Related papers: Long-term instability of the inner Solar System: n…
We consider time-periodic perturbations of analytically integrable systems in the sense of Bogoyavlenskij and study their \emph{real-meromorphic} nonintegrability, using a generalized version due to Ayoul and Zung of the Morales-Ramis…
We consider a basic planetary system composed by a Sun like star, a Jupiter-like planet an a Neptune-like planet in a wide range of orbital configurations not limited to the hierarchical case. We present atlases of resonances showing the…
The upcoming space missions, MESSENGER and BepiColombo with onboard instrumentation capable of measuring the rotational parameters stimulate the objective to reach an accurate theory of the rotational motion of Mercury. For obtaining the…
Of the solar system's four terrestrial planets, the origin of Mercury is perhaps the most mysterious. Modern numerical simulations designed to model the dynamics of terrestrial planet formation systematically fail to replicate Mercury;…
Our Solar system is almost entirely devoid of material interior to Mercury's orbit, in sharp contrast to the multiple Earth masses of material commonly residing within the analogous region of extrasolar planetary systems. Recent work has…
We perform long-term simulations, up to ten billion years, of closely-spaced configurations of 2 -- 6 planets, each as massive as the Earth, traveling on nested orbits about either stellar component in $\alpha$ Centauri AB. The innermost…
The three-planet extrasolar system of HD 181433 has been detected with HARPS. The best-fit solution, announced by the discovery team, describes a highly unstable, self-disrupting configuration. In fact, a narrow observational window, only…
The Jupiter-Saturn 2:5 near-commensurability is analyzed in a fully analytic Hamiltonian planetary theory. Computations for the Sun-Jupiter-Saturn system, extending to the third order of the masses and to the 8th degree in the…
The transiting planet K2-18 b is one of the best candidates for a relatively nearby world harboring biological life. The long-term orbital evolution of this planet is investigated using theoretical and purely numerical techniques for two…
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…
Inter-cycle variations in the series of 11-year solar activity cycles have a significant impact on both the space environment and climate. Whether solar cycle variability is dominated by deterministic chaos or stochastic perturbations…
We present nonlinear three-dimensional simulations of the stably-stratified portion of the solar tachocline in which the rotational shear is maintained by mechanical forcing. When a broad toroidal field profile is specified as an initial…
We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small…
We describe numerical tools for the stability analysis of extrasolar planetary systems. In particular, we consider the relative Poincare variables and symplectic integration of the equations of motion. We apply the tangent map to derive a…
Most stars form in star clusters and stellar associated. To understand the roles of star cluster environments in shaping the dynamical evolution of planetary systems, we carry out direct $N$-body simulations of four planetary systems models…
A planetary instability occurring at time $<100$ My after formation of the giant planets in our solar system can be responsible for some characteristics of the inner solar system. However, the actual influence of the instability on the…
Kepler-56 is a multi-planet system containing two coplanar inner planets that are in orbits misaligned with respect to the spin axis of the host star, and an outer planet. Various mechanisms have been proposed to explain the broad…
Circumstantial evidence suggests that most known extra-solar planetary systems are survivors of violent dynamical instabilities. Here we explore how giant planet instabilities affect the formation and survival of terrestrial planets. We…
Disks of bodies orbiting a much more massive central object are extremely common in astrophysics. When the orbits comprising such disks are eccentric, we show they are susceptible to a new dynamical instability. Gravitational forces between…
We present results of numerical simulations which examine the dynamical stability of known planetary systems, a star with two or more planets. First we vary the initial conditions of each system based on observational data. We then…