Related papers: Hundreds of new satellites of figure-eight orbit c…
In this paper we use a Modified Newton's method based on the Continuous analog of Newton's method and high precision arithmetic for a general numerical search of periodic orbits for the planar three-body problem. We consider relatively…
Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton's method based on the continuous analog of Newton's method and a high precision arithmetic for a specialized…
We present the results of a numerical search for periodic orbits with zero angular momentum in the Newtonian planar three-body problem with equal masses focused on a narrow search window bracketing the figure-eight initial conditions. We…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
Currently, the fifteen new periodic solutions of Newtonian three-body problem with equal mass were reported by \v{S}uvakov and Dmitra\v{s}inovi\'{c} (PRL, 2013) [1]. However, using a reliable numerical approach (namely the Clean Numerical…
A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on…
After the existence proof of the first remarkably stable simple choreographic motion-- the figure eight of the planar three-body problem by Chenciner and Montgomery in 2000, a great number of simple choreographic solutions have been…
Since the discovery of the figure-8 orbit for the three-body problem [Moore 1993] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have…
A specialized high-precision numerical search for equal-mass collisionless three-body periodic free-fall orbits with central symmetry is conducted. The search is based on Newton's method with initial approximations obtained by the…
We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…
We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body…
We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the…
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…
We present a detailed characterization of planes of satellite galaxies in the Milky Way (MW) and M31. For a positional analysis, we introduce an extension to the `4-galaxy-normal density plot' method \citep[][P13]{Pawlowski13}. It finds the…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the mutual gravitational interaction of the three bodies. Triple…
The irregular satellites of the giant planets are believed to have been captured during the evolution of the solar system. Knowing their physical parameters, such as size, density, and albedo is important for constraining where they came…
We study the correlation of orbital poles of the 11 classical satellite galaxies of the Milky Way, comparing results from previous proper motions with the independent data by Gaia DR2. Previous results on the degree of correlation and its…
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…
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…