Related papers: Orbit Elements from Kepler Solutions in Projective…
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three…
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm,…
We show that the introduction of two worldline parameters defines a different approach to computations in the effective field theory approach to the two-body problem in General Relativity and present some preliminary evidence for a…
This report provides some closed form solutions -- and their inversion -- to a satellite's bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the $J_{2}$ spherical zonal harmonic. The equatorial track of…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
The Stark problem is Kepler problem with an external constant acceleration. In this paper, we study the periodic orbits for Stark problem for both planar case and spatial case. We have conducted a detailed analysis of the invariant tori and…
The discovery of interstellar interlopers such as 1I/`Oumuamua, 2I/Borisov, and 3I/ATLAS have highlighted the necessity of understanding the dynamical pathways that eject small bodies from planetary systems into hyperbolic trajectories. In…
The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long…
The Kepler map was derived by Petrosky (1986) and Chirikov and Vecheslavov (1986) as a tool for description of the long-term chaotic orbital behaviour of the comets in nearly parabolic motion. It is a two-dimensional area-preserving map,…
Exact solutions are found for Euler's equations of rigid body motion for general asymmetrical bodies under the influence of torque by using Jacobi elliptic functions. Differential equations are determined for the amplitudes and the…
We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable…
The perturbations of the hyperbolic motion of a test particle due to the general relativistic gravitoelectromagnetic Schwarzschild and Lense-Thirring components of the gravitational field of a rotating massive body are analytically worked…
Many alternative theories of gravity screens a Yukawa-type potential. This article shows Keplerian-type parametrization as a solution of Yukawa type potential accurate equations of motion for two non-spinning compact objects moving in an…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
The true and eccentric anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits, by considering perturbations of the radial part of the kinetic energy in a form of a series of negative powers of the orbital…
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
A static and axisymmetric solution of the Einstein vacuum equations with a finite number of Relativistic Multipole Moments (RMM) is written in MSA coordinates up to certain order of approximation, and the structure of its metric components…