Related papers: The physics of rotational flattening and the point…
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…
Some exact analytical formulas are presented for the generalized Roche model of rotating star. The gravitational field of the central core is described by the model of two equal-mass point centers placed symmetrically at rotation axis with…
We consider a further extension of our previous works in the treatment of the three-dimensional general relativistic Poynting-Robertson effect, which describes the motion of a test particle around a compact object as affected by the…
The exact solution for the shape and gravitational field of a rotating two-layer Maclaurin ellipsoid of revolution is compared with predictions of the theory of figures up to third order in the small rotational parameter of the theory of…
A simple model of a spherically symmetric, pulsating star is calculated. The application to the Sun gives a 166-min radial pulsation. The theory of gravitation in flat space-time implies for a spherically symmetric, nonstationary star small…
We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of…
The effect of a soft phase core appearance in the center of polytropic star is analyzed by means of linear response theory. Approximate formulae for the changes of radius, moment of inertia and mass-energy of non-rotating configuration with…
We develop a new geometrical technique to study relative equilibria for a system of $n$--positive masses, moving on the two dimensional sphere $\mathbb{S}^2$, under the influence of a general potential which only depends on the mutual…
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…
We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian…
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.…
The dark matter accretion theory (around a central body) of the author on the basis of his 5-dimensional Projective Unified Field Theory (PUFT) is applied to the orbital motion of stars around the center of the Galaxy. The departure of the…
We generalize the theory of the inhomogeneity effect to enable comparison among different inhomogeneous planets. A metric of inhomogeneity based on the cumulative distribution function is applied to investigate the dependence of planetary…
We study the motion of a test particle in a stationary, axially and reflection symmetric spacetime of a central compact object, as affected by interaction with a test radiation field of the same symmetries. Considering the radiation flux…
Understanding the consequences of the gravitational interaction between a star and a planet is fundamental to the study of exoplanets. The solution of the two-body problem shows that the planet moves in an elliptical path around the star…
This paper, and its companion, investigate the evolution of dense stellar systems due to the influence of two-body gravitational encounters, physical collisions and stellar evolution. Our goal is the simulation of the densest centers of…
Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit…
Batygin and Brown (2016) have suggested the existence of a new Solar System planet supposed to be responsible for the perturbation of eccentric orbits of small outer bodies. The main challenge is now to detect and characterize this putative…
We investigate the influence of the quadrupole moment of a rotating source on the motion of a test particle in the strong field regime. For this purpose the Hartle-Thorne metric, that is an approximate solution of vacuum Einstein field…
General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order…