Related papers: Isostatic equilibrium in spherical coordinates and…
Isostasy explains why observed gravity anomalies are generally much weaker than what is expected from topography alone, and why planetary crusts can support high topography without breaking up. Classical isostasy, however, neglects internal…
Enceladus's gravity and shape have been explained in terms of a thick isostatic ice shell floating on a global ocean, in contradiction of the thin shell implied by librations. Here we propose a new isostatic model minimizing crustal…
Modeling the internal structure of self-gravitating solid and liquid bodies presents a challenge, as existing approaches are often limited to either overly simplistic constant-density approximations or more complex numerical equations of…
An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular}…
Relative equilibria on a rotating meridian on $\mathbb{S}^2$ in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles,…
The hydrostatic equilibrium of multi-layer bodies lacks a satisfactory theoretical treatment despite its wide range of applicability. Here we show that by using the exact analytical potential of homogeneous ellipsoids we can obtain…
Motivated by the current search for exomoons, this paper considers the stability of tidal equilibrium for hierarchical three-body systems containing a star, a planet, and a moon. In this treatment, the energy and angular momentum budgets…
In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper I gave…
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…
The geologic activity at Enceladus's south pole remains unexplained, though tidal deformations are probably the ultimate cause. Recent gravity and libration data indicate that Enceladus's icy crust floats on a global ocean, is rather thin,…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
(Abridged) We develop an analytical spectral method to solve the equations of equilibrium for a self-gravitating, magnetized fluid body, under the only hypotheses that (a) the equation of state is isothermal, (b) the configuration is…
The dynamical stability of massive thin shells with a given equation of state (EOS) is here compared (both for the barotropic and non-barotropic case) with the results coming from thermodynamical stability. Our results show that the…
We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of…
We investigate the equilibrium properties of self-gravitating magnetized clouds with polytropic equations of state with negative index n. In particular, we consider scale-free isopedic configurations that have constant dimensionless…
Invaginations are partial enclosures formed by surfaces. Typically formed by biological membranes; they abound in nature. In this paper, we consider fundamentally different structures: elastically stabilized invaginations. Focusing on…
In the paper we discuss equilibrium states of stars, using a simplified analytic model. A star is considered as self-graviting body of gas. We use a condition for the equilibrium state of the body in the form of a differential equation,…
Hydrostatic equilibrium of the multiphase interstellar medium in the solar vicinity is reconsidered, with the regular and turbulent magnetic fields treated separately. The regular magnetic field strength required to support the gas is…
We have re-examined the classical problem of the macroscopic equation of state for a hydrostatic isothermal self-gravitating gas cloud bounded by an external medium at constant pressure. We have obtained analytical conditions for its…
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions --- a context in which subtle…