Related papers: Existence for Stable Rotating Star-Planet Systems
We study the stability of rotating collisionless self-gravitating spherical systems by using high resolution N-body experiments on a Connection Machine CM-5. We added rotation to Ossipkov-Merritt (hereafter OM) anisotropic spherical systems…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…
We construct dark energy stars with Chaplygin-type equation of state (EoS) in the presence of anisotropic pressure within the framework of Einstein gravity. From the classification established by Iyer et al. [Class. Quantum Grav. 2, 219…
We obtain equilibrium solutions for rotating compact stars including the special relativistic effects. The gravity is assumed to be Newtonian, but we used the active mass density, which takes into account all the energies such as motions of…
We consider a gravitating spherically symmetric configuration consisting of a scalar field non-minimally coupled to ordinary matter in the form of a perfect fluid. For this system we find static, regular, asymptotically flat solutions for…
Planets are observed to orbit the component star(s) of stellar binary systems on so-called circumprimary or circumsecondary orbits, as well as around the entire binary system on so-called circumbinary orbits. Depending on the orbital…
A key component of characterizing multi-planet exosystems is testing the orbital stability based on the observed properties. Such characterization not only tests the validity of how observations are interpreted but can also place additional…
The existence of neutron stars with masses of $\sim 2\,M_{\odot}$ requires a stiff equation of state at high densities. On the other hand, the necessary appearance also at high densities of new degrees of freedom, such as hyperons and…
In this chapter we review the recent results on the equilibrium configurations of static and uniformly rotating neutron stars within the Hartle formalism. We start from the Einstein-Maxwell-Thomas-Fermi equations formulated and extended by…
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
Large dips in the brightness for a number of stars have been observed, for which the tentative explanation is occultation of the star by a transiting circumplanetary disk or ring system. In order for the circumplanetary disk/rings to block…
We extend the notion of orbital stability to systems of nonlinear Schrodinger equations, then we prove this property under suitable assumptions of the local nonlinearity involved.
Context: Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been…
The recently discovered planetary system in the binary GamCep was studied concerning its dynamical evolution. We confirm that the orbital parameters found by the observers are in a stable configuration. The primary aim of this study was to…
Via minimization arguments and Concentration Compactness Principle, we prove the orbital stability of standing wave solutions for a class of quasilinear Schr\"{o}dinger equation arising from physics.
In this paper we study the existence and the instability of standing waves with prescribed $L^2$-norm for a class of Schr\"odinger-Poisson-Slater equations in $\R^{3}$ %orbitally stable standing waves with arbitray charge for the following…
The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…
Motivated by the current search for exomoons, this paper considers the stability of tidal equilibrium for hierarchical three-body systems containing a star, a planet, and a moon. In this treatment, the energy and angular momentum budgets…