Related papers: Secular Orbit Evolution in Systems with a Strong E…
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…
One of the outstanding problems of classical celestial mechanics was the restricted 3-body prob- lem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for…
The classical disturbing function of the three-body problem widely used in planetary dynamics studies is an expansion of the gravitational interaction of the three-body problem with respect to zero eccentricity and zero inclination. This…
The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a…
We consider the Earth-Moon planar circular restricted three body problem and present a proof of the existence orbits, which approach arbitrarily close to one of the primary masses, and at the same time after each approach they move away…
We present a novel eccentricity parameterization for transit-only fits that allows us to efficiently sample the eccentricity and argument of periastron, while being able to generate a self-consistent model of a planet in a Keplerian orbit…
The 3:1 mean-motion resonance of the planar elliptic restricted three body problem (Sun-Jupiter-asteroid) is considered. The double numeric averaging is used to obtain the evolutionary equations which describe the long-term behavior of the…
Perturbative Post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the Parameterized Post-Newtonian theoretical framework. The results obtained are applied to the…
We examine the evolution of an almost circular Keplerian orbit interacting with unbound perturbers. We calculate the change in eccentricity and angular momentum that results from a single encounter, assuming the timescale for the…
We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular…
This paper considers whether the population of known transiting exoplanets provides evidence for additional outer planets on inclined orbits, due to the perturbing effect of such planets on the orbits of inner planets. As such, we develop a…
We extend our study of the extent of the regions within the $\alpha$ Centauri AB star system where small planets are able to orbit for billion-year timescales (Quarles & Lissauer 2016, AJ 151, 111) to investigate the effects of minimizing…
We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in the light of recent models of solar system evolution. We develop…
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…
We report eclipse timing variation analyses of 26 compact hierarchical triple stars comprised of an eccentric eclipsing ('inner') binary and a relatively close tertiary component found in the {\em Kepler} field. We simultaneously fit the…
Constructing dynamical maps from the filtered output of numerical integrations, we analyze the structure of the $\nu_\odot$ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated to…
The presence of mean-motion resonances (MMRs) in exoplanetary systems is a new exciting field of celestial mechanics which motivates us to consider this work to study the dynamical behaviour of exoplanetary systems by time evolution of the…
We present the results of our investigation on the use of the two-body integrals to compute preliminary orbits by linking too short arcs of observations of celestial bodies. This work introduces a significant improvement with respect to the…
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…
The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the…