Related papers: Planetary Stability Zones in Hierarchical Triple S…
Observations of exoplanets have revealed that systems with planets on closely-spaced orbits are common, which motivates the question "How closely can planets orbit to one another and still be dynamically-stable for very long times?". To…
When exploring the stability of multiplanet systems in binaries, two parameters are normally exploited: the critical semimajor axis ac computed by Holman and Wiegert (1999) within which planets are stable against the binary perturbations,…
Many planets are observed in stellar binary systems, and their frequency may be comparable to that of planetary systems around single stars. Binary stellar evolution in such systems influences the dynamical evolution of the resident…
We examine the stability of hierarchical triple systems using direct $N$-body simulations without adopting a secular perturbation approximation. We estimate their disruption timescales in addition to the mere stable/unstable criterion, with…
Many of the multi-planet systems discovered to date have been notable for their compactness, with neighbouring planets closer together than any in the Solar System. Interestingly, planet-hosting stars have a wide range of ages, suggesting…
In the last few years, a number of planets have been proposed to orbit several post main-sequence binary star systems on the basis of observed variations in the timing of eclipses between the binary components. A common feature of these…
We perform long-term simulations, up to ten billion years, of closely-spaced configurations of 2 -- 6 planets, each as massive as the Earth, traveling on nested orbits about either stellar component in $\alpha$ Centauri AB. The innermost…
The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum and spin variables $[X, P,…
We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. By extending previous work done to leading (quadrupole) order to octupole level (i.e., including…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
Recent work has suggested that many planetary systems lie near instability. If all systems are near instability, an additional planet must exist in stable regions of well-separated extra-solar planetary systems to push these systems to the…
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…
A comprehensive approach is provided to the study of both S-type and P-type habitability in stellar binary systems, which in principle can also be expanded to systems of higher order. P-type orbits occur when the planet orbits both binary…
This paper concentrates on four key tools for performing star cluster simulations developed during the last decade which are sufficient to handle all the relevant dynamical aspects. First we discuss briefly the Hermite integration scheme…
We explore the stability of gravitational triple systems comprising a central massive body and a tight binary of less massive pairs. In the present paper, we focus on improving the Hill-type stability criterion for the binary in those…
According to theoretical considerations, multiplicity of hierarchical stellar systems can reach, depending on masses and orbital parameters, several hundred, while observational data confirm existence of at most septuple (seven-component)…
Accurate $N$-body simulations of multiple systems such as binaries and triples are essential for understanding the formation and evolution of interacting binaries and binary mergers, including gravitational wave sources, blue stragglers and…
Spectroscopic orbits are computed for inner pairs in six nearby hierarchical multiple systems (HIP 35733, 95106/95110, 105441, 105585/105569, 105947, and 109951). Radial velocities and resolved measurements, when available, are used to…
The discovery of multi-planet extrasolar systems has kindled interest in using their orbital evolution as a probe of planet formation. Accurate descriptions of planetary orbits identify systems which could hide additional planets or be in a…
This paper explores the stability of an Earth-like planet orbiting a solar mass star in the presence of an outer-lying intermediate mass companion. The overall goal is to estimate the fraction of binary systems that allow Earth-like planets…