Related papers: Secular Orbit Evolution in Systems with a Strong E…
The subject of this paper is the secular behaviour of a pair of planets evolving under dissipative forces. In particular, we investigate the case when dissipative forces affect the planetary semi-major axes and the planets move…
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…
Hamiltonian normal forms allow for the analytical approximation of center manifold trajectories and their invariant manifolds through the separation of the saddle and center subspaces that make up the dynamics at the collinear libration…
We analyse the secular dynamics of planets on S-type coplanar orbits in tight binary systems, based on first- and second-order analytical models, and compare their predictions with full N-body simulations. The perturbation parameter adopted…
Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional…
We analytically work out several effects which a violation of the Strong Equivalence Principle (SEP) induces on the orbital motion of a binary system constituted of self-gravitating bodies immersed in a constant and uniform external field.…
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…
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in…
Triple body systems are prevalent in nature, from planetary to stellar to supermassive black hole scales. In a hierarchical triple system, oscillations of the inner orbit's eccentricity and inclination can be induced on secular timescales.…
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…
Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help…
We present a self-consistent model for the tidal evolution of circumbinary planets. Based on the weak-friction model, we derive expressions of the resulting forces and torques considering complete tidal interactions between all the bodies…
Planet-planet perturbations can cause planets' orbital elements to change on secular timescales. Previous work has evaluated the nodal precession rate for planets in the limit of low $\alpha$ (semi-major axis ratio, 0$<$$\alpha$$\leq$1).…
In the framework of multi-body dynamics, successive encounters with a third body, even if well outside of its sphere of influence, can noticeably alter the trajectory of a spacecraft. Examples of these effects have already been exploited by…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different…
La teoria di Lagrange per i moti secolari delle eccentricit\`a ed inclinazioni delle orbite planetarie si fondava su un'approssimazione, dettata in larga misura dalla complessit\`a dei calcoli necessari, che consisteva nel considerare solo…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
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…
I consider the dynamics of mean motion resonances between pairs of co-planar planets and derive a new integrable Hamiltonian model for planets' resonant motion. The new model generalizes previously-derived integrable Hamiltonians for…