Temperature on a planet the sun radiates energy approximately as a blackbody, with the effective surface temperature te and radius ro given in section 1.4 of phillips (as well as in a useful table inside the back cover). the distance of earth from the sun d 1 a and the radius of the earth r are given inside the back cover. (a) assume that the earth absorbs all solar radiation that falls into its cross- sectional area of π , and reradiates it as a blackbody from its entire surface area, 4tra. find the consequent equilibrium temperature of the earth, teq (b) known forms of life require liquid water, and temperatures low enough for biological molecules to be stable. find the range of distances from the sun, in au, where the equilibrium temperature of the earth lies in the range tmin - 0 c 〈 teq 〈 100 c-tmaz-(water remains liquid at higher temperatures. at pressures much greater than earth's atmospheric pressure, but biological molecules have a hard time surviving at those high temperatures.) this is sometimes known as the "goldilocks zone" or the "circumstellar habitable zone." arguably, life can arguably exist outside of this zone (and planets within it can certainly be inhospitable to life); but extrasolar planets in this zone might well harbor extraterrestrial life - an exciting possibilit c) proxima centauri is the nearest star to the sun. it has radius 0.141 ro and total (bolometric) luminosity 1.7 × 10-3 lo. find the effective temperature of proxima centauri, in k. find the range of distances, in au where 0 c 〈「q 〈 100 c