相关论文: Comparison between Laplace-Lagrange Secular Theory…
We discuss the influence of the cosmological constant $\Lambda$ on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of…
We extend the formalism of a previous paper to include the effects of flybys and instantaneous perturbations such as supernovae on the long-term secular evolution of hierarchical multiple systems with an arbitrary number of bodies and…
$N$-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be…
We review the orbital dynamics exhibited by the first extra-solar planetary system discovered, Upsilon Andromedae. This system is unique in combining all of the surprising architectural features displayed individually by extrasolar…
Placing the architecture of the Solar System within the broader context of planetary architectures is one of the primary topics of interest within planetary science. Exoplanet discoveries have revealed a large range of system architectures,…
We present a stability analysis of a large set of simulated planetary systems of three or more planets based on architectures of multiplanet systems discovered by \textit{Kepler} and \textit{K2}. We propagated 21,400 simulated planetary…
Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term…
As a direct result of ongoing efforts to detect more exoplanetary systems, an ever-increasing number of multiple-planet systems are being announced. But how many of these systems are truly what they seem? In many cases, such systems are…
This paper presents a study of the use of numerical simulation and Bayesian optimisation techniques to investigate the dynamics of celestial systems. Initially, the study focuses on Lagrange points in restricted three-body systems where a…
Doppler spectroscopy has detected 136 planets around nearby stars. A major puzzle is why their orbits are highly eccentric, while all planets in our Solar System are on nearly circular orbits, as expected if they formed by accretion…
Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem…
We present results of numerical simulations which examine the dynamical stability of known planetary systems, a star with two or more planets. First we vary the initial conditions of each system based on observational data. We then…
The SecularMultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested…
We present a method for studying the secular gravitational dynamics of hierarchical multiple systems consisting of nested binaries, which is valid for an arbitrary number of bodies and arbitrary hierarchical structure. We derive the…
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…
As the number of potential exomoon candidates grows, there is a heightened motivation of pursing orbital stability analyses. In this work, we provide an in-depth investigation into 4-body systems, consisting of a star, planet, moon, and…
We present the secular theory of coplanar $N$-planet system, in the absence of mean motion resonances between the planets. This theory relies on the averaging of a perturbation to the two-body problem over the mean longitudes. We expand the…
We integrate the orbital solutions of the planets orbiting 55 Cnc. In the simulations, we find that not only three resonant arguments $\theta_{1}=\lambda_{1}-3\lambda_{2}+2\tilde\omega_{1}$,…
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…
We use detailed numerical simulations and the $\upsilon$ Andromedae, planetary system as a template to evaluate the capability of the ESA Cornerstone Mission GAIA in detecting and measuring multiple planets around solar-type stars in the…