A number of problems of space cybernetics is considered in the article, connected with optimum terminal control of information interaction processes of a spacecraft with the set discrete set of points on Earth surface. The spacecraft is thus interpreted as an information active movable object, i.e. as a complex mobile system supplied with necessary devices for information interactive with the surrounding physical medium and the appropriate onboard resource. It is shown that the specified tasks are reduced to problems of optimum program control by a finite-dimensional differential dynamic system. The maximum principle of L. S. Pontryagin is used for their solution in the article.