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We study the stability of systems of three giant planets orbiting 3 - 8 M_Sol stars at orbital distances of >10 au as the host star ages through the Main Sequence (MS) and well into the White Dwarf (WD) stage. Systems are stable on the MS…
The presence of mean motion resonances (MMRs) complicates analysis and fitting of planetary systems observed through the radial velocity (RV) technique. MMR can allow planets to remain stable in regions of phase space where strong…
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…
Classical analytic theories of the solar system indicate that it is stable, but numerical integrations suggest that it is chaotic. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the Jovian…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
The origin of Mercury still remains poorly understood compared to the other rocky planets of the Solar System. One of the most relevant constraints that any formation model has to fulfill refers to its internal structure, with a predominant…
This paper is concerned with intermediate range periodicity in the sunspot area spectrum. An empirical model of sunspot area emergence based on Mercury planet conjunctions was developed and the spectra of the model variation and the sunspot…
The motion of Mercury using numerical methods in the framework of a model including only the non-relativistic Newtonian gravitational interactions of the solar system, 9 planets in translation (including Pluto) around the sun has been…
Rare event schemes require an approximation of the probability of the rare event as a function of system state. Finding an appropriate reaction coordinate is typically the most challenging aspect of applying a rare event scheme. Here we…
Mercury is notoriously difficult to form in solar system simulations, due to its small mass and iron-rich composition. Smooth particle hydrodynamics simulations of collisions have found that a Mercury-like body could be formed by one or…
Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR),…
How might an advanced alien civilization manipulate the orbits within a planetary system to create a durable signpost that communicates its existence? While it is still debated whether such a purposeful advertisement would be prudent and…
Earth-based radar observations of the rotational dynamics of Mercury (Margot et al. 2012) combined with the determination of its gravity field by MESSENGER (Smith et al. 2012) give clues on the internal structure of Mercury, in particular…
We combine analytical understanding of resonant dynamics in two-planet systems with machine learning techniques to train a model capable of robustly classifying stability in compact multi-planet systems over long timescales of $10^9$…
It is known since the seminal study of Laskar (1989) that the inner planetary system is chaotic with respect to its orbits and even escapes are not impossible, although in time scales of billions of years. The aim of this investigation is…
Advances in computing power and numerical methodologies over the past several decades sparked a prolific output of dynamical investigations of the late stages of terrestrial planet formation. Among other peculiar inner solar system…
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…
Despite the discovery of thousands of exoplanets in recent years, the number of known exoplanets in star clusters remains tiny. This may be a consequence of close stellar encounters perturbing the dynamical evolution of planetary systems in…
The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the…
A large proportion of transiting planetary systems appear to possess only a single planet as opposed to multiple transiting planets. This excess of singles is indicative of significant mutual inclinations existing within a large number of…