Shared gravity approximations for satellite constellations

This paper introduces two novel methods that make use of gravitational force sharing (GFS) for efficient propagation of satellite constellations in low Earth orbit (LEO). These methods, the evenly-spaced GFS and time-interpolated GFS, leverage the high-order gravitational acceleration information available from nearby satellites to reduce computational costs while still maintaining high accuracy. The evenly-spaced GFS method is tailored for tightly spaced string-of-pearls formations, while the time-interpolated GFS method is more versatile, accommodating varying constellation configurations. Both methods are implemented within the Adaptive Picard-Chebyshev (APC) framework and demonstrate significant reductions in computational load compared to traditional propagation approaches. Trade studies reveal that the GFS methods achieve position errors on the order of nanometers for close constellation distances and significantly outperform (by a few orders of magnitude) low-order gravity models and the Clohessy–Hill–Wiltshire dynamics in terms of accuracy. The results also show that the error scales quadratically with separation distance and logarithmically with altitude, providing a predictable framework for applying these techniques to different orbits. These methods offer a promising solution for efficient and accurate trajectory propagation in modern satellite mission design. • Sharing force computations with satellites in a constellation speeds up propagation. • Two approaches: Evenly-spaced and time-interpolation sharing along the orbit. • Gravitational force sharing maintains accuracy and reduces gravity model evaluations. • Gravitational force sharing outperforms common approximations in low Earth orbit. • Errors scale with satellite spacing and drop at higher orbital altitudes.