We aim to provide satellite operators and researchers with an efficient means for evaluating and mitigating collision risk during the design process of mega-constellations. We first introduce a novel algorithm for conjunction prediction that relies on large-scale numerical simulations and uses a sequence of filters to greatly reduce its computational expense. We then use this brute-force algorithm to establish baselines of endogenous (intra-constellation), or self-induced, conjunction events for the FCC-reported designs of the OneWeb LEO and SpaceX Starlink mega-constellations. We demonstrate how these deterministic results can be used to validate more computationally efficient, stochastic techniques for close-encounter prediction by adopting a new probabilistic approach from Solar-System dynamics as a simple test case. Finally, we show how our methodology can be applied during the design phase of large constellations by investigating Minimum Space Occupancy (MiSO) orbits, a generalization of classical frozen orbits that holistically account for the perturbed-Keplerian dynamics of the Earth-satellite-Moon-Sun system. The results indicate that the adoption of MiSO orbital configurations of the proposed mega-constellations can significantly reduce the risk of endogenous collisions with nearly indistinguishable adjustments to the nominal orbital elements of the constellation satellites.

我们旨在为卫星运营商和研究人员提供一种在巨型星座设计过程中评估和减轻碰撞风险的有效方法。我们首先介绍一种新颖的联合预测算法，该算法依赖于大规模数值模拟，并使用一系列过滤器来大大减少其计算量。然后，我们使用这种蛮力算法为FCC报告的OneWeb LEO和SpaceX Starlink巨型星座设计中的内源性（星座内）或自诱发的联合事件建立基线。我们通过采用来自太阳系动力学的新概率方法作为简单的测试案例，演示了如何将这些确定性结果用于验证更有效的近距离预测的随机技术。最后，通过研究最小空间占用（MiSO）轨道，这是经典冻结轨道的一般化，整体上解释了地球-卫星-月亮-太阳系统的扰动的开普勒动力学，我们展示了如何在大型星座的设计阶段应用我们的方法。结果表明，采用拟议的大型星座的MiSO轨道配置可以显着降低内源碰撞的风险，而对星座卫星的标称轨道元素进行几乎无法区分的调整。