Related papers: A secular theory of coplanar, non-resonant planeta…
A restricted planar circular three-body system, consisting of the Sun and two planets, is studied as a simple model for a planetary system. The mass of the inner planet is considered to be larger and the system is assumed to be moving in a…
The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the…
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…
A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on…
Over the last decades, there has been a tremendous increase in research on extrasolar planets. Many exosolar systems, which consist of a Star and two inclined Planets, seem to be locked in 4/3, 3/2, 2/1, 5/2, 3/1 and 4/1 mean motion…
It has been demonstrated that systems of tightly packed inner planets with giant exterior companions tend to have less regular orbital spacings than those without such companions. We investigate whether this observed increase in the gap…
A general non-relativistic field theory on the plane with couplings to an arbitrary number of abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We…
Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system…
A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem…
We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…
A new general approach is introduced for definining an optimum zero-order Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the…
We study a simple model for which perturbation theory gives ultravioletly divergent results. We show that when the eigen-solution problem of the Hamiltonian of the model is treated nonperturbatively, it is possible for eigenenergies of the…
We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in the light of recent models of solar system evolution. We develop…
We consider a planar Hamiltonian system of the type $Jz' = \nabla_z H(t,z)$, where $H: \mathbb{R} \times \mathbb{R}^2 \to \mathbb{R}$ is a function periodic in the time variable, such that $\nabla_z H(t,0) \equiv 0$ and $\nabla_z H(t,z)$ is…
We provide an 'effective theory' of tidal dissipation in extrasolar planet systems by empirically calibrating a model for the equilibrium tide. The model is valid to high order in eccentricity and parameterised by two constants of bulk…
We derive the conservative secular evolution of precessing compact binaries to second post-Newtonian order accuracy, with leading-order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. The emerging closed system of…
[Abridged] The recent discovery of a transiting planet on a non-circular orbit with a massive highly eccentric companion orbiting HAT-P-13 offers the possibility of probing the structure of the short-period planet. The ability to do this…
Previous full-lifetime simulations of single-star multi-planet systems across all phases of stellar evolution have predominately assumed coplanar or nearly-coplanar orbits. Here we assess the consequences of this assumption by removing it…
The calculation of observable averages in non-equilibrium regimes is one of the most important problems in statistical physics. Using the Hamiltonian approach of nonlinear response theory, we obtain a series expansion of the average excess…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems with well separated components. We investigate systems with initially circular and coplanar orbits and comparable masses. The technique is based on…