Relative trajectory estimation during Chang'e-2 probe's flyby of asteroid Toutatis using dynamics, optical, and radio constraints

The mystery of the asteroid (4179) Toutatis was revealed by Chang'e-2 spacecraft during a close flyby on December 13, 2012. Optical imaging and navigation of the probe during the flyby were performed entirely under ground-based radio tracking and default sequence built on ground. This paper establishes a set of estimation algorithms of the relative trajectory between Chang'e-2 and Toutatis based on dynamics, optical, and radio constraints that are determined by the unique flyby mode. This study is the first time to precisely reproduce the core process of Chang'e-2's encounter with Toutatis based on several optical images. In addition to constructing a strict photogrammetric model, the shadowing effects caused by the illumination and the deviation of the center-of-mass (COM) from the center-of-figure (COF) in optical images are also considered. The spacecraft trajectory with regard to the COF of the body is estimated using images taken from 120 km or less. The formal one sigma uncertainty is (67, 20, and 11 m) in the principal axes frame of the position error ellipse, and the closest approaching distance between Chang'e-2 and Toutatis's COF is calculated as 1557 ± 11 m, which is more precise than previous results with an uncertainty of hundreds of meters. The spacecraft trajectory with regard to the COM of the body is estimated with an uncertainty of (211, 34, and 17 m), and the corresponding closest distance is estimated as 1451 ± 18 m based on the previously developed shape model of Toutatis. The algorithms and results in this study are important for evaluating the performance of this flyby mission and are also valuable for any similar optical navigation during a close approach. In addition, our results can help in precisely determining the axis of Toutatis and sizes of impact craters, which are critical for understanding the formation and evolution of Toutatis.