A planet at a distance of 1.0 AU from its star has a surface temperature of 280 K. Another identical planet orbits the same star at 2.25 AU. Treating both as being in radiative balance with the starli

Question

A planet at a distance of 1.0 AU from its star has a surface temperature of 280 K. Another identical planet orbits the same star at 2.25 AU. Treating both as being in radiative balance with the starlight, find the surface temperature of the second planet, in K.

Answer:

186.70

Solution:

$T^{4} \propto \frac{1}{r ^{2}}$ , so $T \propto r^{- 1/2}$ . $T_{2} = 280 \times \frac{1.0}{2.25} = \frac{280}{1.5} = 186.7$ K.

TestHub · Accepted Answer

T 4 ∝ r 2 1 ​ , so T ∝ r − 1/2 . T 2 ​ = 280 × 2.25 1.0 ​ ​ = 1.5 280 ​ = 186.7 K.

Physics - Heat & Thermo Question with Solution | TestHub

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