Related papers: Nested spheroidal figures of equilibrium I. Approx…
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…
The theory of Nested Figures of Equilibrium, expanded in Papers I and II, is investigated in the limit where the number of layers of the rotating body is infinite, enabling to reach full heterogeneity. In the asymptotic process, the…
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 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…
We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary…
We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach…
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…
We report the existence of hydrostatic equilibrium states for a composite body made of two rigidly rotating, homogeneous layers bounded by spheroidal surfaces, where the core has a prolate shape. These new configurations require an oblate…
An approach is developed to find approximate solutions to the classical Newtonian problem of N bodies. Sets of N gravitating bodies having spherically symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded position…
We consider the two-body problem on surfaces of constant non-zero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show there are two relative equilibria where the masses are…
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 is concerned with the figures of equilibrium of a self-gravitating ideal fluid with density stratification and a steady-state velocity field. As in the classical setting, it is assumed that the figures or their layers uniformly…
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body…
We consider elastic bodies in rigid rotation, both nonrelativistically and in special relativity. Assuming a body to be in its natural state in the absence of rotation, we prove the existence of solutions to the elastic field equations for…
A wide range of exoplanet and exomoon models are characterized by a finite average rigidity and a viscosity much lower than the typical values for terrestrials. Such semiliquid bodies may or may not have rigid crusts with permanent figures.…
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…
In order to simulate rigidly rotating polytropes we have simulated systems of $N$ point particles, with $N$ up to 1800. Two particles at a distance $r$ interact by an attractive potential $-1/r$ and a repulsive potential $1/r^2$. The…
The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…
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…