Related papers: Rotating planets in Newtonian gravity
We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Hamiltonian structure and we then observe…
We develop a formalism to model slowly rotating superfluid Newtonian neutron stars. A two-fluid model is used to describe the matter, where one fluid is the superfluid neutrons that are believed to exist in the inner crust and core of…
In the past 15 years, astronomers have revealed that a significant fraction of the stars should harbor planets and that it is likely that terrestrial planets are abundant in our galaxy. Among these planets, how many are habitable, i.e.…
We consider the Clairaut theory of the equilibrium ellipsoidal figures for differentiated non-homogeneous bodies in non-synchronous rotation adding to it a tidal deformation due to the presence of an external gravitational force. We assume…
We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally…
Earth's fast rotation imposes the Taylor-Proudman Constraint that opposes fluid motion across an imaginary cylindrical surface called the Tangent Cylinder (TC) obtained by extruding the equatorial perimeter of the solid inner core along the…
This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic…
Recent general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids allow one to rederive, in the first post-Newtonian approximation, the well known geometric dragging of frames, and two new weak-field…
By numerically solving the mass distribution in a rotating disk based on Newton's laws of motion and gravitation, we demonstrate that the observed flat rotation curves for most spiral galaxies correspond to exponentially decreasing mass…
This paper examines the onset of the viscous overstability in dense particulate rings. First, we formulate a dense gas kinetic theory that is applicable to the Saturnian system. Our model is essentially that of Araki and Tremaine (1986),…
Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of…
Hypothesis: A broad range of phenomena, such as emulsification and emulsion stability, foam formation or liquid evaporation, are closely related to the dynamics of adsorbing colloidal particles. Elucidation of the mechanisms implied is key…
Any reasonable form of quantum gravity can explain (by phase interference) why on a large scale, inertial frames seem not to rotate relative to the average matter distribution in the universe without the need for absolute space, finely…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
The dynamic shift of the center of mass for a rotating hemisphere prompts us the question of what might be its physical consequences. Despite the fact that accelerating object is known to create gravitational field, there is no known…
We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite…
Planets in extrasolar systems tend to interact such that their orbits lie near a boundary between apsidal libration and circulation, a "separatrix", with one eccentricity periodically reaching near-zero. One explanation, applied to the…
To date, two planetary systems have been discovered with close-in, terrestrial-mass planets (< 5-10 Earth masses). Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
Active matter consumes energy from the environment and transforms it into mechanical work. Notable examples from biology include cell division, bacterial swarms, and muscle contraction. In this work, we investigate the nature of active…