Surveys have revealed many multi-planet systems containing super-Earths and Neptunes in orbits of a few days to a few months. There is debate whether in situ assembly or inward migration is the dominant mechanism of the formation of such planetary systems. Simulations suggest that migration creates tightly packed systems with planets whose orbital periods may be expressed as ratios of small integers (resonances), often in a many-planet series (chain). In the hundreds of multi-planet systems of sub-Neptunes, more planet pairs are observed near resonances than would generally be expected, but no individual system has hitherto been identified that must have been formed by migration. Proximity to resonance enables the detection of planets perturbing each other. Here we report transit timing variations of the four planets in the Kepler-223 system, model these variations as resonant-angle librations, and compute the long-term stability of the resonant chain. The architecture of Kepler-223 is too finely tuned to have been formed by scattering, and our numerical simulations demonstrate that its properties are natural outcomes of the migration hypothesis. Similar systems could be destabilized by any of several mechanisms, contributing to the observed orbital-period distribution, where many planets are not in resonances. Planetesimal interactions in particular are thought to be responsible for establishing the current orbits of the four giant planets in the Solar System by disrupting a theoretical initial resonant chain similar to that observed in Kepler-223.

HR 8799 is a nearby star hosting at least four ∼ 10 m Jup planets in wide orbits up to ∼ 70 au, detected through the direct, high-contrast infrared imaging. Large companions and debris disks reported interior to ∼ 10 au, and exterior to ∼ 100 au indicate massive protoplanetary disc in the past. The dynamical state of the HR 8799 system is not yet fully resolved, due to limited astrometric data covering tiny orbital arcs. We construct a new, orbital model of the HR 8799 system, assuming rapid migration of the planets after their formation in wider orbits. We found that the HR 8799 planets are likely involved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary orbits are coplanar with the stellar equator and inclined by ∼ 25 • to the sky plane. This best-fit orbital configuration matches astrometry, debris disk models, and mass estimates from cooling models. The multiple MMR is stable for the age of the star ∼ 160 Myr, for at least 1 Gyr unless significant perturbations to the N-body dynamics are present. We predict four configurations with the fifth hypothetical innermost planet HR 8799f in ∼ 9.7 au, or ∼ 7.5 au orbit, extending the MMR chain to triple Laplace resonance 1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings may establish strong boundary conditions for the system formation and its early history.

We investigate the dynamical stability of the Kepler-60 planetary system with three super-Earths. We determine their orbital elements and masses by Transit Timing Variation (TTV) data spanning quarters Q1-Q16 of the KEPLER mission. The system is dynamically active but the TTV data constrain masses to ∼ 4 m ⊕ and orbits in safely wide stable zones. The observations prefer two types of solutions. The true three-body Laplace MMR exhibits the critical angle librating around 45 • and aligned apsides of the inner and outer pair of planets. In the Laplace MMR formed through a chain of two-planet 5:4 and 4:3 MMRs, all critical angles librate with small amplitudes ∼ 30 • and apsidal lines in planet's pairs are anti-aligned. The system is simultaneously locked in a three-body MMR with librations amplitude 10 o . The true Laplace MMR can evolve towards a chain of two-body MMRs in the presence of planetary migration. Therefore the three-body MMR formed in this way seems to be more likely state of the system. However, the true three-body MMR cannot be disregarded a priori and it remains a puzzling configuration that may challenge the planet formation theory.