Related papers: Gravitational Orbits and the Lambert Problem
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…
The general relativistic gravitomagnetic clock effect involves a coupling between the orbital motion of a test particle and the rotation of the central mass and results in a difference in the proper periods of two counter-revolving…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
The potential of gravitational lenses for providing direct, physical measurements of the Hubble constant, free from systematic errors associated with the traditional distance ladder, has long been recognized. However, it is only recently…
A gravitational machine is defined as an arrangement of gravitating masses from which useful energy can be extracted. It is shown that such machines may exist if the masses are of normal astronomical size. A simple example of a…
This tutorial leads the reader through the details of calculating the properties of gravitational waves from orbiting binaries, such as two orbiting black holes. Using analogies with electromagnetic radiation, the tutorial presents a…
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…
To estimate influence of the "dark energy" on the Keplerian orbits, we solve the general relativistic equations of motion of a test particle in the field of a point-like mass embedded in the cosmological background formed by the Lambda-term…
Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using…
Planetary orbits, being conic sections, may be obtained as the locus of intersection of planes and cones. The planes involved are familiar to anyone who has studied the classical Kepler problem. We focus here on the cones.
Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics…
A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
In this paper, we consider a satellite orbiting in a Manev gravitational potential under the influence of an atmospheric drag force that varies with the square of velocity. Using an exponential atmosphere that varies with the orbital…
The performance of Brouwer's gravity solution is compared with Deprit's second-order radial intermediary. Taking the main problem of the artificial satellite as the test model, that is perturbations are limited to the effects of the second…
The possibility of detecting the gravitomagnetic clock effect using artificial Earth satellites provides the incentive to develop a more intuitive approach to its derivation. We first consider two test electric charges moving on the same…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
We reexamined the gravitational time delay of light, allowing for various models of modified gravity. We clarify the dependence of the time delay (and induced frequency shift) on modified gravity models and investigate how to distinguish…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
We study approximate solutions of the gravitational lens equation and corresponding lens magnification factor near the critical point. This consideration is based on the Taylor expansion of the lens potential in powers of coordinates and an…