State propagation in uncertain irregular gravity field with differential algebra method

Uncertainty propagation has been addressed extensively in space missions around Earth. For small solar system missions, new challenges come forth mainly due to the generally irregular and weak gravity field and larger uncertainties in system parameters, e.g. gravity field, density and rotation rate etc. Nevertheless, the study on state propagation in the uncertain gravity field of small body is limited and is the focus of this study. To both address the efficiency and meet the required accuracy, this study applies the dynamics-based differential algebra (DA) method to propagate the state of the spacecraft (s/c) in the uncertain gravity field of the small body. The DA allows arbitrary order Taylor expansion of the flow of the highly nonlinear dynamics w.r.t. the uncertain parameters of the dynamics, and fast evaluations of the flow. With the Gaussian distributions of the initial uncertainties, the distribution of the final state are obtained by transforming through the selected order Taylor expansion w.r.t. the second order gravity. Taking asteroid Stein as an example, the error due to the uncertain second order gravity are analysed for different orbital geometry. The retrograde motion is more robust to the uncertainty than the prograde case. The discoveries of this research can help mission designers assessing the posed risks and designing appropriate mission strategies