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We study the time evolution of two protoplanets still embedded in a protoplanetary disk. The results of two different numerical approaches are presented and compared. In the first approach, the motion of the disk material is computed with…

Astrophysics · Physics 2009-11-10 Wilhelm Kley , Jochen Peitz , Geoffrey Bryden

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array…

Earth and Planetary Astrophysics · Physics 2017-09-05 Volker Hoffmann , Simon L. Grimm , Ben Moore , Joachim Stadel

The recently discovered planetary system HD45364 which consists of a Jupiter and Saturn mass planet is very likely in a 3:2 mean motion resonance. The standard scenario to form planetary commensurabilities is convergent migration of two…

Earth and Planetary Astrophysics · Physics 2010-01-29 Hanno Rein , John C. B. Papaloizou , Wilhelm Kley

Planetary systems can evolve dynamically even after the planets themselves have fully formed, and there is circumstantial evidence that most planetary systems become unstable after the disappearance of the gaseous protoplanetary disk.…

Earth and Planetary Astrophysics · Physics 2025-08-20 Antoine C. Petit , Gabriele Pichierri , Max Goldberg , Alessandro Morbidelli

Aims. We clarify the response of extrasolar planetary systems in a 2:1 mean motion commensurability with masses ranging from the super Jovian range to the terrestrial range to stochastic forcing that could result from protoplanetary disk…

Astrophysics · Physics 2009-04-14 Hanno Rein , John C. B. Papaloizou

We study the evolution of a system consisting of two protoplanets still embedded in a protoplanetary disk. Results of two different numerical approaches are presented. In the first kind of model the motion of the disk material is followed…

Astrophysics · Physics 2023-07-19 Willy Kley

Migration is a key ingredient for the formation of close-in super-Earth and mini-Neptune systems, as it sets in which resonances planets can be trapped. Slower migration rates result in wider resonance configurations compared to higher…

Earth and Planetary Astrophysics · Physics 2024-12-18 Bertram Bitsch , Andre Izidoro

We summarize the analytic model and numerical simulations of stochastically forced planets in a turbulent disk presented in a recent paper by Rein and Papaloizou. We identify two modes of libration in systems with planets in mean motion…

Earth and Planetary Astrophysics · Physics 2009-12-22 Hanno Rein , John C. B. Papaloizou

A significant number of the known multiple exoplanetary systems are containing a pair of giant planets engaged in a low order mean motion resonance. Such a resonant condition protects the dynamics of these planets resulting in very stable…

Astrophysics · Physics 2009-11-11 Zsolt Sandor , Willy Kley

The main properties of the observed extrasolar planets are reviewed with respect to their relevance to the formation scenario of planetary systems. Results of numerical computations of embedded planets in viscously evolving disks are…

Astrophysics · Physics 2007-05-23 Willy Kley

In some planetary systems, the orbital periods of two of its members present a commensurability, usually known by mean-motion resonance. These resonances greatly enhance the mutual gravitational influence of the planets. As a consequence,…

Earth and Planetary Astrophysics · Physics 2019-09-18 Alexandre C. M. Correia , Jean-Baptiste Delisle , Jacques Laskar

The formation of resonant pairs of planets in exoplanetary systems involves planetary migration in the protoplanetary disc. After a resonant capture, the subsequent migration in this configuration leads to a large increase of planetary…

Astrophysics · Physics 2009-10-22 A. Crida , Zs. Sándor , W. Kley

Resonant planetary migration in protoplanetary discs can lead to an interplay between the resonant interaction of planets and their disc torques called overstability. While theoretical predictions and N-body simulations hinted at its…

The discovery of multi-planet extrasolar systems has kindled interest in using their orbital evolution as a probe of planet formation. Accurate descriptions of planetary orbits identify systems which could hide additional planets or be in a…

Earth and Planetary Astrophysics · Physics 2015-05-18 Dimitri Veras , Eric B. Ford

The formation of the solar system's giant planets predated the ultimate epoch of massive impacts that concluded the process of terrestrial planet formation. Following their formation, the giant planets' orbits evolved through an episode of…

Earth and Planetary Astrophysics · Physics 2021-06-23 Matthew S. Clement , Nathan A. Kaib , Sean N. Raymond , John E. Chambers

Orbital evolution is a critical process that sculpts planetary systems, particularly during their early stages where planet-disk interactions are expected to lead to the formation of resonant chains. Despite the theoretically expected…

Earth and Planetary Astrophysics · Physics 2024-08-06 Vighnesh Nagpal , Max Goldberg , Konstantin Batygin

The most accurate method for modelling planetary migration and hence the formation of resonant systems is using hydrodynamical simulations. Usually, the force (torque) acting on a planet is calculated using the forces from the gas disc and…

Earth and Planetary Astrophysics · Physics 2020-04-08 S. Ataiee , W. Kley

The great diversity of extrasolar planetary systems has challenged our understanding of how planets form, and how their orbits evolve as they form. Among the various processes that may account for this diversity, the gravitational…

In the context of low-viscosity protoplanetary discs (PPDs), the formation scenarios of the Solar System should be revisited. In particular, the Jupiter-Saturn pair has been shown to lock in the 2:1 mean motion resonance while migrating…

Earth and Planetary Astrophysics · Physics 2024-07-01 Philippine Griveaud , Aurélien Crida , Antoine C. Petit , Elena Lega , Alessandro Morbidelli

In the past two decades, transit surveys have revealed a class of planets with thick atmospheres -- sub-Neptunes -- that must have completed their accretion in protoplanet disks. When planets form in the gaseous disk, the gravitational…

Earth and Planetary Astrophysics · Physics 2025-06-10 Shuo Huang , Chris Ormel , Simon Portegies Zwart , Eiichiro Kokubo , Tian Yi
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