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This chapter concerns the long-term dynamical evolution of planetary systems from both theoretical and observational perspectives. We begin by discussing the planet-planet interactions that take place within our own Solar System. We then…
The high-multiplicity exoplanet systems are generally more tightly packed when compared to the solar system. Such compact multi-planet systems are often susceptible to dynamical instability. We investigate the impact of dynamical…
Planetary satellites are an integral part of the heirarchy of planetary systems. Here we make two predictions concerning their formation. First, primordial satellites, which have an array of distinguishing characteristics, form only around…
Observations of exoplanets and protoplanetary disks show that binary stellar systems can host planets in stable orbits. Given the high binary fraction among stars, the contribution of binary systems to Galactic habitability should be…
At present, because of observational selection effects, we know of no exoplanetary systems with any planetary masses close to that of the Earth. We have therefore used computer models to see whether such planets could be dynamically stable…
Many discovered multiplanet systems are tightly packed. This implies that wide parameter ranges in masses and orbital elements can be dynamically unstable and ruled out. We present a case study of Kepler-23, a compact three-planet system…
The rotation of a star and the revolutions of its planets are not necessarily aligned. This article reviews the measurement techniques, key findings, and theoretical interpretations related to the obliquities (spin-orbit angles) of…
The majority of binary star systems that host exoplanets will spend the first portion of their lives within a star-forming cluster that may drive dynamical evolution of the binary-planet system. We perform numerical simulations of S-type…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
Discoveries of exoplanets using the radial velocity method are progressively reaching out to increasingly longer orbital periods as the duration of surveys continues to climb. The improving sensitivity to potential Jupiter analogs is…
We study the stability of systems of three giant planets orbiting 3 - 8 M_Sol stars at orbital distances of >10 au as the host star ages through the Main Sequence (MS) and well into the White Dwarf (WD) stage. Systems are stable on the MS…
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…
All 4 giant planets in the Solar System host systems of multiple moons, whereas the terrestrial planets only host up to 2 moons. The Earth can capture small asteroids as temporary satellites, which begs the question as to how many moons…
With the increasing number of detected exoplanet samples, the statistical properties of planetary systems have become much clearer. In this review, we summarize the major statistics that have been revealed mainly by radial velocity and…
We evaluate the extent of the regions within the $\alpha$ Centauri AB star system where small planets are able to orbit for billion-year timescales, and we calculate the positions on the sky plane where planets on stable orbits about either…
Extrasolar multiple-planet systems provide valuable opportunities for testing theories of planet formation and evolution. The architectures of the known multiple-planet systems demonstrate a fascinating level of diversity, which motivates…
Among other things, studies of the formation and evolution of planetary systems currently draw on two important observational resources: the precise characterization available for planets that transit their parent stars and the frequency…
Stability of supermassive stars embedded in hot dark matter is investigated on the base of the energetic method. Stability effect of dark mater is compared with rotational stabilization and preference of the last factor is advocated.
We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first order mean motion resonance overlap (Wisdom, 1980). We show that this criterion fits the stability regions in real exoplanet…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…