Search Results (3)

In the study of dual asteroid systems, a model that can rapidly compute the motion and orientation of these bodies is essential. Traditional modeling techniques, such as the double ellipsoid or polyhedron methods, fail to deliver sufficient accuracy in estimating the interactions between dual asteroids. This inadequacy primarily stems from the non-tidally locked nature of asteroid systems, which necessitates continual adjustments to account for changes in gravitational fields. This study adopts the finite element method to precisely model the dynamic interaction forces within irregular, time-varying dual asteroid systems and, thereby, enhance the planning of spacecraft trajectories. It is possible to derive the detailed characteristics of a spacecraft’s orbital patterns via the real-time monitoring of spacecraft orbits and the relative positions of dual asteroids. Furthermore, this study examines the orbital stability of a spacecraft under various trajectories, revealing that orbital stability is intrinsically linked to the geometric configuration of the orbits. And considering the influence of solar pressure on the orbit of asteroid detectors, a method was proposed to characterize the stability of detector orbits in the time-varying gravitational field of binary asteroids using cloud models. The insights gained from the analysis of orbital characteristics can inform the design of landing trajectories for binary asteroid systems and provide data for deep learning algorithms that are aimed at optimizing such orbits. By introducing the application of the finite element method, detailed analysis of spacecraft orbit characteristics, and a stability characterization method based on a cloud model, this paper systematically explores the logic and structure of spacecraft orbit planning in a dual asteroid system. Full article

For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular at the poles, i.e., degradation phenomena. Unlike other spherical discrete grids (e.g., square, triangular, and rhombic grids) that can fit the curvature, the Discrete Global Grid System (DGGS) grid can not only fit the curvature but also effectively avoid degradation phenomena at the poles. In addition, since it has only edge-adjacent grids, DGGS grids have consistent adjacency and excellent angular resolution. Hence, DGGS grids are the best choice for discretizing the sphere into cells with an approximate shape and continuous scale. Compared with the tesseroid, which has no analytical solution but has a well-defined integral limit, the DGGS cell (prisms obtained from DGGS grids) has neither an analytical solution nor a fixed integral limit. Therefore, based on the isoparametric transformation, the non-regular DGGS cell in the system coordinate system is transformed into the regular hexagonal prism in the local coordinate system, and the DGGS-based forwarding algorithm of the gravitational field is realized in the spherical coordinate system. Different coordinate systems have differences in the integral kernels of gravity fields. In the current literature, the forward modeling research of polyhedrons (the DGGS cell, which is a polyhedral cell) is mostly concentrated in the Cartesian coordinate system. Therefore, the reliability of the DGGS-based forwarding algorithm is verified using the tetrahedron-based forwarding algorithm and the tesseroid-based forwarding algorithm with tiny tesseroids. From the numerical results, it can be concluded that if the distance from observations to sources is too small, the corresponding gravity field forwarding results may also have ambiguous values. Therefore, the minimum distance is not recommended for practical applications. Full article

In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth’s crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data inversion, we face three problems: topography with large amplitude, the sphericity of the planet, and a long computation time because of the large amount of data. In our previous works, we have already considered those problems separately but without explaining the details of the computation of the closed-form solution for a polyhedron. In this paper, we present for the first time a performance-effective numerical method for the inversion of gravity data based on topography. The method is based on closed-form expression for the gravity field of a spherical density model of the Earth’s crust with the upper topography layer, and provides great accuracy and speed of calculation. There are no restrictions on the model’s geometry or gravity data grid. As a case study, a spherical density model of the Earth’s crust of the Urals is created. Full article