Draw a free body diagram of a person as their board accelerates them up into the sky. Be sure that, if a force is bigger than an
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(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