Related papers: AMD-stability and the classification of planetary …
We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…
Protoplanetary disks are quasi-steady structures whose evolution and dispersal determine the environment for planet formation. I review the theory of protoplanetary disk evolution and its connection to observations. Substantial progress has…
The stability of potential exoplanets in binary star systems remains a critical challenge in celestial mechanics. This study investigates the stability of a hypothetical Jupiter-mass planet in the Alpha Centauri AB system by drawing…
Although the long-term numerical integrations of planetary orbits indicate that our planetary system is dynamically stable at least +/- Gyr, the dynamics of our Solar System includes both chaotic and stable motions: the large planets…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
The fates of planetary systems provide unassailable insights into their formation and represent rich cross-disciplinary dynamical laboratories. Mounting observations of post-main-sequence planetary systems necessitate a complementary level…
The known extrasolar multiple-planet systems share a surprising dynamical attribute: they cluster just beyond the Hill stability boundary. Here we show that the planet-planet scattering model, which naturally explains the observed exoplanet…
Applying the technique of dynamical maps we study the orbital stability of test particles in the Solar System in the space (a,e,i) defined by 0.1<a<38 au, 0<e<0.9 and 0<i<180 identifying the unstable and stable regions. We find stable…
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…
(Abridged) We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly concentrate on the study of the HD 82943 system by employing two sets of the…
We present theoretical analysis of the astrometric searches for extrasolar planets with the Space Interferometry Mission (SIM). Particularly, we derive a model for the future measurements with SIM and discuss the problem of reliable…
With 40 or more transiting exoplanets now known, the time is ripe to seek patterns and correlations among their observed properties, which may give important insights into planet formation, structure, and evolution. This task is made…
Astrometry as a technique has so far proved of limited utility when employed as either a follow-up tool or to independently search for planetary mass companions orbiting nearby stars. However, this is bound to change during the next decade.…
Due to the exquisite photometric precision, transiting exoplanet discoveries from the Kepler mission are enabling several new techniques of confirmation and characterization. One of these newly accessible techniques analyzes the phase…
Recent results have shown that many of the known extrasolar planetary systems contain regions which are stable for massless test particles. We examine the possibility that Saturn-mass planets exist in these systems, just below the detection…
Mean motion commensurabilities in multi-planet systems are an expected outcome of protoplanetary disk-driven migration, and their relative dearth in the observational data presents an important challenge to current models of planet…
For much of human history we have wondered how our solar system formed, and whether there are any other planets like ours around other stars. Only in the last 20 years have we had direct evidence for the existence of exoplanets, with the…