Related papers: The Gravisphere Method Algorithm Programming
The Lambert problem is to determine the gravitational orbit between two points that has a specified time of flight, allowing the second point to be a moving target such as a satellite. After a review of gravitational orbits, a solution of…
The four-spacecraft formation is essential for measurements of various physical fields. The use of this formation on substantially elliptical heliocentric Kepler orbits allows measuring gradients of gravitation field in Solar system. The…
The 11-year and 22-year modulation of galactic cosmic rays (GCRs) in the inner heliosphere are studied using a numerical model developed by Qin and Shen in 2017. Based on the numerical solutions of Parker's transport equations, the model…
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…
Approaching a tumbling target safely is a critical challenge in space debris removal missions utilizing robotic manipulators onboard servicing satellites. In this work, we propose a trajectory planning method based on nonlinear optimization…
The goal of this work is to follow the displacement and possible deformation of a free particle in a fluid flow in 2D axi-symmetry, 2D or 3D using the classical finite elements method without the usual drawbacks finite elements bring for…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
The interaction between Jupiter's magnetosphere and the solar wind is not well-constrained: while internal energetic plasma processes are thought to dominate plasma circulation, the solar wind nonetheless exerts significant control over the…
A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near asteroids are very…
We report a calculation of time-dependent quasi-geostrophic core flows for 1940-2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely the model errors arising from interactions…
In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones.…
It is shown that the motion of a multielectron atom in an external gravitational field in a good approximation is described by system of the Mathisson-Papapetrou equations, if we put as a classical angular momentum of the atom the…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating…
After a preliminary discussion of the relevance of the field nature of gravitation interaction, both for the fundamental interaction of particles and the topology of space time, a method is proposed to produce and detect a dynamical…
We present a method to efficiently compute the eigenfunctions of classically chaotic systems. The key point is the definition of a modified Gram-Schmidt procedure which selects the most suitable elements from a basis set of scar functions…
The radii polynomial approach is an a posteriori validation method based on the contraction of a quasi-Newton operator. We apply this strategy to give a computer-assisted proof of a transverse heteroclinic orbit in the Shimizu--Morioka…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…