Radiation Pressure Force on Earth

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SUMMARY

The discussion focuses on calculating the radiation pressure force on Earth due to sunlight, which is measured at an intensity of 1360 W/m². The radiation pressure force (F_r) was calculated to be 5.78 x 10^8 N, while the gravitational force (F_g) exerted by the Sun on Earth was determined to be 3.53 x 10^22 N. The ratio of these forces, F_r/F_g, was found to be 1.64 x 10^-14. The confusion arose regarding the requirement for the answer to be expressed in percentage terms, leading to a misunderstanding of unitless quantities.

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Homework Statement


The intensity of sunlight reaching the Earth is 1360 \frac{W}{m^2}.
a.) Assuming all sunlight is absorbed, what is the radiation pressure force on the earth? Give your answer in Newtons. F_r=
b.) Give your answer as a fraction of the suns gravitational force on the earth. \frac{F_r}{F_g}=

Homework Equations


Intenisty is given by I= \frac{P}{A} where P power and A is the cross sectional area.
Force is given by F=\frac{P}{c}=\frac{IA}{c} where c is the speed of light in a vacuum.

The Attempt at a Solution


I solved the first part correctly, no problem. I got that the radiation pressure force was 5.78*10^8 N
For the second part, I simply divided this number by the gravitational force of the sun on the earth, which I found to be F_g=3.53*10^{22} N
When I divided these two numbers, I got \frac{F_r}{F_g}= 1.64*10^{-14} which of course should have no units. However, the problem asks for units, so I put in Newtons anyways, and I was told the my answer must have dimensions of percent (I wasn't aware a unitless quantity had dimensions). So, I slapped in % sign. I was then told to try again; that I was wrong. What am I missing?
 
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A fraction of 1 would correspond to 100%. A fraction of 1.64*1014 corresponds to...?
 

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