Related papers: A generalization of the equinoctial orbital elemen…
Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves - as opposed to their…
Of all the solar fundamental parameters (mass, diameter, gravity at the surface,...), the gravitational moments have been quite often ignored in the past, mainly due to the great difficulty to get a reliable estimate. Even though the order…
We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity. In particular, we focus on perturbations in the form of power laws and calculate…
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…
The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…
In orbital and attitude dynamics the coordinates and the Euler angles are expressed as functions of the time and six constants called elements. Under disturbance, the constants are endowed with time dependence. The Lagrange constraint is…
We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit,…
In a previous paper, using ergodic theory, Lo [1] derived a simple definite integral that provided an estimate of the view periods of ground stations to satellites. This assumes the satellites are in circular orbits with non-repeating…
We show that the optical properties of an oblique layered system with two kinds of isotropic materials can be described using the concept of transformation media as long as the thickness of the layers is much smaller than the wavelength.…
An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…
It was believed until very recently that a near-equatorial satellite would always keep up with the planet's equator (with oscillations in inclination, but without a secular drift). As explained in Efroimsky and Goldreich (2004), this…
Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
The Eckart frame is used to separate out the collective rotations in the quantum three-body problem. Explicit expressions for the corresponding rotational and vibro-rotational (i.e. Coriolis) Hamiltonians are derived. Special attention is…
Using a collapsing matter model at the center of an expanding universe as described by Weinberg we assume a special type of generated pressure. This pressure transmits into the surrounding expanding universe. Under certain restriction the…
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript we present a different 2D construct that…
The navigation satellite constellations in medium-Earth orbit exist in a background of third-body secular resonances stemming from the perturbing gravitational effects of the Moon and the Sun. The resulting chaotic motions, emanating from…
The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over most of a planet's orbit can be inverted…
Starting with an entropy that includes volumetric, area and length terms as well as logarithmic contributions, we derive the corresponding modified Newtonian gravity and derive the expression for planetary orbits. We calculate the shift of…
This paper aims to illustrate the applications of resonant Hamiltonian normal forms to some problems of galactic dynamics. We detail the construction of the 1:1 resonant normal form corresponding to a wide class of potentials with…