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].
[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.
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.