Force on Earth by the radiation pressure of Sun

[SL_1719]

Homework Statement

Estimate the force on Earth due to the pressure of the radiation on Earth by the Sun. (At Earth's orbit, the intensity of sunlight is 1.37 kW/m^2.)

Homework Equations

Radiation Pressure=I/c
Pressure=F/A
Using SA of earth=510,072,000 km2

The Attempt at a Solution

So I have been working at this problem for a while now and can't seem to get the correct answer. I found the radiation pressure to be 4.5667e-6 N/m^2. I have since then tried taking this and multiplying it by the surface area of the Earth in many different forms to no avail. What am I missing? I have tried these coefficients to Prad*SA, 1 (acting on whole surface), 1/2 (half the surface since sun is on one side), 1/(2sqr2) (thought possibly rms), 1/sqr2 (similar to before, just trying anything), and 1/(4sqr2), 1/4. My force for Prad*SA=2.329e9 N.

 

[Delphi51]

Welcome to PF!
I agree with 4.5667e-6 N/m^2.
I'm puzzled with what area to use. The sun only shines on one side of the Earth at a time so you certainly wouldn't use the whole surface area. Half of it doesn't seem right either because the sun hits a good part of it at a very high angle, drastically reducing the intensity. I think taking the area to be πr² is the best first estimate because it counts all of the radiation hitting the Earth. Of course all this assumes that the radiation is absorbed rather than reflected.

 

[SL_1719]

Thank you for welcoming me and thank you for the help, using just pi*r^2 worked. 5.823e8 N is the answer.