How Does Sunlight Intensity Translate to Force on Earth?

[sgoeke]

Homework Statement

The intensity of light from the Sun is 1.3 kW/m^2 at the distance of the Earth. The Earth’s radius is 6.4 × 10^6 m. If all the sunlight that hits the Earth were absorbed, what would be the magnitude of the resulting force on the Earth?

Homework Equations

F=IA/c

The Attempt at a Solution

I converted KW/m^2 to W/m^2 and got 1300 W/m^2. For area I used 4pi*r^2 and plugged those values into the equation but I can't seem to get the correct answer. Any help?

 

[alphysicist]

Hi sgoeke,

Homework Statement

The intensity of light from the Sun is 1.3 kW/m^2 at the distance of the Earth. The Earth’s radius is 6.4 × 10^6 m. If all the sunlight that hits the Earth were absorbed, what would be the magnitude of the resulting force on the Earth?

Homework Equations

F=IA/c

The Attempt at a Solution

I converted KW/m^2 to W/m^2 and got 1300 W/m^2. For area I used 4pi*r^2

This formula gives the surface area of a sphere. Do you see why this is the wrong area to use for this problem?

and plugged those values into the equation but I can't seem to get the correct answer. Any help?

 

[sgoeke]

would i need to find the volume of the earth?

 

[alphysicist]

would i need to find the volume of the earth?

No, the formula needs an area; the question is which area to use. It's not the surface area of the Earth (after all, the "back" of the Earth is not getting sunlight at all). And it is not just half of the total surface area. What type of area is important here? Remember that the idea is to find how much of the sunlight the Earth is "catching", in a sense.