# Radiation Pressure Force on Earth

1. Apr 25, 2013

### sharrington3

1. The problem statement, all variables and given/known data
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. $$\frac{F_r}{F_g}=$$

2. Relevant 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.

3. 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?

2. Apr 25, 2013

### Staff: Mentor

A fraction of 1 would correspond to 100%. A fraction of 1.64*1014 corresponds to...?