The problem of nonlinear uncertainty propagation represents a crucial issue in celestial mechanics. In this paper, a method for nonlinear propagation of uncertainty based on differential algebra is presented. Working in the differential algebra framework enables a general approach to nonlinear uncertainty propagation that can provide highly accurate estimate with low computational cost. The nonlinear mapping of the statistics is shown here, adopting the two-body problem as the working framework, including coordinate system transformations. The general feature of the proposed method is also demonstrated by presenting long-term integrations in complex dynamic systems, such as the n-body problem or the simplified general perturbation model.

Space debris have become exceedingly dangerous over the years as the number of objects in orbit continues to increase. Active debris removal (ADR) missions have gained significant interest as effective means of mitigating the risk of collision between objects in space. This study focuses on developing a multi-ADR mission that utilizes controlled reentry and deorbiting. The mission comprises two spacecraft: a Servicer that brings debris to a low altitude and a Shepherd that rendezvous with the debris to later perform a controlled reentry. A preliminary mission design tool (PMDT) was developed to obtain time and fuel optimal trajectories for the proposed mission while considering the effect of J₂, drag, eclipses, and duty cycle. The PMDT can perform such trajectory optimizations for multi-debris missions with computational time under a minute. Three guidance schemes are also studied, taking the PMDT solution as a reference to validate the design methodology and provide guidance solutions to this complex mission profile.