—_Adapting known devices._ To answer the question “How can we make optical measurements on a satellite?” the story was somewhat different: Devices that already had been developed—mirrors, telescopes, and cathode ray tubes—were utilized in a new and different way. —_Developing entirely new equipment._ Another question—“How do we keep solar cell power plants working in space?”—deals with an entirely new area of investigation; it could only be answered by perfecting some entirely new techniques. —_Experimentation._ Sometimes there is no definite answer to a problem. In the case of “Would time delay be a problem in using a synchronous satellite?” investigation is still going on. Our report tells of one set of experiments that helped add to our information about this problem—the final answer, if there is one, must come later. But, as with many problems, experimentation continues. —“_Detective work._” Our sixth problem is really a unique one—and, for want of a better way to describe it, we use this title. It tells how the problem of “How can we repair an orbiting satellite?”—something never even attempted before—was ingeniously solved by means of scientific deduction hundreds of miles away from the problem itself. CASE HISTORY NO. 1 How Do We Calculate a Satellite’s Orbit? Franz T. Geyling _Mechanics Specialist—Head, Analytic and Aerospace Mechanics Department_ THE PROBLEM _Before you can do anything with a communications satellite you have to know where it is at every instant of its motion around the earth. In other words, you need to know its orbit quite accurately. When you know this, you can predict when a particular station on the ground will be able to see the satellite and communicate with it. You also can tell when two or more stations can see the satellite simultaneously and communicate with each other. And you can estimate how many satellites will be needed to provide a group of ground stations with enough working time to maintain a communications service. This last, after all, is the ultimate goal of all our efforts in the communications satellite field._ _In determining a satellite’s orbit, we find that we must do three things:_ —_We must obtain information on the position—and perhaps also the velocity—of the satellite whenever possible by observing it with scientific instruments._ —_We must use this information to determine the satellite’s orbit at the time of the observations._ —_We must be able to tell how this orbit changes between the times when we observe it, because a satellite’s orbit does not remain constant with the passage of time._