Satellite Communications Physics

by Unknown

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°.

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.

By the time we started work on the mirrors, the final design of Telstar I was almost complete; this meant that we had to squeeze our mirrors aboard it as best we could. The most stringent physical requirement in designing them was weight; they could not add more than half a pound to Telstar’s total load. Nor could they project more than one-eighth inch from the satellite’s surface, or they might interfere with the radiation pattern for the main antenna. We also decided to make the mirrors out of highly polished metal, since any other possible material might break too easily. And the mirrors had to be as flat as possible, so the beam of reflected sunlight would not diverge by more than one degree.

Thus we had to design mirrors that would be very thin, very shiny, very flat, very light, and almost unbreakable. After much experimenting, we solved this rather tricky problem. The mirrors we added onto Telstar I, as you can see in [the illustration below], were machined from aluminum alloy sheet, carefully polished by hand with abrasive papers, and buffed on a cloth wheel. Finally, we evaporated a thin layer of pure aluminum onto their surfaces to improve their reflection coefficients and make them resistant to corrosion. The three mirrors were fastened to the surface of the satellite with small screws, which had to be tightened and shimmed very carefully so that the mirrors stayed as flat as possible.