Related papers: Planetary systems with forces other than gravitati…
It was recently proposed that the effects usually attributed to particle dark matter on galaxy scales are due to the displacement of dark energy by baryonic matter, a paradigm known as emergent gravity. This formalism leads to predictions…
We examine the dynamics and stability of circumbinary particles orbiting around the Earth-Moon binary system. The moon formed close to the Earth (semi-major axis $a_{EM}\approx 3\, R_\oplus$) and expanded through tides to its current day…
Eighty planetary systems of two or more planets are known to orbit stars other than the Sun. For most, the data can be sufficiently explained by non-interacting Keplerian orbits, so the dynamical interactions of these systems have not been…
In this paper we propose a notion of stability, that we call $\epsilon -N$-stability, for systems of particles interacting via Newton's gravitational potential, and orbiting a much bigger object. For these systems the usual thermodynamical…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets…
The final orbital configuration of a planetary system is shaped by both its early star-disk environment and late-stage gravitational interactions. Assessing the relative importance of each of these factors is not straightforward due to the…
Corrections to Newton's inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here we give a model of a warped 6D world with an extra 2D sphere. We take a…
Gas giant planets have been detected on eccentric orbits several hundreds of astronomical units in size around other stars. It has been proposed that even the Sun hosts a wide-orbit planet of 5-10 Earth masses, often called Planet Nine,…
About two years ago, Wolszczan and Frail announced the detection of a possible planetary system consisting of two Earth-mass planets around a millisecond pulsar. It was pointed out shortly thereafter that the mutual gravitational…
The hypothesis that gravitational self-binding energy may be the source for the vacuum energy term of cosmology is studied in a Newtonian Ansatz. For spherical spaces the attractive force of gravitation and the negative pressure of the…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
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…
Motions of stars in close binary systems with a conservative mass exchange are examined. It is shown that Paczynski-Huang model widely used now for obtaining the semi-major axis variation of a relative stars orbit is incorrect, because it…
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…
We considered the problem of stability for planets of finite mass in binary star systems. We selected a huge set of initial conditions for planetary orbits of the S-type, to perform high precision and very extended in time integrations. For…
Three bodies moving in a periodic orbit under the influence of Newtonian gravity ought to emit gravitational waves. We have calculated the gravitational radiation quadrupolar waveforms and the corresponding luminosities for the 13+11…
In this letter we consider the evolution of a planetary system around a star inside a wide binary. We simulate numerically the evolution of the planetary orbits for both co-planar and highly-inclined systems. We find that the Kozai…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…