Related papers: Kepler's Orbits and Special Relativity in Introduc…
The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses…
The determination of velocities of stars from precise Doppler measurements is described here using relativistic theory of astronomical reference frames so as to determine the Keplerian and post-Keplerian parameters of binary systems. We…
Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known $1/r$ (Keplerian) and logarithmic…
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…
Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back…
We analytically work out the long-term, i.e. averaged over one orbital revolution, time variations of some direct observable quantities Y induced by classical and general relativistic dynamical perturbations of the two-body pointlike…
On incorporating special relativity theory into an extended equivalence principle, post-Newtonian gravitational phenomena beyond that originally predicted by Einstein are predicted (required), such as geodetic and gravitomagnetic…
We derive the first-order orbital equation employing a complex variable formalism. We then examine Newton's theorem on precessing orbits and apply it to the perihelion shift of an elliptic orbit in general relativity. It is found that…
We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel…
The theory of General Relativity explaines the advance of Mercury perihelion using space curvature and the Schwartzschild metric. We demonstrate that this phenomena can also be interpreted due to the cogravitational field produced by the…
The development of both special and general relativity is accomplished in a series of 6 papers using a simple approach. The purpose is to explain the how and why of relativity to a broad public, and to be useful for students of physics by…
Through the Rossiter-McLaughlin effect, several hot Jupiters have been found to exhibit spin-orbit misalignment, and even retrograde orbits. The high obliquity observed in these planets can be attributed to two primary formation mechanisms,…
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,…
The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most…
I show that the precession of the orbit of Mercury and the deflection of starlight by the Sun are effects of special relativity alone when the gravitational field of a particle is treated in the same way as the electric field of a charged…
The study of relativistic Coulomb systems in velocity space is prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space, although less familiar than the analytic solutions in ordinary space, provides a much…
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the…
The theory of General Relativity explaines the advance of Mercury perihelion using space curvature and the Schwartzschild metric. We demonstrate that this phenomena can also be interpreted due to the cogravitational field produced by the…
The long-term dynamics of perturbed Keplerian motion is usually analyzed in simplified models as part of the preliminary design of artificial satellites missions. It is commonly approached by averaging procedures that deal with literal…
Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution.…