Related papers: Mean-motion resonances in satellite-disc interacti…
We explore the possibility that extrasolar planets might be found in the 1:1 mean-motion resonance. There are a variety of stable co-orbtial configurations, and we specifically examine three different versions of the 1:1 resonance. These…
Martin & Lubow (2017) showed through simulations that an initially tilted disc around an eccentric binary can evolve to polar alignment in which the disc lies perpendicular to the binary orbital plane. We apply linear theory to show both…
Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…
Building initial conditions for generic binary black-hole evolutions without initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure…
The stellar obliquity of a planetary system is often used to help constrain the system's formation and evolution. One of the mechanisms to reorient the stellar spin involves a secular resonance crossing due to the dissipation of the…
Using the anelastic approximation of linearised hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. The sixth-order dispersion equation is derived and numerically solved…
The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period…
We investigate the distributions of the orbital period ratios of adjacent planets in high multiplicity \kepler\ systems (four or more planets) and low multiplicity systems (two planets). Modeling the low multiplicity sample as essentially…
In a population of multiple protostellar systems with discs, the sub-population of circumbinary discs whose orbital plane is highly misaligned with respect to the binary's orbital plane constrains the initial distribution of orbital…
We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are…
The width of a resonance in a nearly integrable system, i.e. in a non-integrable system where chaotic motion is still not prominent, can tell us how a perturbation parameter is driving the system away from integrability. Although the tool…
In this paper we look at the gravitational spin--spin interaction between macroscopic astronomical bodies. In particular, we calculate their post--Newtonian orbital effects of order $\mathcal{O}(c^{-2})$ on the trajectory of a spinning…
Accretion discs that are tilted with respect to their compact hosts can warp out-of-plane through general relativistic frame-dragging. Warp influences disc dynamics in ways that have been studied extensively, especially as regards…
An important and widely neglected aspect of the interaction between an accretion disc and a massive companion with a coplanar orbit is the vertical component of the tidal force. As shown by Lubow, the response of the disc to vertical…
Accretion disks around stars, or other central massive bodies, can support long-lived, slowly precessing $m=1$ disturbances in which the fluid motion is nearly Keplerian with non-zero eccentricity. We study such `slow modes' in disks that…
Taking into account the mass transfer effect, we derive the equations of motion of a compact binary system at the second-half post-Newtonian order. Applying such equations of motion to quasi-circular orbits, we obtain the time derivative of…
Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that…
A random motion on the Poincar\'e half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the case where returns to the starting point are…
In this paper, two models of interest for Celestial Mechanics are presented and analysed, using both analytic and numerical techniques, from the point of view of the possible presence of regular and/or chaotic motion, as well as the…
The orbits of the confirmed exoplanets from all multiple systems known to date are investigated. Observational data from 1890 objects, of which 1176 are found in multiplanetary systems, are compiled and analyzed. Mean motion resonances and…