相关论文: The interval description of dynamics of celestial …
Instabilities and strong dynamical interactions between multiple giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities seem…
This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson…
We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in $\sim20\%$ of the cases on a wide range of timescales (up to $5\times10^9$ orbits) and over an…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
We show that stability of planetary systems is intimately connected with their internal order. An arbitrary initial distribution of planets is susceptible to catastrophic events in which planets either collide or are ejected from the…
A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by…
The existence of elliptic periodic solutions of a perturbed Kepler problem is proved. The equations are in the plane and the perturbation depends periodically on time. The proof is based on a local description of the symplectic group in two…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
Eighty planetary systems of two or more planets are known to orbit stars other than the Sun. For most, the data can be sufficiently explained by non-interacting Keplerian orbits, so the dynamical interactions of these systems have not been…
The dynamics of any spherical cosmology with a scalar field (`scalaron') coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the `time' parameter. The…
We discuss the influence of the cosmological constant $\Lambda$ on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of…
We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between…
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…
Several dynamical systems of interest in celestial mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin-orbit model and the…
The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly-averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure…
The orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in the Keplerian…
The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…
Using Gauss' averaged equations, we compute the secular relativistic effects generated by the Sun on the argument of the perihelion and the mean anomaly of an orbit. Then we test different alternative simpler models that have been proposed…
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…
The Kepler space mission has detected a large number of exoplanets in multiple transiting planet systems. Previous studies found that these Kepler multiple planet systems exhibit an intra-system uniformity, namely planets in the same system…