Question

Radiation In Radiation Out Tr(o.7 x 1370 Wlm)- 4Trx ET 2. Why is Mars so much colder than Earth? Please explain using the radiative balance equation and be sure to include differences in solar radiation, albedo, and emissivity between the two planets. 3. Our current emissivity is approximately 0.612.

Answer 1

Taking data from the literature (tables), for radi, and respective distances from the sun for the planets, the calculations are done. for stefan's law provides power radiated by a body with e emissivity's PocoAtt ; To 5.67X 10th out a constant Ta temp of body, The Surface temp of Sun is Tz 580k (Ts) . Radius of Earth & 6400 km ; Radiusd masso 3390km . (re) > 6.4x10²m o como 8.39 xloom Orbital radings of Earth 21.5x10"m ; orbit gadius of massa 2.3x10" m. • (de) Now lets proceed with Calculating temperature of planets. • At distane equal to de , Psun is spread over spherical radius of tude , and the earth covers a circular area of rure ² in that spread. So power absorbed by earth can be given as D. leelare i ; where le is emissivity Punon earth? 'ses is laude) of planet earth. f This past is due to solar radiation b e , the emissivity accounts for surface property of the planet. Albedo, which is a measure of reflectivity of a surfeul is this a factor which influences the emmisivity of the surface. Similasty od distance from sun, dm, pland mass will cover area terus of the Ps spread of uuden, And this power absorbed will be Psun on man? Psm > Ps femur) to This is again a sadiative (scar) absorbition by mans. herr also we can say that albedo or reflective property influences the emissivity em. the would have been a (If there was a presence of greenhouse gas function of wavelength of radiation)

* for presence of GHG's the 'e': emissivity would have been a function of wavelength as is the case with venus.

. Then for earth and temperature Te, and radiating in all directions with power те блест, 4 сте вест & the emissivity for radiaken & abserption are the same? Similarly for the case of mass at Tm, we have Pmo o Amemima a tu rm o emana. In steady state we find .. Papi ee ure z Pezoha me de la TAP Yo te se an der Suure hudele » Totals . ; So we see that role of emissivity é 'cancells 16 urte? Similarly for Tms. Tm Ps. llarda cout. =) Tma de 1 Tm <Tel as de <dm | Tet dn Substituting the values form literatione gives us TA, Ps, a 5.88x105 kt z) Te & 247 K = 0°c e lourde The Tetx de ² a 223 k = -50°C Hence having are counted from solar) radiation, albedo & emissivity, for the respective planets, we have shown that Mars is colder than Earth.