Related papers: The Gravisphere Method Algorithm Programming
We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight…
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…
Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the…
A binary system, composed of a compact object orbiting around a massive central body, will emit gravitational waves which will depend on the central body's spacetime geometry. We expect that the gravitational wave observables will somehow…
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
We present a general analytic framework to assess whether impact ejecta launched from the surface of a satellite can escape the gravitational influence of the planet--satellite system and enter heliocentric orbit. Using a patched-conic…
The effective action on an orbifolded sphere is computed for minimally coupled scalar fields. The results are presented in terms of derivatives of Barnes zeta-functions and it is shown how these may be evaluated. Numerical values are shown.…
We present a method for extracting actions, angles and frequencies from an orbit's time series. The method recovers the generating function that maps an analytic phase-space torus to the torus to which the orbit is confined by…
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…
Approximate equations are derived for the motion of a gyroscope on the earth's gravitational field using the Einstein, Infeld, Hoffmann surface integral method. This method does not require a knowledge of the energy-momentum-stress tensor…
The problem of the two-body gravitational interaction has been solved numerically based on the classical mechanics principles. One of the bodies is a deformable three-axis ellipsoid (central body) and the other is a material point…
Interplanetary shocks are fundamental constituents of the heliosphere, where they form as a result of solar activity. We use previously unavailable measurements of interplanetary shocks in the inner heliosphere provided by Solar Orbiter,…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
Inverse techniques are used to extract information about an exoplanet's atmosphere. These techniques are prone to biased results if the appropriate forward model is not used. One assumption used in a forward model is to assume that the…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
In the so-called "global polytropic model", we assume planetary systems in hydrostatic equilibrium and solve the Lane--Emden equation in the complex plane. We thus find polytropic spherical shells providing hosting orbits to planets. On the…
This article investigates long-term orbits within the Earth's magnetosphere, specifically focusing on orbits where the argument of periapsis is synchronized with changes induced by lunar gravity assists and the Earth's argument of latitude…
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of…
A nonhydrostatic dynamical core has been developed by using the multi-moment finite volume method that ensures the rigorous numerical conservation. To represent the spherical geometry free of polar problems, the cubed-sphere grid is…
We present an analytical proof assisted by computer calculations for the dynamical stability of the eight main planets and Pluto for the next 100,000 years. It means that the semi-major axes of the planets will not change significantly…