Related papers: On the relativistic Lagrange-Laplace secular dynam…
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…
This paper studies the long term evolution of planetary systems containing short-period planets, including the effects of tidal circularization, secular excitation of eccentricity by companion planets, and stellar damping. For planetary…
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…
This paper studies the effects of dynamical interactions among the planets in observed extrasolar planetary systems, including hypothetical additional bodies, with a focus on secular perturbations. These interactions cause 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 develop a simplified model for studying the long-term evolution of giant planets in protoplanetary discs. The model accounts for the eccentricity evolution of the planets and the dynamics of eccentric discs under the influences of…
The secular Laplace-Lagrange orbital solution, decomposing eccentricities into a set of uniformly precessing eigenmodes is a classical result that is typically solved numerically. However, in the limit where orbits are closely spaced,…
The long-term evolution of astrophysical systems is driven by a Hamiltonian that is independent of the fast angle. As this Hamiltonian may contain explicitly time-dependent parameters, the conservation of mechanical energy is not guaranteed…
The long-term habitability of Earth-like planets requires low orbital eccentricities. A secular perturbation from a distant stellar companion is a very important mechanism in exciting planetary eccentricities, as many of the extrasolar…
This paper considers general relativistic (GR) effects in currently observed extrasolar planetary systems. Although GR corrections are small, they can compete with secular interactions in these systems and thereby play an important role.…
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and…
We describe the long-term evolution of compact systems of terrestrial planets, using a set of simulations that match the statistical properties of the observed exoplanet distribution. The evolution is driven by tidal dissipation in the…
Exoplanets are often found with short periods or high eccentricities, and multiple-planet systems are often in resonance. They require dynamical theories that describe more extreme motions than those of the relatively placid planetary…
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 Lagrange planetary equations are used to study to secular evolution of a small, eccentric satellite that orbits within a narrow gap in a broad, self-gravitating planetary ring. These equations show that the satellite's secular…
We present a method to study the time variation of the orbital parameters of a Post-Keplerian binary system undergoing a generic external perturbation. The method is the relativistic extension of the planetary Lagrangian equations. The…
The non-resonant secular dynamics of compact planetary systems are modeled by a perturbing function which is usually expanded in eccentricity and absolute inclination with respect to the invariant plane. Here, the expressions are given in a…
We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. We use the symplectic integrator SyMBA to numerically…
Pairs of planets in a system may end up close to their host star on eccentric orbits as a consequence of planet planet scattering, Kozai or secular migration. In this scenario, general relativity and secular perturbations have comparable…