[Illustration: 1. _Solar aspect cells on the satellite report via telemetry the amount of sunlight they receive; from these data we can calculate the angle θ between the satellite’s spin axis, OP, and the satellite-sun line, OS. This means that OP can be anywhere on the surface of cone OPP′._] [Illustration: 2. _When sunlight is reflected to observing station T on the earth, we know that the angle of incidence i must be equal to the angle of reflection i′, and, if ORB is a line perpendicular to the reflector R, we know that the sun, the observer, and line ORB must all lie in one plane. Since we also know the position of the satellite in its orbit and the distance from it to the earth, we can locate line ORB precisely. The reflector R is set at an angle θ′ of 68° from the spin axis OP. This tells us that the spin axis must lie on the cone OPP″, which is now precisely determined by its axis ORB and its vertex angle 2θ′, equal to 136°._] [Illustration: 3. _Cones OPP′ and OPP″ intersect along the two lines OP and OQ, so these are the only possible spin axis locations. From our general knowledge of the situation (or from any third measurement of glint time), OQ can be ruled out, and we conclude that only OP can be the true spin axis._] In _Diagram 3_ we have combined our two measurements of the satellite’s spin axis. You can see that the two cones will intersect along two straight lines, OP and OQ; these are thus the only possible positions that will satisfy both our measurements. Actually, of course, only one of these lines is the true location of the spin axis. And it is usually obvious which one it is, when we consider all our other data about the satellite’s position. Using this technique, if we measure the exact times when we see flashes of reflected sunlight from Telstar, we can combine that information with data from our six solar aspect cells and get a good plot of the position of the satellite’s spin axis. In theory, this looked like a very promising idea. But finding a satisfactory way to put it into practice was something else again. Our first thought was simply to make use of the light reflected from the sapphire covers on the satellite’s solar cells. However, these covers have a low coefficient of reflection and do not form a completely flat surface. This means that the light reflected from them is very much reduced in intensity and spreads out too much to give us the precise readings we want. On the other hand, if we attached a plane mirror with a high reflection coefficient to the satellite, we thought we could pick up the minute flashes of reflected light from a distance of as much as a few thousand miles. So we decided to press ahead with this scheme and install one or more reflectors on the satellite.