Related papers: Kepler's Platonic Model and Its Application to Exo…
The known extrasolar multiple-planet systems share a surprising dynamical attribute: they cluster just beyond the Hill stability boundary. Here we show that the planet-planet scattering model, which naturally explains the observed exoplanet…
We develop a general method to fit the planetary distribution function (PLDF) to exoplanet survey data. This maximum likelihood method accommodates more than one planet per star and any number of planet or target star properties.…
We investigate the distributions of the orbital period ratios of adjacent planets in high multiplicity \kepler\ systems (four or more planets) and low multiplicity systems (two planets). Modeling the low multiplicity sample as essentially…
Although the discovery of the chaotic motion of the inner planets in the solar system dates back to more than thirty years ago, the secular chaos of their orbits still dares more analytical analyses. Apart from the high-dimensional…
Although resonant planets have orbital periods near commensurability, resonance is also dictated by other factors, such as the planets' eccentricities and masses, and therefore must be confirmed through a study of the system's dynamics.…
One of the most important developments in exoplanet science in the past decade is the discovery of multi-planet systems with sub-Neptune-sized planets interior to 1~AU. This chapter explores the architectures of these planetary systems,…
Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. These…
In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try…
We examine the formation of planets around binary stars in light of the recently discovered systems Kepler 16, 34 and 35. We conduct hydrodynamical simulations of self gravitating disks around binary systems. The selected binary and disk…
Transit surveys have revealed a significant population of compact multi-planet systems, containing several sub-Neptune-mass planets on close-in, tightly-packed orbits. These systems are thought to have formed through a final phase of giant…
Instabilities and strong dynamical interactions between several giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities would…
We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of the Earth, respectively. The binary star consists of a…
The exoplanet population characterized by relatively short orbital periods ($P<100$ d) around solar-type stars is dominated by super-Earths and sub-Neptunes. However, these planets are missing in our Solar System and the reason behind this…
Most attempts to unify general relativity with the standard model of particle physics predict violations of the equivalence principle associated in some way with the composition of the test masses. We test this idea by using observational…
The recent Kepler discovery of KOI-152 reveals a system of three hot super-Earth candidates that are in or near a 4:2:1 mean motion resonance. It is unlikely that they formed in situ, the planets probably underwent orbital migration during…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
A successful solar system model must reproduce the four terrestrial planets. Here, we focus on 1) the likelihood of forming Mercury and the four terrestrial planets in the same system (a 4-P system); 2) the orbital properties and masses of…
The population of exoplanetary systems detected by Kepler provides opportunities to refine our understanding of planet formation. Unraveling the conditions needed to produce the observed exoplanets will sallow us to make informed…
The existence of planets orbiting a central binary star system immediately raises questions regarding their formation and dynamical evolution. Recent discoveries of circumbinary planets by the Kepler space telescope has shown that some of…
While Kepler was still working in Graz during 1598, some letters to his mentor Michael Maestlin demonstrate his interest in astronomical clocks and machines. The first letter, dated January 6, 1598 contains a detailed description of a…