The intensity of sunlight reaching the earth is 1360 w/m2. assuming all the sunligh is absorbed, what is the radiation pressure force on the earth? give your answers in (a) newtons (b) as a fraction of the sun's gravitational force on the earth

(a)

For an electromagnetic wave incident on a surface, the radiation pressure is given by (assuming all the radiation is absorbed)

where

I is the intensity

c is the speed of light

In this problem, ; substituting this value, we find the radiation pressure:

the force exerted on the Earth depends on the surface considered. Assuming that the sunlight hits half of the Earth's surface (the half illuminated by the Sun), we have to consider the area of a hemisphere, which is

where

is the Earth's radius. Substituting,

And so the force exerted by the sunlight is

(b)

The gravitational force exerted by the Sun on the Earth is

where

G is the gravitational constant

is the Sun's mass

is the Earth's mass

is the distance between the Sun and the Earth

Substituting,

And so, the radiation pressure force on Earth as a fraction of the sun's gravitational force on Earth is

a straight line sloped