit reasonably well with a model in which both the eccentricity and the inclination of the ringlet have "forced" components (that maintain a fixed orientation relative to the Sun) as well as "free" components (that drift around the planet at steady rates determined by Saturn's oblateness). While the magnitude of the forced eccentricity is roughly consistent with theoretical expectations for radiation pressure acting on 10-to-100-micron-wide icy grains, the existence of significant free eccentricities and inclinations poses a significant challenge for models of low-optical-depth dusty rings.Comment: 31 pages, 6 figures, accepted for publication in Icarus. Slight edits made to match various proof correction

On the use of rigorous microwave interaction models to support remote sensing of natural surfaces

A study has been undertaken which objective is to contribute to the investigation of the validity of microwave surface scattering models used in remote sensing applications, particularly when applied to realistic representations of natural surfaces. These investigations are based on recent implementations of rigorous methods (MoM and FDTD) and cover a wide range of configurations of observation (mono- and bi-static). Both land (bare soils) and sea surfaces are being investigated

Superhumps: Confronting Theory with Observation

We review the theory and observations related to the ``superhump'' precession of eccentric accretion discs in close binary sytems. We agree with earlier work, although for different reasons, that the discrepancy between observation and dynamical theory implies that the effect of pressure in the disc cannot be neglected. We extend earlier work that investigates this effect to include the correct expression for the radius at which resonant orbits occur. Using analytic expressions for the accretion disc structure, we derive a relationship between the period excess and mass-ratio with the pressure effects included. This is compared to the observed data, recently derived results for detailed integration of the disc equations and the equivalent empirically derived relations and used to predict values for the mass ratio based on measured values of the period excess for 88 systems.Comment: 11 pages, 7 figures, 4 tables, accepted for publication in MNRA