Subjects: Astronomy submitted time 2023-10-07 Cooperative journals: 《天文学报》
Abstract： Satellite constellations are widely used for communication, navigation and Earth observation purposes. They provide good ground coverages and serve better for these needs. Of all the configurations, the Walker constellation is extensively applied in many navigation satellite systems and some low Earth orbit communication constellations, since it can be easily designed and has good coverage. Despite of these advantages, the satellites in Walker constellation generally have different ground tracks. When multiple Walker constellations are to be coordinated, in terms that the orbital planes precess synchronously with the same satellite mean motion $\Omega_1$, the semi-major axes of these Walker constellations would be significantly different even when the orbital inclinations differ by a small amount. The Space Exploration Corp (SpaceX) claimed a new constellation design in a patent for their multi-shell Starlink satellite constellation. Constellation shells with different inclinations have small altitude differences, which facilitates regulatory approval and deployment. Satellites in the same shell can also be easily designed to share the same ground track. Although they claimed these features in the patent, SpaceX shared little technical details regarding how to design these constellations. Here in this paper, we analyze the features of the Starlink constellation and try to find a practical approach to design a Starlink-like constellation, as well as how to determine the rules for inter-satellite links within the constellation.
Subjects: Astronomy submitted time 2023-10-07 Cooperative journals: 《天文学报》
Abstract： Tesseral perturbation is a major part in analytical orbit propagation, which involves a significant amount of calculations of inclination functions and their partial derivatives. Recursion formula is widely applied for accuracy and efficiency purposes. Based on the modified Gooding's method proposed in the literature, an optimized program is proved to reduce 24\% of calculation time for all inclination functions up to degree/order 50 ($L\le 50$). Furthermore, considering that the mean inclination varies slightly in orbit prediction for 1--3 days, the functions are expanded as Taylor series, which speeds up calculations significantly, and the time consumed during orbit prediction is reduced by 48\% while the tesseral perturbation is calculated up to degree/order 50. Moreover, with expansion of inclination functions up to the second order, the predicted ephemerides deviate slightly from those calculated using full recursion formula. For a 500\;km low Earth satellite, propagating its orbits for 3 days using modified Gooding's method and second-order Taylor expansion respectively to calculate the inclination functions within degree/order 50, the ephemeris deviation RMS (Root Mean Square) is less than 1\;mm and decreases as the altitude increases.
Subjects: Astronomy submitted time 2023-08-02 Cooperative journals: 《天文学报》
Abstract： Classical methods for initial orbit determination (IOD) include Laplace method, Gauss method and their variations. In addition to this, based on the characteristic of optical observation data nowadays, experts propose some other IOD methods, like Double-$r$ method and admissible region method. One of the ways to determinate the orbit through double-$r$ method is to guess distances of the target from the observer at two epochs---usually at the first and the last one. By doing so, we can solve the Lambert problem and use its solution as the initial guess of the orbit. Furthermore, we can improve the initial guess by iterations to reduce the root mean square (RMS) of the observations. The admissible method is based on the concept of attributable (longitude, latitude and their rates). With some conceptions, the admissible region described by the range and range rate from the observer is characterized. Using triangulation we can find the nodal point that makes the RMS minimal. In our work, we apply one intelligent optimization method---the particle swarm optimization method to the two methods, based on simulated and real data, and compare the results with that of modified Laplace method. At last, we briefly discuss the possibility of applying the double-$r$ method to the orbit link problem.
Subjects: Astronomy submitted time 2023-08-02 Cooperative journals: 《天文学报》
Abstract： In different orbit prediction scenarios, the dynamic models used are also different. For example, the atmospheric drag is a very important perturbation force in the prediction of space debris in low orbits, but at mid-to-high orbits, the atmospheric drag can be ignored. In order to select the most suitable dynamic models for orbit prediction in different scenarios, this article provides a large number of orbits for different accuracy requirements and different orbit types. By comparing the prediction results with different dynamic models, the optimal dynamic models for various prediction scenarios are recommended. This work can serve as references and standards for the selection of reference dynamics models for different orbital types of space debris in orbit prediction.
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