This equation is well known in astronomy, and has been used for more than 80 years to calculate the temperatures of various objects in the sky. Today, we still find it useful for measuring the surface temperatures of man-made satellites such as Telstar. Since both _S_ and σ are known constants (in this case, we use the quantities _S_ = 445 and σ = 0.173 × 10⁻⁸), you can see that temperature is dependent on the α/ε ratio.
[Illustration: _Cutaway view of the inside of the Telstar I satellite, showing the electronics canister covered with its protective blanket of many layers of Mylar. To control temperature, shutters automatically open all the way if the canister gets hotter than 80°F, close completely if it goes down to 50°F._]
shutter (closed) electrical heat transfer insulation blanket heat transfer by radiation shutter (open) solar cells electronic chassis heat transfer by circulation thermal control mechanism nylon lacing microwave antennas frame
In designing the Telstar satellite, both its internal and external temperatures had to be controlled. The electronics canister inside the satellite operates best if it stays at approximately room temperature of 65 to 75°F. This much heat is supplied in the canister by dissipation of electrical energy from the solar cells. The container is well insulated to keep its temperature relatively stable, and it has shutters that open automatically if it begins to get overheated (_see above_). The operating characteristics of the solar cells on Telstar’s surface also had to be considered; they work better at rather cool temperatures. So we decided to keep the satellite’s skin at an average temperature of about 0°F, although temperatures actually will range quite a bit above and below the average as the satellite moves from sun to shadow.
Now, using this average temperature of 0°F (converted to 460°R) as _T_ in our formula, we can solve for α/ε. We find that this gives us a ratio of approximately 0.7 for the satellite’s surface. However, this presents a problem. Almost 40 per cent of Telstar’s surface is taken up by its power plant of 3600 sapphire-covered solar cells. These cells, unfortunately, have a relatively high α/ε ratio—their α is 0.8 and their ε is 0.54, for an α/ε of 1.5. This means that the portion of the surface not used by either solar cells or antenna openings must, in order to give us an over-all average of about 0.7, have a very low α/ε ratio—less than 0.3.