Related papers: Shapes and gravitational fields of rotating two-la…
A point mass at the center of an ellipsoidal homogeneous fluid is used as a simple model to study the effect of rotation on the shape and external gravitational field of planets and stars. Maclaurin's analytical result for a homogenous body…
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 show that the two-dimensional structure of a rigidly rotating self-gravitating body is accessible with relatively good precision by assuming a purely spheroidal stratification. With this hypothesis, the two-dimensional problem becomes…
We present a vectorial formalism to determine the approximate solutions to the problem of a composite body made of $L$ homogeneous, rigidly rotating layers bounded by spheroidal surfaces. The method is based on the 1st-order expansion of…
We show that a rigidly rotating, homogeneous ellipsoid of revolution threaded by a uniform, coaxial magnetic field is a possible figure of equilibrium. While the spheroidal shape is fully preserved, the rotation rate is modified.…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
This paper contains a review of Clairaut's theory with focus on the determination of a gravitational rigidity modulus $\gamma$ defined as $\left(\frac{C-I_o}{I_o}\right)\gamma=\frac{2}{3}\Omega^2$, where $C$ and $I_o$ are the polar and mean…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
We establish, in the framework of the theory of nested figures, the expressions for the gravitational moments $J_{2n}$ of a systems made of ${\cal L}$ homogeneous layers separated by spheroidal surfaces and in relative rotational motion. We…
Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of General Relativity instead of the effect of Dark Matter…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
Variational techniques have been used in applications of hydrodynamics in special cases but an action that is general enough to deal with both potential flows and solid-body flows, such as cylindrical Couette flow and rotating planets, has…
A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for…
Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum…
We have analyzed the effects of rotation on mass-radius relationships for single-layer and two-layer planets having a core and an envelope made of pure materials among iron, perovskite and water in solid phase. The numerical surveys use the…
We present a rigorous framework for determining equilibrium configurations of uniformly rotating self-gravitating fluid bodies. This work addresses the longstanding challenge of modeling rotational deformation in celestial objects such as…
We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that…
Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods,…