Neglecting the effects of radiation absorption, emission, and scattering within

Question

Neglecting the effects of radiation absorption, emission, and scattering within their atmospheres, calculate the average temperature of Earth, Venus, and Mars, assuming diffuse, gray behavior. The average distance from the sun of each of the three planets, Lsp, along with their measured average temperatures, Tp, are shown in the table below. Based upon a comparison of the calculated and measured average temperatures, which planet is most affected by radiation transfer in its atmosphere?

Planet Lsp (m) Tp (K)
Venus 1.08*10^11 735
Earth 1.50*10^11 287
Mars 2.30*10^11 227

Explanation / Answer

let the temp of sun be T
radiation energy emitted=*4*r2*(T4-Tp4),r is radius of sun

this energy is emitted in 360 degree angle

angle subtended by any planet=r/Lsp

so radiation received=*4*r2*(T4-Tp4)*r/(Lsp*2)

=*2r3*(T4/Lsp-Tp4/Lsp)

since change in Tp is more dominant so ratio of Tp4/Lsp is determining factor,greater it is smaller is radiation received as it is subtracted,

so Mars is most affected

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