Uncertainty maps for motion around binary asteroids

Abstract

In this work, two novel dynamics indicators are introduced and used to characterise the uncertain dynamics around a binary asteroid. These indicators are derived from the propagated expansion of the states in polynomial series of the uncertainty in initial conditions and dynamical model parameters. Thus, each indicator encapsulates in a single scalar the effect of the uncertainty in multiple model parameters. The first indicator directly calculates the second statistical moment of the propagated uncertainty set. This indicator gives a measure of the rate of divergence of an ensemble of trajectories in phase space. The second indicator estimates the approximation error of the polynomial expansion. Hence, it captures the nonlinearity in the distribution of the propagated states that is induced by the uncertainty. The two indicators are then used to create a map in phase space, which relates initial conditions to the sensitivity of the state over time to multiple realisation of the uncertain parameters. The case of the a spacecraft orbiting the binary asteroid system Didymos is considered in this paper. The uncertainty maps proposed in this paper are shown to reveal the characteristics of the motion around Didymos under uncertainty in the masses of both bodies.