We can also calculate the heat from the sun that will be absorbed by a body. If we let _S_ be the total amount of solar energy that would be absorbed by a perfect black body, α_S_ will be the amount that is actually absorbed by a body with an absorptivity of α for solar radiation. If our body is a spherical satellite, the sun’s rays will only strike it from a single direction. Thus only an area equivalent to the sphere’s cross-section (largest inscribed circle) will receive energy at any one time. Since, _as shown in the sketch_, this area (_a_ = π_r_²) is one-fourth that of the sphere’s total surface area (_A_ = 4π_r_²), we know that the radiant energy from the sun that is absorbed will be _Q__sun = (_A_)/(4)α_S_. A man-made satellite’s position relative to the earth is very like that of the earth in relation to the sun; the earth, after all, is itself a satellite of the sun. And during most of its useful life a satellite will be in _thermal equilibrium_—it will be losing just as much heat energy by its own radiation into space as it will be gaining from other sources, primarily the sun. Since the total amount of energy it absorbs is equal to the amount of energy it emits, _Q__body is equal to _Q__sun. This means that we have the equality ε_A_σ_T_⁴ = (_A_)/(4)α_S_. Now, if we solve this for temperature, we will get _T_ = ((α)/(ε) × (_S_)/(4σ))(^¼). [Illustration: _Although the total surface area, A, of a sphere is 4πr², light rays from the sun only strike half the surface at any one time. This area, a, is effectively equal to the sphere’s cross-section, πr²._] 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. Finding the Right Surface for Telstar [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