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.
Locating the Mirrors on the Satellite
As we mentioned above, the flash angle θ′ between the satellite’s spin axis and a line perpendicular to the mirror is very important in our calculations. We made detailed studies of the various flash angles that would be possible during the first 60 days after launch. We plotted the times when the satellite would be above the horizon while our Crawford’s Hill, New Jersey, observing station was in darkness, and we made allowance for satellite orbits that might deviate slightly from the planned one. These calculations told us that the best flash angle for the mirror would be 68 degrees—which is the angle made by the first facets above Telstar’s equatorial antenna band. So we located a flat mirror on one of these facets. Because one of the solar aspect cells was already installed in the center of this facet, we were forced to cut a circular hole out of the center of the mirror.
But we knew that one mirror could not do the whole job. After Telstar I had been in orbit more than 30 days, the 68-degree mirror would only be in position to give infrequent flashes, and one at about 95 degrees would be more useful. This presented two problems. First, no facet on the satellite makes a 95-degree angle with the spin axis. However, we could use one of the facets just below the equatorial antenna, which makes a 112-degree angle, and groove or facet the mirror so that its reflecting faces became narrow strips slanted 17 degrees away from the base at the angle of 95 degrees (112 - 17 = 95). Our second problem was space—since there was not enough room left on any of the 112-degree facets to mount a second large mirror, we substituted two smaller mirrors and mounted them 120 degrees apart. This arrangement lets us know from which mirror we see flashes—the plane mirror gives one flash for each revolution of the satellite; the faceted mirrors give two flashes for each revolution of the satellite.