We also wanted to get a continuing report on the effects of the magnetic field of the earth at high altitudes. We knew these would cause the spin axis to change with time, or precess, but we couldn’t be exactly sure what these changes would be.
Since the orientation of Telstar’s spin axis was so important we installed a torque coil in the satellite. This is a coil of wire in which, upon a signal from the ground, an electric current can be made to flow. The current produces a magnetic field that interacts with the earth’s magnetic field to change the position of the satellite’s spin axis. However, we could not be sure that this device would work properly—and this is another reason why we wanted to keep track of the exact position of the spin axis.
Ways of Measuring the Spin Axis
One of the devices built into Telstar is a set of six solar aspect cells spaced at regular intervals around the satellite. These give a fairly accurate indication of the angle between the spin axis of the satellite and a line joining the satellite and the sun. When sunlight strikes these solar cells, they produce electric currents, and the value of the current from each cell is sent back to the ground via telemetry. Three of the cells are in the satellite’s northern hemisphere; three are in the southern hemisphere. If Telstar’s north pole were pointing to the sun, for example, the three northern cells would record large, equal currents; those in the southern hemisphere would show zero current. But if the spin axis were perpendicular to the satellite-sun line (as we want it to be) all six cells would report equal, average-sized currents, which would fluctuate as the satellite spun around. The solar cells were carefully calibrated before Telstar was launched, and we estimate that they can tell us the angle between the satellite’s spin axis and the satellite-sun line to within one or two degrees.
However, this one angle is not enough to locate the spin axis exactly. As you can see in [Diagram 1], there are many possible positions for the spin axis OP that have the same angle θ with the satellite-sun line OS. These positions all would lie on the surface of an imaginary cone OPP′ that has OS as its axis and 2θ as its vertex angle. We need to have a second measurement to find a single position for the spin axis. As late as November 1961 we had not found a satisfactory way to make such a second measurement. Then Donald Gibble of Bell Telephone Laboratories suggested that we observe the reflections of sunlight from mirrors fitted onto the satellite[2].
Only when a satellite is in the right position can you see the reflection of sunlight from a plane surface on its body. [Diagram 2] shows how flashes of reflected light are observed. The light of the sun, S, is reflected from a plane surface, R, on the satellite to our observing station, T, on the earth. If we imagine the line ORB drawn perpendicular to R, we know, from the law of reflection, that the angle of incidence, i, made by the sunlight to this line will be equal to the angle of reflection, i′, between the reflected light and the same line. The law of reflection also tells us that the sun, the line ORB, and the observing station all must now lie in the same plane. And, since we can calculate where the satellite is in its orbit at this exact moment, we can locate line ORB. But what about the spin axis? We know where on the satellite our reflector R is located, so we know ahead of time what the angle θ′ between ORB and the spin axis, OP, will be. We call it the flash angle. Thus we can tell that the spin axis will be somewhere on the surface of an imaginary cone OPP″ that has ORB as its axis and 2θ′ as its vertex angle[3].
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′.
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°.