In Chapter 5 you learned about the equilibrium between the absorption of sunlight and the radiation of infrared light into space, and in Chapter 9 you saw how the resulting equilibrium temperature is modified by the greenhouse effect on Venus, Earth, and Mars. Yet when this equilibrium for the giant planets is calculated, something seems amiss. According to these calculations, the equilibrium temperature for Jupiter, for example, should be 109 K, but when it is measured, scientists find instead an average temperature of about 124 K. A difference of 15 K might not seem like much, but according to the Stefan-Boltzmann law, the energy radiated by an object depends on its temperature raised to the fourth power. Applying this relationship to Jupiter, we get: ( Tacutal _______ Texpected ) 4 = ( 124 K ______ 109 K ) 4 = 1.67
The implications of this result are somewhat startling: Jupiter is radiating roughly two-thirds more energy into space than it absorbs in the form of sunlight. Similarly, the internal energy escaping from Saturn is observed to be about 1.8 times greater than the sunlight that it absorbs. Neptune emits 2.6 times more energy than it absorbs from the Sun. Strangely, whatever internal energy may be escaping from Uranus is small compared to the absorbed solar energy—for reasons not well understood. With energy continually escaping from the interiors of the giant planets, how have they maintained their high internal temperatures over the past 4.5 billion years? They are still shrinking, converting gravitational potential energy into thermal energy. This continual production of thermal energy is sufficient to replace the energy that is escaping from their interiors.