Related papers: Gravitational Orbits and the Lambert Problem
The equations for gravitational plane waves produced by a typical binary system as a solution of linear approximation of Einstein equations is derived. The dynamics of the corresponding gravitational field is analyzed in a 4-dimensional…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry…
The gravitational couplings of matter are studied in the presence of Lorentz and CPT violation. At leading order in the coefficients for Lorentz violation, the relativistic quantum hamiltonian is derived from the gravitationally coupled…
The paper contains a proposed experiment for testing the gravitomagnetic effect on the propagation of light around a rotating mass. The idea is to use a rotating spherical laboratory-scale shell, around which two mutually orthogonal…
When gravitational waves travel from their source to an observer, they interact with matter structures along their path, causing distinct deformations in their waveforms. In this study we introduce a novel theoretical framework for wave…
A method for asteroid deflection that makes use of a spacecraft moving back and forth on a segment of a Keplerian orbit about the asteroid is studied with the aim of optimizing the initial gross mass of the spacecraft. The corresponding…
We suggest that a satellite with a stable atomic clock on board be sent through the Earth-Sun gravitational saddle point to experimentally determine whether Nature prefers static solutions of the field equations of General Relativity, such…
We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection,…
The identification of the electromagnetic(EM) counterpart of gravitational wave(GW) trigger in the sky localization is a very difficult task because of the large uncertainty. Two complementary approaches are used in order to search for EM…
Particle trajectories in the form of a logarithmic spiral with specified angular time dependence, "ZK spirals," are shown to be analytic solutions for motion in non-central, but simple force power-laws. Each ZK spiral is a particular…
Analyzing two simple experimental situations we show that from Newton's law of gravitation and Special Relativity it follows that the motion of particle in an external gravitational field can be described in terms of effective spatial…
The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a…
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…
The asymmetry in the time delay for light rays propagating on opposite sides of a spinning body is analyzed. A frequency shift in the perceived signals is found. A practical procedure is proposed for evidencing the asymmetry, allowing for a…
Gravitational redshift is being generally calculated without considering the rotation of a body. Neglecting the rotation, the geometry of space time can be described by using the spherically symmetric Schwarzschild geometry. Rotation has…
Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…
Gravitational waves have been directly detected and astronomical observations indicate that our Universe has a positive cosmological constant $\Lambda$. Nevertheless, a theoretical gauge-invariant notion of gravitational waves arriving at…