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.
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