Related papers: Improved equations for eccentricity generation in …
Approximately half of the planets discovered by NASA's Kepler mission are in systems where just a single planet transits its host star, and the remaining planets are observed to be in multi-planet systems. Recent analyses have reported a…
The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long…
Numerical relativity simulations of merging black holes provide the most accurate description of the binary dynamics and the emitted gravitational wave signal. However, practical considerations such as imperfect initial data and initial…
We develop a method to analyze the effect of an asymmetric supernova on hierarchical multiple star systems and we present analytical formulas to calculate orbital parameters for surviving binaries or hierarchical triples and runaway…
We study the chaotic and secular evolution of hierarchical quadruple systems in the $3+1$ configuration, focusing on the evolution of mutual inclination of the inner binaries as the system undergoes coupled Lidov-Kozai (LK) oscillations. We…
In this paper, we give a summary of stability criteria that have been derived for hierarchical triple systems over the past few decades. We give a brief description and we discuss the criteria that are based on the generalisation of the…
Many close stellar binaries are accompanied by a far-away star. The "eccentric Kozai-Lidov" (EKL) mechanism can cause dramatic inclination and eccentricity fluctuations, resulting in tidal tightening of inner binaries of triple stars. We…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
About 25 per cent of `hot Jupiters' (extrasolar Jovian-mass planets with close-in orbits) are actually orbiting counter to the spin direction of the star. Perturbations from a distant binary star companion can produce high inclinations, but…
Modern applications of celestial mechanics include the study of closely packed systems of exoplanets, circumbinary planetary systems, binary-binary interactions in star clusters, and the dynamics of stars near the galactic centre. While…
Hot Jupiters (HJs) are Jupiter-like planets orbiting their host star in tight orbits of a few days. They are commonly believed not to have formed in situ, requiring inwards migration towards the host star. One of the proposed migration…
Statistics of the angle \Phi between orbital angular momenta in hierarchical triple systems with known inner visual or astrometric orbits are studied. Correlation between apparent revolution directions proves partial orbit alignment known…
The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are…
Hierarchical two-planet systems, in which the inner body's semi-major axis is between 0.1 and 0.5 AU, usually present high eccentricity values, at least for one of the orbits. As a result of the formation process, one may expect that…
A widely explored pathway for hot Jupiter (HJ) formation is high-eccentricity migration driven by von Zeipel-Lidov-Kozai cycles induced by an exterior companion. However, for a distant or low-mass companion, this mechanism typically demands…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
We study the dynamical evolution of eccentric massive black hole binaries (MBHBs) interacting with unbound stars by means of an extensive set of three body scattering experiments. Compared to previous studies, we extend the investigation…
We examine the distributions of eccentricities of orbits within mass distributions like those we see for galaxies and clusters. A comprehensive understanding of these orbital properties is essential to calculate the rates of physical…
Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help…
A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by…