The intensity of sunlight at the Earth\'s distance from the Sun is 1370 W/m 2 .

Question

The intensity of sunlight at the Earth's distance from the Sun is 1370 W/m2. (a) Assume the Earth absorbs all the sunlight incident upon it. Find the total force the Sun exerts on the Earth due to radiation pressure b) explain how this force compares with the Sun's gravitational attraction. strength__________times stronger please explain/show work answer for points! (a) Assume the Earth absorbs all the sunlight incident upon it. Find the total force the Sun exerts on the Earth due to radiation pressure b) explain how this force compares with the Sun's gravitational attraction. strength__________times stronger please explain/show work answer for points!

Explanation / Answer

Check units: W/m^2 = Js^(-1) m^(-2)
J= N m =>W/m^2= Js^(-1)m^(-2)=Nm^(-1)s^(-1)

so W/m^2/(m/s) = Nm^(-1)s^(-1)/ms^(-1) = Nm^(-2) = pressure

so we have verified that the units of intensity/speed of light = units of radiation pressure

therefore, the force of radiation acting on the earth is:

force = radiation pressure x area = (intensity/c)xpi R^2
force = 1370W/m^2 x pi x( 6.37x10^6m)^2/3x10^8m/s
force = 5.82x10^8 N

I am presuming that the sun's gravitational attraction means the magnitude of the solar gravitational force on earth: If that's the case, the answer is approx 10^22 N:

F=GMm/r^2

G=6.67x10^(-11)=6.67e-11
M=mass sun = 2x10^30kg=2e30
m=mass earth = 6x10^24kg
r=earth sun distance = 1.5x10^11m

F=(6.6e-11)(2e30)(6e24)/(1.5e11)^2 = 3.56e22N

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