The analysis of satellite coverage to determine the visibility of ground targets from satellites has been extensively studied, particularly through geometric-based methods that provide analytical results. However, there exists a key limitation that these methods do not precisely consider the elevation-angle constraint. To address this limitation, this article provides a geometric approach for computing the visibility considering the elevation-angle constraint. First, the mathematical model of the elevation-angle constraint is established, and the elevation-element equation describing the geometrical relationship between satellite and ground target satisfying the elevation-angle constraint is deduced. Additionally, based on the analytical solution to the elevation-element equation, a two-dimensional map, named the elevation mapping, is proposed. Subsequently, the presented geometric approach is established by incorporating the elevation-angle constraint model into the satellite-target visibility model, and an extended field mapping is proposed to rapidly compute access intervals while adhering to the elevation-angle constraint. Specifically, it achieves this by converting the task into a straightforward problem involving the intersection of a set of lines with the time-invariant regions generated by the extended field mapping. Furthermore, the extended constellation field mapping is presented, which can simplify the multisatellite coverage problem into an easier single-satellite coverage problem, enabling it to solve the constellation coverage problem considering elevation-angle constraints analytically and rapidly. Simulation results demonstrate that the proposed intuitive methodology can accurately and rapidly compute access intervals while considering the elevation-angle constraint, which suggests its wide applications in satellite coverage analysis.

This paper proposes an analytical calculation method of the ground point visibility from a satellite in a circular orbit for an arbitrary sensor field considering the J2 perturbation based on the g...

In this work, an efficient multi-stage constant-vector thrust control algorithm is proposed for spacecraft to achieve finite-thrust Lambert transfer considering J ₂ perturbation. In contrast to most designs that apply continuous-thrust requiring time-varying direction and the magnitude of the thrust, the proposed control scheme utilizes a multi-stage constant-vector thrust which means the modulus and direction of the thrust are constant in each stage determined by a given set of time nodes dividing the whole transfer time, which reduces the control complexity of the engine. Based on the multi-stage sensitivity matrix, which describes the first-order relationship between the thrust and the change of the orbital elements, a rapid algorithm is presented to obtain the multi-stage constant-vector thrust solution with the required accuracy. Furthermore, the optimization problem of the multi-stage constant-vector thrust solution is established, and the direct optimization method is proposed to obtain an optimal multi-stage constant-vector thrust solution for a given set of time nodes. Based on this approach, the node-sequence optimization method is further proposed to obtain a series of feasible optimized solutions rapidly corresponding to a monotonically increasing time-node sets. Compared with the existing finite-thrust methods, the presented methods balance the fuel consumption and control requirements of the engine because the situation that the engine always needs to change the direction and the magnitude of the thrust could be avoided, which are practical options for engineering applications.

This paper proposes a geometric-based method of the ground-point visibility from a satellite or satellite constellation in elliptical orbit considering the J ₂ perturbation. First, the field-element equations describing the relationship between the elliptical satellite orbit, field parameters, and ground point are introduced and can be solved semi-analytically. Also, using a two-dimensional map composed of the mean argument of latitude and geographic longitude of the ascending node, the problem of calculating visible intervals is transformed into a simple intersection problem of a group of parallel lines and a time-invariant region generated by the field-element equations. Furthermore, based on the geometric relationship between any two satellites, the relative field mapping and constellation field mapping are described, which can simplify the multi-satellite coverage problem to a single-satellite coverage problem and can be used to obtain the coverage performance of the constellation analytically and rapidly for the target. The simulation results demonstrate that the proposed method is rapid, efficient, intuitive, and accurate, suggesting its wide applications in constellation studies .