Abstract: Optimal trajectories are obtained by using a direct adjoining approach (so called the D form Lagrangian)for the interception or the rendezvous of a target in low circular Earth orbit by a vehicle which is initially in a high orbit. The interception condition is that the attack vehicle has the same position as the target at final time, but the rendezvous condition is that both vehicles have same position and same velocity vector at final time. In this paper, a minimum linear combination of target-escape, or fuel-consumption and flight time as the performance index, and the thrust programming in aeroassisted maneuvers are considered, which will lead to a singular thrust arc over the heating rate boundary in optimal control problem for the special case in which the thrust is singular while the aerodynamic controls are regular. These results show that the complexities introduced by the synergetic maneuver with thrust programming and the necessity to find the solutions in the optimal aeroassisted orbit interception and rendezvous should be carefully treated.