Kustaanheimo–Stiefel Variables for Planetary Protection Compliance Analysis

Abstract

Planetary protection in trajectory design aims to assess the impact probability of space-mission-disposed objects based on their initial uncertain conditions, to avoid contaminating other planetary environments. High-precision dynamic models and propagation methods are required to reach high confidence levels on small estimated impact probabilities. These requirements have so far confined planetary protection analyses to robust Monte Carlo–based approaches, using the Cartesian formulation of the full force problem dynamics. This work presents the improvements brought by adopting the Kustaanheimo–Stiefel (KS) formulation of the dynamics. The KS formulation is combined with reference frame switch procedures and adaptive nondimensionalization upon detection of close encounters. The fibration property of the KS space, namely, the parameterizable locus of point arising when mapping to a higher-dimensional space, is exploited to minimize the computational time, because of the minimized numerical stiffness of the system. Impact probability estimation tasks become more efficient than the single-simulation case, since the regularization of the dynamics removes the singularity of gravitational potentials for distances approaching zero. Despite an almost halved computational burden for Monte Carlo analysis, the precision of the single simulations is increased by nearly one order of magnitude, setting a new performance benchmark for planetary protection tasks.