Radiation from the Sun reaching Earth (just outside the atmosphere) has an inten

Question

Radiation from the Sun reaching Earth (just outside the atmosphere) has an intensity of 1.41 kW/m^2. (a) Assuming that Earth (and its atmosphere) behaves like a flat disk perpendicular to the Sun's rays and that all the incident energy is absorbed, calculate the force on Earth due to radiation pressure. (b) For comparison, calculate the force due to the Sun's gravitational attraction. Assume that the speed of light and Earth radius are 2.998 times 10^8 m/s and 6.37 thousand km respectively. Number Units Number Units

Explanation / Answer

Intensity I = 1.4 kW/m2 = 1400W/m2

SURFACE AREA OF EARTH IS A = R2

R = 6400 km = 6400000 m

c = 3*108 m/s

we know that radiation pressure if all the incident energy isabsorbed is P = I/c

               P = 1400 W/m2/ 3*108 m/s =466.67*10-8 N/m2

Now force DUE TO RADIATION IS FR = P*A

                                                                = (466.67*10-8 N/m2)**(6400000 m)2

                                                                = 6.005*108 N

Gravitational force due to the Sun is Fg =GMm/r2

G =6.67*10-11Nm2/kg2

   M = mass of sun = 2*1030 kg

m = mass of earth = 6*1024kg

r = distance between the sun and earth =1.5*1011m

Then Fg = 6.67*10-11*2*1030*6*1024/(1.5*1011)2

             = 35.57*1021N

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