Related papers: Stability Boundaries for Resonant Migrating Planet…
A resonant chain may be formed in a multi-planetary system when ratios of the orbital periods can be expressed as ratios of small integers $T_1:T_2: \cdots :T_N=k_1: k_2: \cdots: k_N$. We investigate the dynamics and possible formation of…
A question driving many studies is whether the thousands of exoplanets known today typically formed where we observe them or formed further out in the disk and migrated in. Early discoveries of giant exoplanets orbiting near their host…
Context: The Circular Restricted Three-Body Problem provides a fundamental framework for understanding resonant dynamics in binary star systems. Aims: We develop a unified Hamiltonian formulation for mean-motion resonances that encompasses…
We investigate the evolution of two-planet systems embedded in a protoplanetary disc, which are composed of a Jupiter-mass planet plus another body located further out in the disc. We consider outermost planets with masses ranging from 10…
Early dynamical evolution of close-in planetary systems is shaped by an intricate combination of planetary gravitational interactions, orbital migration, and dissipative effects. While the process of convergent orbital migration is expected…
Orbits of known extrasolar planets that are located outside the tidal circularization regions of their parent stars are often substantially eccentric. By contrast, planetary orbits in our Solar System are approximately circular, reflecting…
We derive the transit timing variations (TTVs) of two planets near a second order mean motion resonance on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of $j n_2-(j-2)n_1$, where $j…
The convergent migration of two planets in a gaseous disc can lead to capture in mean motion resonance (MMR). In addition, pairs of planets in or near MMRs are known to produce strong transit timing variations (TTVs). In this paper we study…
We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets' masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos…
We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…
Co-orbital planets (in a $1:1$ mean motion resonance) can be formed within a Laplace resonance chain. Here, we develop a secular model to study the dynamics of the resonance chain $p:p:p+1$, where the co-orbital pair is in a first-order…
Our concern here is the nature of secondary resonances--commensurabilities between apsidal and libration periods lying within first-order mean motion resonances [mmr] in the solar system. At the 4/3 and 3/2 mmr in the asteroid belt, we find…
The spatial distribution of Kuiper belt objects (KBOs) in 2:1 exterior resonance with Neptune constrains that planet's migration history. Numerical simulations demonstrate that fast planetary migration generates a larger population of KBOs…
Mean motion resonances (MMR) are a frequent phenomenon among extrasolar planetary systems. Current observations indicate that many systems have planets that are close to or inside the 2:1 MMR, when the orbital period of one of the planets…
We present a mechanism related to the migration of giant protoplanets embedded in a protoplanetary disc whereby a giant protoplanet is caught up, before having migrated all the way to the central star, by a lighter outer giant protoplanet.…
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),…
We consider planetary systems evolving under the effect of a Stokes-type dissipative force mimicking the outcome of a type II migration process. As inward migration proceeds and the planets follow the circular family (they start on circular…
Mean motion resonances (MMRs) are a key phenomenon in orbital dynamics. The traditional disturbing function expansion in celestial mechanics shows that, at low eccentricities, $p$:$p-q$ MMRs exhibit a clear hierarchy of strengths, scaling…
This study employs numerical simulations to explore the relationship between the dynamical instability of planetary systems and the uniformity of planetary masses within the system, quantified by the Gini index. Our findings reveal a…
The existence of extrasolar planets with short orbital periods suggests that planetary migration induced by tidal interaction with the protoplanetary disk is important. Cores and terrestrial planets may undergo migration as they form. In…