Related papers: Relative Equilibria and Periodic Orbits in a Binar…
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…
The proper elements of asteroids are obtained from the instantaneous orbital elements by removing periodic oscillations produced by gravitational interactions with planets. They are unchanging in time, at least if chaotic dynamics and…
This paper explores the stability of an Earth-like planet orbiting a solar-mass star in the presence of a stellar companion using ~ 400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a…
We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary…
This work extends the still modest number of multiple stars with known relative orbit orientation. Accurate astrometry and radial velocities are used jointly to compute or update outer and inner orbits in three nearby triple systems HIP…
Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the…
The evolution of rotation states of small asteroids is governed by the YORP effect, nonetheless some asteroids can stop their YORP evolution by attaining a stable equilibrium. The same is true for binary asteroids subjected to the BYORP…
So far, multiple stellar systems harbor more than 130 extra solar planets. Dynamical simulations show that the outcome of planetary formation process can lead to various planetary architecture (i.e. location, size, mass and water content)…
Multiplicity is ubiquitous among massive stars. While the stellar components usually display similar masses, some binaries with extremely low mass ratios were also observed. Some of them are primordial, while others arise from binary…
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…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
The continuation of resonant periodic orbits from the restricted to the general three body problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular restricted…
An asteroid pair can be described as two asteroids with highly similar heliocentric orbits that are genetically related but not gravitationally bound. They can be produced by asteroid collisions or rotational fission. Although over 200…
We investigate the orbital dynamics of four-planet systems consisting of Earth-mass planets on initially-circular, coplanar orbits around a star of one solar mass. In our simulations, the innermost planet's semimajor axis is set at 1 AU,…
The 2:1 mean motion resonance orbit was integrated at the restricted planar 3-body problem in absolute frame. Orbit of Jupiter was assumed circular. Initial Jupiter longitude was assumed zero. The Runge-Kutta method was used. The start of…
We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the…
For $n$-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the…
The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…
Numerical solutions are presented for a family of finite angular momentum orbits with three equal masses which connects the classical circular Lagrange orbit with the recently discovered planar figure eight orbit. Each member of this family…
In this work, we performed a dynamical analysis of a spacecraft around a nearly equal-mass binary near-Earth asteroid with application to the asteroid 2017 YE5, which is also a possible dormant Jupiter-family comet. Thus, we investigated…