Related papers: Structuring eccentric-narrow planetary rings
We use a simple model of the dynamics of a narrow-eccentric ring, to put some constraints on some of the observable properties of the real systems.In this work we concentrate on the case of the `Titan ringlet of Saturn'.Our approach is…
The discovery of ring systems around objects of the outer Solar System provides a strong motivation to apply theoretical models in order to better estimate their physical and orbital parameters, which can constrain scenarios for their…
The boundaries of the Uranian epsilon, alpha, and beta rings can be fitted by Keplerian ellipses. The pair of ellipses that outline a given ring share a common line of apsides. Apse alignment is surprising because the quadrupole moment of…
We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it…
These 1992 lectures notes present a powerful formalism mostly developed in the 1980s by Borderies, Goldreich and Tremaine to address planetary ring dynamical issues. These notes make a special emphasis on ring microphysics, quantified with…
In this paper we develop a framework for studying unstratified, magnetised eccentric discs and compute uniformly precessing eccentric modes in a cylindrical annulus which provide convenient initial conditions for numerical simulations. The…
We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non-interacting particles where open motion (escape) takes place, and includes the quasi-periodic…
The present material covers the features of large scale ring dynamics in perturbed flows that were not addressed in part 1 (astro-ph/1606.00759); this includes an extensive coverage of all kinds of ring modes dynamics (except density waves…
Narrow planetary rings are eccentric and inclined. Particles within a given ring must therefore share the same pericenter and node. We solve for the three-dimensional geometries and mass distributions that enable the Uranian Alpha and Beta…
In a previous work (Pichardo et al. 2005), we studied stable configurations for circumstellar discs in eccentric binary systems. We searched for "invariant loops": closed curves (analogous to stable periodic orbits in time-independent…
Global m=1 asymmetries are observed in many self-gravitating astrophysical systems and are often interpreted as large-scale slow modes in near-Keplerian potentials. Prominent examples include eccentric nuclear disks in galactic centres,…
A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chaotic layer around the separatrix of non-linear resonance. This is a condition for the existence of a…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
Narrow eccentric planetary ringlets have sharp edges, sizable eccentricity gradients, and a confinement mechanism that prevents radial spreading due to ring viscosity. Most proposed ringlet confinement mechanisms presume that there are one…
We calculate global $m=1$ modes with low pattern speed corresponding to introducing a finite eccentricity into a protoplanetary disc. We consider disc models which are either isolated or contain one or two protoplanets orbiting in an inner…
In this paper we address the stability of resonantly forced density waves in dense planetary rings. Already by Goldreich & Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the…
Instabilities and strong dynamical interactions between multiple giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities seem…
It is well known that the simple criterion proposed originally by Polyachenko and Shukhman (1981) for the onset of the radial orbit instability, although being generally a useful tool, faces significant exceptions both on the side of mildly…
We investigate the dynamics of a nonzero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semi--major axis by means of numerical…
The Lagrange planetary equations are used to study to secular evolution of a small, eccentric satellite that orbits within a narrow gap in a broad, self-gravitating planetary ring. These equations show that the satellite's secular…