Radiation from the Sun reaching Earth (just outside the atmosphere) has an intensity of 1.35 kW/m2. (a)...

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Radiation from the Sun reaching Earth (just outside theatmosphere) has an intensity of 1.35 kW/m².(a) Assuming that Earth (and its atmosphere)behaves like a flat disk perpendicular to the Sun's rays and thatall the incident energy is absorbed, calculate the force on Earthdue 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 Ã—10⁸ m/s and 6.37 thousand km respectively.

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4.3 Ratings (562 Votes)

Intensity I = 1.35 kW/m² = 1350W/m²

SURFACE AREA OF EARTH IS A =?R²

R = 6370 km = 6370000 m

c = 2.998*10⁸ m/s

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â P = 1350 W/m²/ 2.998*10⁸ m/s =450.3*10^-8 N/m²

Now force DUE TO RADIATION IS F_R = P*A

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (450.3*10^-8 N/m²)*?*(6370000 m)²

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 5.74*10⁸N

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

G =6.67*10^-11Nm²/kg²

Â Â 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

Â Â Â Â Â Â Â Â Â Â Â Â Â = 35.57*10²¹N

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