Specific conditions in the optimization problem for fail-safe injection trajectories are considered on the base of PMP. In this case the imaginary emergency trajectories of a reentry vehicle after STS ascent abortion form a continual set. The method of reduction of this problem to the ordinary through optimization of branching trajectories with a finite number of branches is represented. Another problem under consideration is the STS injection with constraints on drop points of spent parts in view of random atmosphere perturbations. Imaginary reentry trajectories, corresponding random events, form cones of branches with apex at staging points on the main STS injection trajectory. The impact of random perturbations is determined on the basis of the minimax approach, in which perturbations are considered as an additional nature control with antagonistic goals in relation to the STS injection target. This approach let the problem reduce to the ordinary through optimization of branching trajectories with a finite number of branches.