Related papers: Secular Evolution of Hierarchical Planetary System…
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…
The eccentricity evolution of multiple planet systems can provide valuable constraints on planet formation models. Unfortunately, the inevitable uncertainties in the current orbital elements can lead to significant ambiguities in the nature…
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…
We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits. The dynamics are investigated in wide ranges of semi-major axes ratios (0.1-0.667), and planetary…
The secular approximation for the evolution of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple-star systems. In this approximation the orbits may change shape and…
The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the…
Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the…
We investigate the non-resonant, 3-D (spatial) model of the hierarchical system composed of point-mass stellar (or sub-stellar) binary and a low-mass companion (a circumbinary planet or a brown dwarf). We take into account the leading…
The distribution of period ratios for 580 known two-planet systems is apparently nonuniform, with several sharp peaks and troughs. In particular, the vicinity of the 2:1 commensurability seems to have a deficit of systems. Using Monte Carlo…
Two planets with orbital period ratio approximately 10:1 have been discovered around the star HD 83443. The inner and more massive planet, HD 83443b, has the smallest semi-major axis among all currently known exoplanets. Unlike other short…
Since exoplanets were detected using the radial velocity method, they have revealed a diverse distribution of orbital configurations. Amongst these are planets in highly eccentric orbits (e > 0.5). Most of these systems consist of a single…
We construct a secular theory of a coplanar system of N-planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual interactions, we consider the general…
We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20 degrees). Using the…
We determine the evolution of a giant planet-disk system that orbits a member of a binary star system and is mildly inclined with respect to the binary orbital plane. The planet orbit and disk are initially mutually coplanar. We analyze the…
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 study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincar\'e canonical variables, we determine the fundamental…
We study orbital evolution of multi-planet systems that form a resonant chain, with nearest neighbours close to first order commensurabilities, incorporating orbital circularisation produced by tidal interaction with the central star. We…
We study the secular gravitational dynamics of quadruple systems consisting of a hierarchical triple system orbited by a fourth body. These systems can be decomposed into three binary systems with increasing semimajor axes, binaries A, B…
We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation…
Recent observations have shown that at least some close-in exoplanets maintain eccentric orbits despite tidal circularization timescales that are typically shorter than stellar ages. We explore gravitational interactions with a distant…