Related papers: On the dynamics of the three dimensional planetary…
Motivated by the stellar wind ejected from the upper atmosphere (Corona) of a star, we explore a boundary problem of the two-species nonlinear relativistic Vlasov-Poisson systems in the 3D half space in the presence of a constant vertical…
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…
The inner two planets around the 55 Cancri were found to be trapped in the 3:1 mean motion resonance. In this paper, we study the dynamics of this extra-solar planetary system. Our numerical investigation confirms the existence of the 3:1…
The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by…
The recent discovery of a three-planet extrasolar system of HR 8799 by Marois et al. is a breakthrough in the field of the direct imaging. This great achievement raises questions on the formation and dynamical stability of the HR 8799…
Librational motion in celestial mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an…
We revisit the secular 3D planetary three-body problem aiming to provide a unified formalism for studying the structure of the phase space for progressively higher values of the mutual inclination $i_{mut}$ between the two planets' orbits.…
Multi-planetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai-Lidov…
Many recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20% of the known extrasolar planetary systems are associated with one or more stellar companions. The orbits of…
Some systems of close-in "super-Earths" contain five or more planets on non-resonant but compact and nearly coplanar orbits. The Kepler-11 system is an iconic representative of this class of system. It is challenging to explain their…
In this paper, we investigate whether hypothetical Earth-like planets have high probability of remaining on stable orbits inside the habitable zones around the stars A and B of {\alpha} Centauri, for lengths of time compatible with the…
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…
About 5-15% of stellar systems are at least triple. About 1% of systems with a primary of $\tgs 1 \Mscun$ are triple with a {\it longer} peri od that is less than 30y, and so may in principle be capable of Roche-lobe overflow in both the…
Many recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20%, and presumably a larger fraction of the known extrasolar planetary systems are associated with one or more…
Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been…
Exoplanet systems with multiple planets in mean motion resonances have often been hailed as a signpost of disk driven migration. Resonant chains like Kepler-223 and Kepler-80 consist of a trio of planets with the three-body resonant angle…
The Upsilon Andromedae system is the first exoplanetary system to have the relative inclination of two planets' orbital planes directly measured, and therefore offers our first window into the 3-dimensional configurations of planetary…
We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading…
The three-planet extrasolar system of HD 181433 has been detected with HARPS. The best-fit solution, announced by the discovery team, describes a highly unstable, self-disrupting configuration. In fact, a narrow observational window, only…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…