An Introduction to Modern Astrophysics · Problem 20.7
The Formation of Planetary Systems — Carroll & Ostlie
Physics — Astrophysics · greenhouse-effect-venus
Problem
(a) Modeling the greenhouse effect using one atmospheric layer, as was done in Problem 19.13, is equivalent to assuming that the optical depth is about one. If the optical depth is τ, and if we can neglect circulation in the atmosphere, show that the surface temperature should be approximately
Tsurf=(1+τ)1/4Tbb,
where Tbb is the blackbody temperature of an airless planet.
(b) The optical depth of Venus's atmosphere is approximately τ=70. Make an estimate of its surface temperature using this crude greenhouse model. Take the average albedo to be 0.77.