Related papers: Dynamics of two planets in co-orbital motion
Having a massive moon has been considered as a primary mechanism for stabilized planetary obliquity, an example of which being our Earth. This is, however, not always consistent with the exoplanetary cases. This article details the…
We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature. Our goal is to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem…
Frozen orbits are always important foci of orbit design because of their valuable characteristics that their eccentricity and argument of pericentre remain constant on average. This study investigates quasi-circular frozen orbits and…
We consider a $(1+N)$-body problem in which one particle has mass $m_0 \gg 1$ and the remaining $N$ have unitary mass. We can assume that the body with larger mass (central body) is at rest at the origin, coinciding with the center of mass…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…
We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 0.001, analyzing their stability and bifurcations into 3-dimensional periodic orbits. We explain the role played by periodic orbits in…
In some planetary systems, the orbital periods of two of its members present a commensurability, usually known by mean-motion resonance. These resonances greatly enhance the mutual gravitational influence of the planets. As a consequence,…
We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
The dynamical interactions of planetary systems may be a clue to their formation histories. Therefore, the distribution of these interactions provides important constraints on models of planet formation. We focus on each system's apsidal…
Planetary formation might occur at different stages of the stellar evolution of compact binaries. In recent years, the formation of second-generation planets has been tested in circumbinary discs formed by the ejection of stellar material…
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…
It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter $\beta$ and on the eccentricity $e$ of the orbit. We consider only the circular case ($e…
The presence of mean motion resonances (MMRs) complicates analysis and fitting of planetary systems observed through the radial velocity (RV) technique. MMR can allow planets to remain stable in regions of phase space where strong…
A considerable fraction of multi-planet systems discovered by the observational surveys of extrasolar planets reside in mild proximity to first-order mean motion resonances. However, the relative remoteness of such systems from nominal…
We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework…
The stability of planets in the alpha-Centauri AB stellar system has been studied extensively. However, most studies either focus on the orbital plane of the binary or consider inclined circular orbits. Here, we numerically investigate the…
This paper considers the stability of tidal equilibria for planetary systems in which stellar rotation provides a significant contribution to the angular momentum budget. We begin by applying classic stability considerations for two bodies…
Context: Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the…