some answers are there in chegg but they are just wrong. i am checking my answer

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some answers are there in chegg but they are just wrong. i am checking my answer here. id rather you give the right answer than the process.

1. The earth as a habitable planet The power density (power per unit area) of the solar radiation is about 1 kW/m2 at the surface of the carth, and 1.4 kW/m2 above the atmosphere. So you feel the heat when walking in the sun, even though it is 150 million kilometers away! (a) Calculate the magnitude of the Poynting vector at the surface of the sun. The radius of the sun is about 7 x 103 m, approximately 110 times that of the earth. (b) How large is an area on the surface of the sun that radiates one gigawatt? This is similar to the electric power generated by a large nuclear power station. If the earth were either closer in or farther out, the temperature would be either too high or too lovw. Or if the earth's orbit were much more ellipical than it is, with the same average distance, then the temperature would be too high for part of the year, and too low the rest of the time. The orbit is in fact nearly a perfect circle, with the ratio of the maximum distance to the minimum distance being 1.00014. (c) What percentage change in the radius of the earth's orbit could we tolerate if the radiative power input could vary by ±20% without causing too much harm? (d) Think about other factors, e.g. daily rotation rate, magnetic field, gravitational force, etc. that make the earth as a habitable planet for the human kind. Take at least two items and explain!

Explanation / Answer

1. a. radius of sun, R = 7*10^8 m

distance of sun from earth, d = 150*10^9 m

intensity of sunlinght at the radius of sun = S = magnitude of poynting vector

S at surface of earth S' = 1000 W/m^2

S = S'*d^2/R^2 = 1000*(150*10^9 / 7*10^8)^2

S = 45918367.3469 W/m^2 = 45.91836 MW/m^2

b. area on the surface of sun that radiates 10^9 W = A

then 10^9 = SA = 45.9183*10^6*A

A = 21.77 m^2

c. intensity of dsolar radiation at distance d from the sun = S'

now, S'*4*pi*d^2 = constnat

so, for 20 % change in S', let d' be the new distance form sun

then

S'*4*pi*d^2 = 1.2S'*4*pi*d'^2

d^2 = 1.2d'^2

d' = 0.91287d

% change in d = ( d - d')*100/d = 8.712 %

so change tolerable in distance from sun is +-8.712%

d. the magnetic field of earth stops the potential ionising radiation from sun to reach earth's surface. Because the earth gets closer to sun, tihs magnetic field quantity would have to change to keep things normal

the temperature of the planet would also change causing global warming, global rise in temperature, which as a secondary effect could have adverse effects on mankind, and those would have to be accounted for as well

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