Related papers: Sums Associated with Orbits in the Binary Dynamica…
We develop analytical tools and perform three-body simulations to investigate the orbital evolution and dynamical stability of binary planets within star clusters. Our analytical results show that the orbital stability of a planetary-mass…
We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second-order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced in Phys. Rev.…
We determine the evolution of a giant planet-disk system that orbits a member of a binary star system and is mildly inclined with respect to the binary orbital plane. The planet orbit and disk are initially mutually coplanar. We analyze the…
Roughly half of Solar-type planet hosts have stellar companions, so understanding how these binary companions affect the formation and evolution of planets is an important component to understanding planetary systems overall. Measuring the…
We present the first fully relativistic longterm numerical evolutions of three equal-mass black holes in a system consisting of a third black hole in a close orbit about a black-hole binary. We find that these close-three-black-hole systems…
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…
Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…
The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…
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…
Close, compact, hierarchical, multiple stellar systems, i.e., multiples having an outer orbital period from months to a few years, comprise a small, but continuously growing group of the triple and multiple star zoo. Many of them consist of…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
The angle between the stellar spin-axis and the orbital plane of a stellar or planetary companion has important implications for the formation and evolution of such systems. A study by Hale (1994) found that binaries with separations $a <…
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…
We compute next-to-next-to-leading order spin contributions to the post-Newtonian equations of motion for binaries of compact objects, such as black holes or neutron stars. For maximally spinning black holes, those contributions are of…
Let $b \geq 2$ be an integer, and write the base $b$ expansion of any non-negative integer $n$ as $n=x_0+x_1b+\dots+ x_{d}b^{d}$, with $x_d>0$ and $ 0 \leq x_i < b$ for $i=0,\dots,d$. Let $\phi(x)$ denote an integer polynomial such that…
The effects which star cluster concentration and binarity have on observable parameters, that characterise the dynamical state of a population of stars after their birth aggregate dissolves, are investigated. To this end, the correlations…
There are well-known examples of dynamical systems for which the Birkhoff averages with respect to a given observable along some or all of the orbits do not converge. It has been suggested that such orbits could be classified using higher…
We study the dynamical evolution of a satellite orbiting outside of a companion spherical galaxy. The satellite is subject to a back-reaction force resulting from the density fluctuations excited in the primary stellar system. We evaluate…
Fix irrational numbers $\alpha,\hat\alpha>1$ of finite type and real numbers $\beta,\hat\beta\ge 0$, and let $B$ and $\hat B$ be the Beatty sequences $$ B:=(\lfloor\alpha m+\beta\rfloor)_{m\ge 1}\quad\text{and}\quad\hat…
The sets of the synchronous equations are derived from the sets of non-synchronous equations The analytical solutions are given by solving the set of differential equations. The results of the evolutionary tendency of the orbit-spin are…