Cold Silence of Space

In the “cold silence of space” begins many a description of space between planets. Can this statement survive a physics analysis?

Answer

Yes and no. The very good vacuum between Earth and Venus, for example, certainly does not conduct sound, so the space is silent. But what is the temperature of outer space? This question is an improper question, for we must instead ask: “What temperature would be recorded by a thermometer placed in space between the Venus and Earth orbital distances?” Whatever kind of thermometer we use, if the sensor is not rotated, one side will be exposed always to the direct rays from the Sun and the other side will be in shadow. At thermal equilibrium, the amounts of outgoing radiation energy and incoming radiation energy in all directions will balance.

The equilibrium temperature T for an object at Earth’s average distance from the Sun is about 280 K, or +7°C, the actual value being lower because there will be some energy reflected away and not absorbed by the thermometer. One calculates T from this equation: flux absorbed = flux emitted. If we assume for simplicity that the sensor is a sphere of radius R, then the equation becomes S (1 – A) πR² = σT⁴ (4πR²), where S = 1.4 kW s^–1 is the solar constant at Earth distance and σ = 5.67 × 10^–8 W m^–2 K^–4. The parameter A is the reflectivity, which we take as zero in the ideal case of a perfect absorber and radiator. Real materials will have an A value between 0 and 1.

If you are orbiting at the Earth distance from the Sun, you may desire to rotate your spacecraft slowly in space so that all sides cook evenly! This passive heating can be augmented by active heating from within to maintain a cozy environment.

If you are orbiting closer to the Sun than Earth, the equilibrium temperature will be higher, the solar flux increasing as the ratio of the squared distances. Near the orbit of Mercury you may be too hot! If you are farther away, the temperature decreases, so you may need artificial heating. Some rotation may produce a system that requires less fuel for heating, but the details need to be worked out.

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