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 thetotal force the Sun exerts on the Earth due to radiation pressure.
1 N

(b) Explain how this force compares with the Sun's gravitational attraction.

strength	2 times stronger
direction	same opposite

Answer 1

1370 W/m^2 is the intensity of sunlight reaching the earth, and is the value of the Poynting vector at the top of the earth's atmosphere. The pressureexerted by this radiation is Intensity/c where c is the speed of light.

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 isapprox 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