Most stars form in some sort of stellar cluster or association. In such environments the number density of stars is much higher than in the solar neighbourhood, which means that close encounters between stars may be relatively common. Using numerical simulations we quantify the fraction of single stars in the solar neighbourhood that have never suffered a close encounter or been part of a binary system. We call such stars singletons. Furthermore, we study what would happen to a solar-system-like planetary system if its host star was exchanged into a binary system during an exchange encounter in a young stellar cluster. The perturbation of the companion star might in such a system trigger strong planet-planet scatterings. This would subsequently lead to the ejection of one or more planets, leaving those remaining on tighter and more eccentric orbits. We find that only if the gas giants in solar-system-like planetary systems most often have rather similar masses does the resulting eccentricity distribution resemble that of the observed extrasolar planets.

We consider the hierarchical three-body problem, with a binary and a planet-mass object. We investigate the effect of general relativity (GR) corrections to the Newtonian interactions. We focus on the Lidov-Kozai resonance, and the secular dynamics are analyzed over wide ranges of the semi-major axes and masses. We found regions in the parameter space where the GR corrections may be important for the long-term dynamics. We try to constrain the inclinations of putative Jovian planets in the recently announced binary systems of HD 4113 and HD 156846.

The planetary system of HD 69830 is uniquely constrained by observations of (i) an infrared excess indicative of a debris disk with warm dust and (ii) radial velocity variations indicative of three planets. This presents a valuable opportunity to test planet formation models by integrating dynamical models of planetary formation and migration with those for the sculpting of a dust-producing planetesimal disk. We perform n-body simulations and investigate the excitation of both planet and planetesimal eccentricities, the accretion of planetesimals onto the planets, and the clearing of a planetesimal disk by the planets as they grow in mass and migrate through the disk. In simulations tuned to closely follow previous semi-analytic models for the growth and migration of the planets, we find that the inner planet accretes significantly more planetesimals than previously estimated. We find that eccentricity excitation due to mutual planetary perturbations during and after the migration do not naturally produce the observed eccentricities. Our simulations suggest that this discrepancy may be reduced or possibly reconciled if the planets are significantly more massive than expected (possible if the planetary system's angular momentum were nearly parallel to our line of sight). Even if the planets are significantly more massive than previously assumed, we find that the migrating planets are inefficient at clearing the outer planetesimal disk and that a significant fraction of the planetesimal population beyond 1 AU remains bound on moderately eccentric and inclined orbits. While much of the remaining planetesimal belt would have eroded via a collisional cascade and radiation pressure, we explore whether some of the highly excited planetesimals may be able to persist over the age of the central star, producing the dust observed in the HD 69830 system.

Recently the multi-planet system OGLE-06-109L has been discovered, where the two planets show similarities with the Jupiter-Saturn configuration of our Solar System. The orbital parameters of this new system indicate a high inclination for the outer planet. In this parameter study we show the stability of the two planets for different relative inclinations and semi-major axes of the two planets. Using the errors in semi-major axes given by the observations, the best result concerning dynamical stability has been obtained when planet b is at 2.1 AU and planet c at 5.1 AU. The worst result has been found for the closest configuration, when planet b is at 2.5 AU and planet c at 4.1 AU. The second part of this study examines the stability of test planets in the so-called habitable zone (HZ). This is the region around a star where liquid water is stable on the surface of an Earth-like planet. The stability of test-planets in the HZ is shown for different relative inclinations (up to 50°) of the two giant planets in OGLE-06-109L system and then compared to the results of a similar study in the Jupiter-Saturn system. For high relative inclinations we observe strong perturbations in the HZ in both results, which is probably caused by the Kozai resonance. In the OGLE-06-109L system we also observe secular perturbations for low inclinations around 0.3 AU. For certain mutual inclinations of the two giant planets we have found nearly circular planetary motion in the HZ.

We analyze the long-term tidal evolution of a single-planet system through the use of numerical simulations and averaged equations giving the variations of the semi-major axis and eccentricity of the relative orbit. For different types of planets, we compute the variations due to the planetary and stellar tides. We then calculate the critical value of the eccentricity for which the stellar tide becomes dominant over the planetary tide. The timescales for orbital decay and circularization are also discussed and compared.

Direct imaging searches have begun to detect planetary and brown dwarf companions and to place constraints on the presence of giant planets at large separations from their host star. This work helps to motivate such planet searches by predicting a population of young giant planets that could be detectable by direct imaging campaigns. Both the classical core accretion and the gravitational instability model for planet formation are hard-pressed to form such planets in situ. Therefore, direct imaging searches have traditionally appealed to the possibility of in situ planet formation via a large scale gravitational instability. Here, we show that dynamical instabilities among planetary systems that originally formed multiple giant planets much closer to the host star could produce a population of giant planets at large separations. The number and distribution of such planets is a strong function of time, complicating the statistical analysis of direct imaging surveys. The number and radial distribution of such planets is related to the number of giant planets formed per host star and the timescale for the disk evolution. Thus, direct imaging programs with sufficient sensitivity and survey size could place interesting constraints on planet formation models.

This timely meeting (appropriately held in Toruń, the “city of Copernicus”) provided an excellent venue for researchers to review the theoretical and observational progress in the intervening years, share recent results, and make preparations for progress in the quests to learn whether our Solar System is typical and to understand how our own Solar System relates to the rest of the Universe. It had been nearly six years since the last major scientific meeting focusing soley on multiple planet systems and planets in multiple star systems in Saas Fee, Switzerland during September of 2002 (Udry et al. 2006). Here I review some of the observational and theoretical progress in understanding multi-body systems reported in Toruń.