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arXiv 2012.09240astro-ph.EPmath.DS
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近地轨道空间占位

Space Occupancy in Low-Earth Orbit

Claudio Bombardelli, Gabriele Falco, Davide Amato, Aaron J. Rosengren

摘要:

随着即将在低地球轨道区域发射大型卫星群,组织不同运行卫星所占用的物理空间以便尽量减少关键会合和避免碰撞将变得十分重要。在这里,我们引入空间占用的定义,作为一个单独的卫星所占据的域,因为它沿着其标称轨道下的环境扰动的影响下,在整个给定的时间间隔移动。在表明带状问题的空间占用与冻结轨道和适当偏心率的概念密切相关之后,我们在密切元空间中提供冻结轨道初始条件,并获得冻结轨道极坐标方程来描述封闭解析形式的空间占用区域。然后,我们分析的问题,最大限度地减少空间占用在一个现实的模型,包括田谐波,第三体摄动,太阳辐射压力,和阻力。相应的初始条件,导致我们所说的最小空间占用(MiSO)轨道,数值计算得到的一组代表性的配置在低地球轨道。使用的MiSO轨道,以优化设计的巨型星座的影响进行了讨论。

英文摘要:

With the upcoming launch of large constellations of satellites in the low-Earth orbit (LEO) region it will become important to organize the physical space occupied by the different operating satellites in order to minimize critical conjunctions and avoid collisions. Here, we introduce the definition of space occupancy as the domain occupied by an individual satellite as it moves along its nominal orbit under the effects of environmental perturbations throughout a given interval of time. After showing that space occupancy for the zonal problem is intimately linked to the concept of frozen orbits and proper eccentricity, we provide frozen-orbit initial conditions in osculating element space and obtain the frozen-orbit polar equation to describe the space occupancy region in closed analytical form. We then analyze the problem of minimizing space occupancy in a realistic model including tesseral harmonics, third-body perturbations, solar radiation pressure, and drag. The corresponding initial conditions, leading to what we call minimum space occupancy (MiSO) orbits, are obtained numerically for a set of representative configurations in LEO. The implications for the use of MiSO orbits to optimize the design of mega-constellations are discussed.

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