Making reasonable assumptions, estimate the surface temperature of Neptune. Neglect any possible internal sources of heat. What assumptions have you made about the planet's surface and/or atmosphere?
Astronomical data which may be helpful: radius of sun = 7 × 10 5 km; radius of Neptune = 2.2 × 10 4 km; mean sun-earth distance = 1.5 × 10 8 km; mean sun-Neptune distance = 4.5 × 10 9 km; T S = 6000 K; rate at which sun's radiation reaches earth = 1.4 kW/m 2 ; Stefan-Boltxman constant = 5.7 × 10 –8 W/m 2 K 4 .
Text Solution
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We assume that the surface of Neptune and the thermodynamics of its atmosphere are similar to those of the earth. The radiation flux on the earth's surface is
The equilibrium condition on Neptune's surface gives
Hence
and we have 
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