State uncertainty propagation and sensitivity analysis of the post-impact binary asteroid system

The Double Asteroid Redirection Test (DART) mission demonstrated the feasibility of altering an asteroid’s orbit through kinetic impact. However, uncertainties associated with the collision and the complex dynamics of the binary asteroid system often result in rough and inefficient predictions of the system’s post-impact evolution. This paper proposes the use of arbitrary polynomial chaos expansion (aPCE) to efficiently evaluate the state uncertainty of a post-impact binary asteroid system without requiring complete information on the uncertainty sources. First, a perturbed full two-body problem model is developed to assess the momentum transfer during the collision and the system’s subsequent evolution. The irregular shapes of the components and the momentum enhancement from the ejecta are considered to achieve reasonable evaluations. Next, aPCE is employed to construct a surrogate model capable of efficiently quantifying uncertainties. Global sensitivity analysis is then conducted to identify the main sources of uncertainty affecting the system’s evolution. Benchmarking tests show that the aPCE model produces results comparable to Monte Carlo simulations, offering a good balance between accuracy and efficiency. The data-driven nature of aPCE is further demonstrated by comparing its performance to generalized polynomial chaos expansion. Under the framework of the DART mission, the aPCE solution yields results consistent with observed data. Additionally, global sensitivity analysis reveals that the shape and density of the primary, as well as the collision target’s strength and porosity, contribute most to the system uncertainty.