Adaptive Polydisperse Sphere Packings for High Accuracy Computations of the Gravitational Field

Autonomous missions to small bodies are an essential part of recent space exploration. This increasing interest in asteroids and moons leads to an increased need for high-fidelity trajectory simulations to guarantee mission success. Although their shape might vary greatly, most of those small bodies we know have an irregular shape, thus, a gravity field that is challenging to compute. We present a new method to model the mass of celestial bodies based on adaptive polydisperse sphere packings. Using poly-disperse spheres in the mascon model has shown to deliver a very good approximation of the mass distribution of celestial bodies while allowing fast computations of the gravitational field. However, small voids between the spheres reduce the accuracy especially close to the surface. Hence, the idea of our adaptive sphere packing is to place more spheres close to the surface instead of filling negligible small gaps deeper inside the body. Although this reduces the packing density, we achieve greater accuracy close to the surface. For the adaptive sphere packing, we propose a mass assignment algorithm that uniformly samples the volume of the body. Additionally, we present a method to further optimize the mass distribution of the spheres based on least squares optimization. The sphere packing and the gravitational acceleration remain computable entirely on the GPU (Graphics Processing Unit). We have evaluated our method by comparing it to analytical solutions (such as a cube) and detailed shape models of real asteroids, for which we have used the traditional polyhedral method as a reference. We compute the gravitational acceleration on the surface since the most significant relative error lies there, which is also crucial for landing maneuvers. Our adaptive sphere packing approach produces reliable gravitation data for physically - based simulation of space missions and shows more accurate results than previous similar methods.