Optimization and Estimation of Orbital Capacity for Low-Earth Resources

The rapid increase in satellites deployment numbers and schedules for low-earth orbit mega-constellations have brought to the fore the issue of limited orbital resource in recent years. But the exploitation of the intrinsic capacity estimation of orbit-based resources has consistently posed a challenge in terms of reaching a clear and unified conclusion. We are attempting to research this. Our analysis covers two key perspectives, static distribution optimization and dynamic safe rendezvous, offering a comprehensive understanding of the issue. We then employ the spherical gradient descent method to conduct theoretical derivation, followed by experiments and numerical analysis, including dynamic simulations of rendezvous distances. Through these, we can make the estimation of maximum number of satellites within a single shell while ensuring a safe distance of at least 50 km at any given time. Simulation results show that the optimization can increase the single-shell capacity while also increasing the safety distance. Finally, based on the experimental results, recommendations for the constraints on the low-earth orbit capacity and the total number of deployable satellites are proposed.