木星借力飞行过程误差演化分析

High-order Taylor polynomials are employed to uncover the patterns of orbital uncertainty propagation during planet gravity assist（PGA），with Jupiter gravity assist（JGA）serving as an illustrative example. Firstly，the PGA model and a reference JGA trajectory are presented. Then，utilizing Jet Transport，a method that integrates differential algebra and polynomial algebra，the high-order Taylor polynomial of the deviation from the reference trajectory state is derived. Based on this derived Taylor polynomial，the influence of initial velocity errors on Jovian orbital states during JGA is analyzed. Lastly，the effects of different velocity perturbations on the terminal two-body orbital energy are investigated. The results indicate that for initial velocity errors，the Jovian position and velocity error envelopes exhibit globe-ellipsoid-disc variations，with the divergence trends of the two envelopes differing as they pass by the periapsis. Regarding velocity perturbations along the reference trajectory，the gradients of the terminal orbital energy consistently deviate from the velocity direction and point towards Jupiter’s side. The magnitudes of these gradients are greatest at the beginning of JGA，with a smaller maximum occurring after the periapsis. This research sheds light on the patterns of orbital uncertainty propagation during PGA，elucidating the amplifying effect of PGA on orbital states and the gradient of velocity perturbations along the reference trajectory.