Related papers: Equipotential Surfaces and Lagrangian points in No…
Close binary systems of compact stars, due to the emission of gravitational radiation, may evolve into a phase in which the less massive star transfers mass to its companion. We describe mass transfer by using the model of Roche lobe…
Many giant exoplanets are found near their Roche limit and in mildly eccentric orbits. In this study we examine the fate of such planets through Roche-lobe overflow as a function of the physical properties of the binary components,…
The Roche potential is the sum of the gravitational and rotational potentials experienced by a massless body rotating alongside two massive bodies in a circular orbit. The Lagrangian points are five stationary points in the Roche potential.…
Evolutionary calculations for stars in close binary systems are in high demand to obtain better constraints on gravitational wave source progenitors, understand transient events from stellar interactions, and more. Modern one-dimensional…
The nonlinear stability domain of Lagrange's celebrated 1772 solution of a three-body problem is obtained numerically as a function of the masses of the bodies and the common eccentricity of their Keplerian orbits. This domain shows that…
Exceptional points (EPs) are special singularities of non-Hermitian Hamiltonians. At an EP, two or more eigenvalues and the corresponding eigenstates coalesce. Recently, EP-based optical gyroscope near an EP was extensively investigated to…
We present a new formulation for numerically obtaining axisymmetric equilibrium structures of rotating stars in two spatial dimensions. With a view to apply it to the secular evolution of rotating stars, we base it on the Lagrangian…
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same…
Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the…
The rapid circularization and synchronization of the stellar components in an eccentric binary system at the onset of Roche lobe overflow (RLO) is a fundamental assumption common to all binary stellar evolution and population synthesis…
To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant,…
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on…
The Roche limit, or the threshold separation within which a celestial object (the donor) M cannot remain in a stable configuration due to a companion's tidal field, has been well established when M is in hydrostatic equilibrium and has…
Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…
Circularly orbiting black hole-gaseous star close binary systems are examined by using numerically exact stationary configurations in the framework of Newtonian gravity. We have chosen a polytropic star for the fluid component of the binary…
We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and…
We present numerical computations of the equilibrium configurations of tidally-locked homogeneous binaries, rotating in circular orbits. Unlike the classical Roche approximations, we self-consistently account for the tidal and rotational…
We present a new formulation to construct numerically equilibrium configurations of rotating stars in general relativity. Having in mind the application to their quasi static evolutions, we adopt a Lagrangian formulation of our own…
Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using…
In this paper we consider Roche accretion in an Extreme Mass-Ratio Inspiral (EMRI) binary system formed by a star orbiting a massive black hole. The ultimate goal is to detect the mass and spin of the black hole and provide a test of…