Related papers: The Gravisphere Method Algorithm Programming
This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange…
The process of capture in the coorbital region of a solar system planet is studied. Absolute capture likelihood in the 1:1 resonance is determined by randomly constructed statistical ensembles numbering $7.24\times 10^5$ of massless…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
Jupiter's magnetosphere is considered to be the most powerful particle accelerator in the Solar System, accelerating electrons from eV to 70 MeV and ions to GeV energies. How electromagnetic processes drive energy and particle flows,…
The circular orbits and elliptical orbits of moving objects in a gravitational field are essential information in astronomy. There have been many methods developed in the literature and textbooks to describe these orbits. In this report, I…
Within the framework of linearized Einstein field equations we compute the gravito-magnetic effects on a test particle orbiting a slowly rotating, spherical body with a rotating matter ring fixed to the equatorial plane. Our results show…
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…
In this paper, we address the problem of predicting collision for objects moving on the surface of a spherical manifold. Toward this end, we develop the notion of a collision triangle on such manifolds. We use this to determine analytical…
Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes.…
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
A semi-numerical method is used in order to locate the position and calculate the period of periodic orbits in a 3D composite bisymmetrical potential, in a number of resonant cases. The potential consists of a 3D harmonic oscillator and a…
I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
The Gutzwiller's trace formula for the anisotropic Kepler problem is Fourier transformed with a convenient variable $u=1/\sqrt{-2E}$ which takes care of the scaling property of the AKP action $S(E)$. Proper symmetrization procedure…
Dyson spheres are hypothetical megastructures encircling stars in order to harvest most of their energy output. During the 11th edition of the GTOC challenge, participants were tasked with a complex trajectory planning related to the…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…