Class of Trajectories in ${{\mathbb{R}}^{3}}$ Most Remote from Observers

Abstract—The set of extremal trajectories is completely described. Their construction is reduced to finding the best routes on a directed graph whose vertices are subsets (boxes) of $Y{\backslash }\bigcup\limits_S^{} {K(S)}$ and whose edges are segments $\mathcal{T}(S)$ of the trajectory $\mathcal{T}$ that intersect the cones K(S) in the “best way.” The edge length is the deviation of S from $\mathcal{T}(S)$. The best routes are ones for which the length of the shortest edge is maximal.